Add files using upload-large-folder tool

llmeval-env/lib/python3.10/site-packages/sympy/categories/tests/test_drawing.py

@@ -0,0 +1,919 @@
+from sympy.categories.diagram_drawing import _GrowableGrid, ArrowStringDescription
+from sympy.categories import (DiagramGrid, Object, NamedMorphism,
+                              Diagram, XypicDiagramDrawer, xypic_draw_diagram)
+from sympy.sets.sets import FiniteSet
+
+
+def test_GrowableGrid():
+    grid = _GrowableGrid(1, 2)
+
+    # Check dimensions.
+    assert grid.width == 1
+    assert grid.height == 2
+
+    # Check initialization of elements.
+    assert grid[0, 0] is None
+    assert grid[1, 0] is None
+
+    # Check assignment to elements.
+    grid[0, 0] = 1
+    grid[1, 0] = "two"
+
+    assert grid[0, 0] == 1
+    assert grid[1, 0] == "two"
+
+    # Check appending a row.
+    grid.append_row()
+
+    assert grid.width == 1
+    assert grid.height == 3
+
+    assert grid[0, 0] == 1
+    assert grid[1, 0] == "two"
+    assert grid[2, 0] is None
+
+    # Check appending a column.
+    grid.append_column()
+    assert grid.width == 2
+    assert grid.height == 3
+
+    assert grid[0, 0] == 1
+    assert grid[1, 0] == "two"
+    assert grid[2, 0] is None
+
+    assert grid[0, 1] is None
+    assert grid[1, 1] is None
+    assert grid[2, 1] is None
+
+    grid = _GrowableGrid(1, 2)
+    grid[0, 0] = 1
+    grid[1, 0] = "two"
+
+    # Check prepending a row.
+    grid.prepend_row()
+    assert grid.width == 1
+    assert grid.height == 3
+
+    assert grid[0, 0] is None
+    assert grid[1, 0] == 1
+    assert grid[2, 0] == "two"
+
+    # Check prepending a column.
+    grid.prepend_column()
+    assert grid.width == 2
+    assert grid.height == 3
+
+    assert grid[0, 0] is None
+    assert grid[1, 0] is None
+    assert grid[2, 0] is None
+
+    assert grid[0, 1] is None
+    assert grid[1, 1] == 1
+    assert grid[2, 1] == "two"
+
+
+def test_DiagramGrid():
+    # Set up some objects and morphisms.
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    D = Object("D")
+    E = Object("E")
+
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    h = NamedMorphism(D, A, "h")
+    k = NamedMorphism(D, B, "k")
+
+    # A one-morphism diagram.
+    d = Diagram([f])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 2
+    assert grid.height == 1
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid.morphisms == {f: FiniteSet()}
+
+    # A triangle.
+    d = Diagram([f, g], {g * f: "unique"})
+    grid = DiagramGrid(d)
+
+    assert grid.width == 2
+    assert grid.height == 2
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[1, 0] == C
+    assert grid[1, 1] is None
+    assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(),
+                              g * f: FiniteSet("unique")}
+
+    # A triangle with a "loop" morphism.
+    l_A = NamedMorphism(A, A, "l_A")
+    d = Diagram([f, g, l_A])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 2
+    assert grid.height == 2
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[1, 0] is None
+    assert grid[1, 1] == C
+    assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), l_A: FiniteSet()}
+
+    # A simple diagram.
+    d = Diagram([f, g, h, k])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 3
+    assert grid.height == 2
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[0, 2] == D
+    assert grid[1, 0] is None
+    assert grid[1, 1] == C
+    assert grid[1, 2] is None
+    assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), h: FiniteSet(),
+                              k: FiniteSet()}
+
+    assert str(grid) == '[[Object("A"), Object("B"), Object("D")], ' \
+        '[None, Object("C"), None]]'
+
+    # A chain of morphisms.
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    h = NamedMorphism(C, D, "h")
+    k = NamedMorphism(D, E, "k")
+    d = Diagram([f, g, h, k])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 3
+    assert grid.height == 3
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[0, 2] is None
+    assert grid[1, 0] is None
+    assert grid[1, 1] == C
+    assert grid[1, 2] == D
+    assert grid[2, 0] is None
+    assert grid[2, 1] is None
+    assert grid[2, 2] == E
+    assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), h: FiniteSet(),
+                              k: FiniteSet()}
+
+    # A square.
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, D, "g")
+    h = NamedMorphism(A, C, "h")
+    k = NamedMorphism(C, D, "k")
+    d = Diagram([f, g, h, k])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 2
+    assert grid.height == 2
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[1, 0] == C
+    assert grid[1, 1] == D
+    assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), h: FiniteSet(),
+                              k: FiniteSet()}
+
+    # A strange diagram which resulted from a typo when creating a
+    # test for five lemma, but which allowed to stop one extra problem
+    # in the algorithm.
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    D = Object("D")
+    E = Object("E")
+    A_ = Object("A'")
+    B_ = Object("B'")
+    C_ = Object("C'")
+    D_ = Object("D'")
+    E_ = Object("E'")
+
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    h = NamedMorphism(C, D, "h")
+    i = NamedMorphism(D, E, "i")
+
+    # These 4 morphisms should be between primed objects.
+    j = NamedMorphism(A, B, "j")
+    k = NamedMorphism(B, C, "k")
+    l = NamedMorphism(C, D, "l")
+    m = NamedMorphism(D, E, "m")
+
+    o = NamedMorphism(A, A_, "o")
+    p = NamedMorphism(B, B_, "p")
+    q = NamedMorphism(C, C_, "q")
+    r = NamedMorphism(D, D_, "r")
+    s = NamedMorphism(E, E_, "s")
+
+    d = Diagram([f, g, h, i, j, k, l, m, o, p, q, r, s])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 3
+    assert grid.height == 4
+    assert grid[0, 0] is None
+    assert grid[0, 1] == A
+    assert grid[0, 2] == A_
+    assert grid[1, 0] == C
+    assert grid[1, 1] == B
+    assert grid[1, 2] == B_
+    assert grid[2, 0] == C_
+    assert grid[2, 1] == D
+    assert grid[2, 2] == D_
+    assert grid[3, 0] is None
+    assert grid[3, 1] == E
+    assert grid[3, 2] == E_
+
+    morphisms = {}
+    for m in [f, g, h, i, j, k, l, m, o, p, q, r, s]:
+        morphisms[m] = FiniteSet()
+    assert grid.morphisms == morphisms
+
+    # A cube.
+    A1 = Object("A1")
+    A2 = Object("A2")
+    A3 = Object("A3")
+    A4 = Object("A4")
+    A5 = Object("A5")
+    A6 = Object("A6")
+    A7 = Object("A7")
+    A8 = Object("A8")
+
+    # The top face of the cube.
+    f1 = NamedMorphism(A1, A2, "f1")
+    f2 = NamedMorphism(A1, A3, "f2")
+    f3 = NamedMorphism(A2, A4, "f3")
+    f4 = NamedMorphism(A3, A4, "f3")
+
+    # The bottom face of the cube.
+    f5 = NamedMorphism(A5, A6, "f5")
+    f6 = NamedMorphism(A5, A7, "f6")
+    f7 = NamedMorphism(A6, A8, "f7")
+    f8 = NamedMorphism(A7, A8, "f8")
+
+    # The remaining morphisms.
+    f9 = NamedMorphism(A1, A5, "f9")
+    f10 = NamedMorphism(A2, A6, "f10")
+    f11 = NamedMorphism(A3, A7, "f11")
+    f12 = NamedMorphism(A4, A8, "f11")
+
+    d = Diagram([f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, f11, f12])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 4
+    assert grid.height == 3
+    assert grid[0, 0] is None
+    assert grid[0, 1] == A5
+    assert grid[0, 2] == A6
+    assert grid[0, 3] is None
+    assert grid[1, 0] is None
+    assert grid[1, 1] == A1
+    assert grid[1, 2] == A2
+    assert grid[1, 3] is None
+    assert grid[2, 0] == A7
+    assert grid[2, 1] == A3
+    assert grid[2, 2] == A4
+    assert grid[2, 3] == A8
+
+    morphisms = {}
+    for m in [f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, f11, f12]:
+        morphisms[m] = FiniteSet()
+    assert grid.morphisms == morphisms
+
+    # A line diagram.
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    D = Object("D")
+    E = Object("E")
+
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    h = NamedMorphism(C, D, "h")
+    i = NamedMorphism(D, E, "i")
+    d = Diagram([f, g, h, i])
+    grid = DiagramGrid(d, layout="sequential")
+
+    assert grid.width == 5
+    assert grid.height == 1
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[0, 2] == C
+    assert grid[0, 3] == D
+    assert grid[0, 4] == E
+    assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), h: FiniteSet(),
+                              i: FiniteSet()}
+
+    # Test the transposed version.
+    grid = DiagramGrid(d, layout="sequential", transpose=True)
+
+    assert grid.width == 1
+    assert grid.height == 5
+    assert grid[0, 0] == A
+    assert grid[1, 0] == B
+    assert grid[2, 0] == C
+    assert grid[3, 0] == D
+    assert grid[4, 0] == E
+    assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), h: FiniteSet(),
+                              i: FiniteSet()}
+
+    # A pullback.
+    m1 = NamedMorphism(A, B, "m1")
+    m2 = NamedMorphism(A, C, "m2")
+    s1 = NamedMorphism(B, D, "s1")
+    s2 = NamedMorphism(C, D, "s2")
+    f1 = NamedMorphism(E, B, "f1")
+    f2 = NamedMorphism(E, C, "f2")
+    g = NamedMorphism(E, A, "g")
+
+    d = Diagram([m1, m2, s1, s2, f1, f2], {g: "unique"})
+    grid = DiagramGrid(d)
+
+    assert grid.width == 3
+    assert grid.height == 2
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[0, 2] == E
+    assert grid[1, 0] == C
+    assert grid[1, 1] == D
+    assert grid[1, 2] is None
+
+    morphisms = {g: FiniteSet("unique")}
+    for m in [m1, m2, s1, s2, f1, f2]:
+        morphisms[m] = FiniteSet()
+    assert grid.morphisms == morphisms
+
+    # Test the pullback with sequential layout, just for stress
+    # testing.
+    grid = DiagramGrid(d, layout="sequential")
+
+    assert grid.width == 5
+    assert grid.height == 1
+    assert grid[0, 0] == D
+    assert grid[0, 1] == B
+    assert grid[0, 2] == A
+    assert grid[0, 3] == C
+    assert grid[0, 4] == E
+    assert grid.morphisms == morphisms
+
+    # Test a pullback with object grouping.
+    grid = DiagramGrid(d, groups=FiniteSet(E, FiniteSet(A, B, C, D)))
+
+    assert grid.width == 3
+    assert grid.height == 2
+    assert grid[0, 0] == E
+    assert grid[0, 1] == A
+    assert grid[0, 2] == B
+    assert grid[1, 0] is None
+    assert grid[1, 1] == C
+    assert grid[1, 2] == D
+    assert grid.morphisms == morphisms
+
+    # Five lemma, actually.
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    D = Object("D")
+    E = Object("E")
+    A_ = Object("A'")
+    B_ = Object("B'")
+    C_ = Object("C'")
+    D_ = Object("D'")
+    E_ = Object("E'")
+
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    h = NamedMorphism(C, D, "h")
+    i = NamedMorphism(D, E, "i")
+
+    j = NamedMorphism(A_, B_, "j")
+    k = NamedMorphism(B_, C_, "k")
+    l = NamedMorphism(C_, D_, "l")
+    m = NamedMorphism(D_, E_, "m")
+
+    o = NamedMorphism(A, A_, "o")
+    p = NamedMorphism(B, B_, "p")
+    q = NamedMorphism(C, C_, "q")
+    r = NamedMorphism(D, D_, "r")
+    s = NamedMorphism(E, E_, "s")
+
+    d = Diagram([f, g, h, i, j, k, l, m, o, p, q, r, s])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 5
+    assert grid.height == 3
+    assert grid[0, 0] is None
+    assert grid[0, 1] == A
+    assert grid[0, 2] == A_
+    assert grid[0, 3] is None
+    assert grid[0, 4] is None
+    assert grid[1, 0] == C
+    assert grid[1, 1] == B
+    assert grid[1, 2] == B_
+    assert grid[1, 3] == C_
+    assert grid[1, 4] is None
+    assert grid[2, 0] == D
+    assert grid[2, 1] == E
+    assert grid[2, 2] is None
+    assert grid[2, 3] == D_
+    assert grid[2, 4] == E_
+
+    morphisms = {}
+    for m in [f, g, h, i, j, k, l, m, o, p, q, r, s]:
+        morphisms[m] = FiniteSet()
+    assert grid.morphisms == morphisms
+
+    # Test the five lemma with object grouping.
+    grid = DiagramGrid(d, FiniteSet(
+        FiniteSet(A, B, C, D, E), FiniteSet(A_, B_, C_, D_, E_)))
+
+    assert grid.width == 6
+    assert grid.height == 3
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[0, 2] is None
+    assert grid[0, 3] == A_
+    assert grid[0, 4] == B_
+    assert grid[0, 5] is None
+    assert grid[1, 0] is None
+    assert grid[1, 1] == C
+    assert grid[1, 2] == D
+    assert grid[1, 3] is None
+    assert grid[1, 4] == C_
+    assert grid[1, 5] == D_
+    assert grid[2, 0] is None
+    assert grid[2, 1] is None
+    assert grid[2, 2] == E
+    assert grid[2, 3] is None
+    assert grid[2, 4] is None
+    assert grid[2, 5] == E_
+    assert grid.morphisms == morphisms
+
+    # Test the five lemma with object grouping, but mixing containers
+    # to represent groups.
+    grid = DiagramGrid(d, [(A, B, C, D, E), {A_, B_, C_, D_, E_}])
+
+    assert grid.width == 6
+    assert grid.height == 3
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[0, 2] is None
+    assert grid[0, 3] == A_
+    assert grid[0, 4] == B_
+    assert grid[0, 5] is None
+    assert grid[1, 0] is None
+    assert grid[1, 1] == C
+    assert grid[1, 2] == D
+    assert grid[1, 3] is None
+    assert grid[1, 4] == C_
+    assert grid[1, 5] == D_
+    assert grid[2, 0] is None
+    assert grid[2, 1] is None
+    assert grid[2, 2] == E
+    assert grid[2, 3] is None
+    assert grid[2, 4] is None
+    assert grid[2, 5] == E_
+    assert grid.morphisms == morphisms
+
+    # Test the five lemma with object grouping and hints.
+    grid = DiagramGrid(d, {
+        FiniteSet(A, B, C, D, E): {"layout": "sequential",
+                                   "transpose": True},
+        FiniteSet(A_, B_, C_, D_, E_): {"layout": "sequential",
+                                        "transpose": True}},
+        transpose=True)
+
+    assert grid.width == 5
+    assert grid.height == 2
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[0, 2] == C
+    assert grid[0, 3] == D
+    assert grid[0, 4] == E
+    assert grid[1, 0] == A_
+    assert grid[1, 1] == B_
+    assert grid[1, 2] == C_
+    assert grid[1, 3] == D_
+    assert grid[1, 4] == E_
+    assert grid.morphisms == morphisms
+
+    # A two-triangle disconnected diagram.
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    f_ = NamedMorphism(A_, B_, "f")
+    g_ = NamedMorphism(B_, C_, "g")
+    d = Diagram([f, g, f_, g_], {g * f: "unique", g_ * f_: "unique"})
+    grid = DiagramGrid(d)
+
+    assert grid.width == 4
+    assert grid.height == 2
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[0, 2] == A_
+    assert grid[0, 3] == B_
+    assert grid[1, 0] == C
+    assert grid[1, 1] is None
+    assert grid[1, 2] == C_
+    assert grid[1, 3] is None
+    assert grid.morphisms == {f: FiniteSet(), g: FiniteSet(), f_: FiniteSet(),
+                              g_: FiniteSet(), g * f: FiniteSet("unique"),
+                              g_ * f_: FiniteSet("unique")}
+
+    # A two-morphism disconnected diagram.
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(C, D, "g")
+    d = Diagram([f, g])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 4
+    assert grid.height == 1
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+    assert grid[0, 2] == C
+    assert grid[0, 3] == D
+    assert grid.morphisms == {f: FiniteSet(), g: FiniteSet()}
+
+    # Test a one-object diagram.
+    f = NamedMorphism(A, A, "f")
+    d = Diagram([f])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 1
+    assert grid.height == 1
+    assert grid[0, 0] == A
+
+    # Test a two-object disconnected diagram.
+    g = NamedMorphism(B, B, "g")
+    d = Diagram([f, g])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 2
+    assert grid.height == 1
+    assert grid[0, 0] == A
+    assert grid[0, 1] == B
+
+
+def test_DiagramGrid_pseudopod():
+    # Test a diagram in which even growing a pseudopod does not
+    # eventually help.
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    D = Object("D")
+    E = Object("E")
+    F = Object("F")
+    A_ = Object("A'")
+    B_ = Object("B'")
+    C_ = Object("C'")
+    D_ = Object("D'")
+    E_ = Object("E'")
+
+    f1 = NamedMorphism(A, B, "f1")
+    f2 = NamedMorphism(A, C, "f2")
+    f3 = NamedMorphism(A, D, "f3")
+    f4 = NamedMorphism(A, E, "f4")
+    f5 = NamedMorphism(A, A_, "f5")
+    f6 = NamedMorphism(A, B_, "f6")
+    f7 = NamedMorphism(A, C_, "f7")
+    f8 = NamedMorphism(A, D_, "f8")
+    f9 = NamedMorphism(A, E_, "f9")
+    f10 = NamedMorphism(A, F, "f10")
+    d = Diagram([f1, f2, f3, f4, f5, f6, f7, f8, f9, f10])
+    grid = DiagramGrid(d)
+
+    assert grid.width == 5
+    assert grid.height == 3
+    assert grid[0, 0] == E
+    assert grid[0, 1] == C
+    assert grid[0, 2] == C_
+    assert grid[0, 3] == E_
+    assert grid[0, 4] == F
+    assert grid[1, 0] == D
+    assert grid[1, 1] == A
+    assert grid[1, 2] == A_
+    assert grid[1, 3] is None
+    assert grid[1, 4] is None
+    assert grid[2, 0] == D_
+    assert grid[2, 1] == B
+    assert grid[2, 2] == B_
+    assert grid[2, 3] is None
+    assert grid[2, 4] is None
+
+    morphisms = {}
+    for f in [f1, f2, f3, f4, f5, f6, f7, f8, f9, f10]:
+        morphisms[f] = FiniteSet()
+    assert grid.morphisms == morphisms
+
+
+def test_ArrowStringDescription():
+    astr = ArrowStringDescription("cm", "", None, "", "", "d", "r", "_", "f")
+    assert str(astr) == "\\ar[dr]_{f}"
+
+    astr = ArrowStringDescription("cm", "", 12, "", "", "d", "r", "_", "f")
+    assert str(astr) == "\\ar[dr]_{f}"
+
+    astr = ArrowStringDescription("cm", "^", 12, "", "", "d", "r", "_", "f")
+    assert str(astr) == "\\ar@/^12cm/[dr]_{f}"
+
+    astr = ArrowStringDescription("cm", "", 12, "r", "", "d", "r", "_", "f")
+    assert str(astr) == "\\ar[dr]_{f}"
+
+    astr = ArrowStringDescription("cm", "", 12, "r", "u", "d", "r", "_", "f")
+    assert str(astr) == "\\ar@(r,u)[dr]_{f}"
+
+    astr = ArrowStringDescription("cm", "", 12, "r", "u", "d", "r", "_", "f")
+    assert str(astr) == "\\ar@(r,u)[dr]_{f}"
+
+    astr = ArrowStringDescription("cm", "", 12, "r", "u", "d", "r", "_", "f")
+    astr.arrow_style = "{-->}"
+    assert str(astr) == "\\ar@(r,u)@{-->}[dr]_{f}"
+
+    astr = ArrowStringDescription("cm", "_", 12, "", "", "d", "r", "_", "f")
+    astr.arrow_style = "{-->}"
+    assert str(astr) == "\\ar@/_12cm/@{-->}[dr]_{f}"
+
+
+def test_XypicDiagramDrawer_line():
+    # A linear diagram.
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    D = Object("D")
+    E = Object("E")
+
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    h = NamedMorphism(C, D, "h")
+    i = NamedMorphism(D, E, "i")
+    d = Diagram([f, g, h, i])
+    grid = DiagramGrid(d, layout="sequential")
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[r]^{f} & B \\ar[r]^{g} & C \\ar[r]^{h} & D \\ar[r]^{i} & E \n" \
+        "}\n"
+
+    # The same diagram, transposed.
+    grid = DiagramGrid(d, layout="sequential", transpose=True)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[d]^{f} \\\\\n" \
+        "B \\ar[d]^{g} \\\\\n" \
+        "C \\ar[d]^{h} \\\\\n" \
+        "D \\ar[d]^{i} \\\\\n" \
+        "E \n" \
+        "}\n"
+
+
+def test_XypicDiagramDrawer_triangle():
+    # A triangle diagram.
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+
+    d = Diagram([f, g], {g * f: "unique"})
+    grid = DiagramGrid(d)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[d]_{g\\circ f} \\ar[r]^{f} & B \\ar[ld]^{g} \\\\\n" \
+        "C & \n" \
+        "}\n"
+
+    # The same diagram, transposed.
+    grid = DiagramGrid(d, transpose=True)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[r]^{g\\circ f} \\ar[d]_{f} & C \\\\\n" \
+        "B \\ar[ru]_{g} & \n" \
+        "}\n"
+
+    # The same diagram, with a masked morphism.
+    assert drawer.draw(d, grid, masked=[g]) == "\\xymatrix{\n" \
+        "A \\ar[r]^{g\\circ f} \\ar[d]_{f} & C \\\\\n" \
+        "B & \n" \
+        "}\n"
+
+    # The same diagram with a formatter for "unique".
+    def formatter(astr):
+        astr.label = "\\exists !" + astr.label
+        astr.arrow_style = "{-->}"
+
+    drawer.arrow_formatters["unique"] = formatter
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar@{-->}[r]^{\\exists !g\\circ f} \\ar[d]_{f} & C \\\\\n" \
+        "B \\ar[ru]_{g} & \n" \
+        "}\n"
+
+    # The same diagram with a default formatter.
+    def default_formatter(astr):
+        astr.label_displacement = "(0.45)"
+
+    drawer.default_arrow_formatter = default_formatter
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar@{-->}[r]^(0.45){\\exists !g\\circ f} \\ar[d]_(0.45){f} & C \\\\\n" \
+        "B \\ar[ru]_(0.45){g} & \n" \
+        "}\n"
+
+    # A triangle diagram with a lot of morphisms between the same
+    # objects.
+    f1 = NamedMorphism(B, A, "f1")
+    f2 = NamedMorphism(A, B, "f2")
+    g1 = NamedMorphism(C, B, "g1")
+    g2 = NamedMorphism(B, C, "g2")
+    d = Diagram([f, f1, f2, g, g1, g2], {f1 * g1: "unique", g2 * f2: "unique"})
+
+    grid = DiagramGrid(d, transpose=True)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid, masked=[f1*g1*g2*f2, g2*f2*f1*g1]) == \
+        "\\xymatrix{\n" \
+        "A \\ar[r]^{g_{2}\\circ f_{2}} \\ar[d]_{f} \\ar@/^3mm/[d]^{f_{2}} " \
+        "& C \\ar@/^3mm/[l]^{f_{1}\\circ g_{1}} \\ar@/^3mm/[ld]^{g_{1}} \\\\\n" \
+        "B \\ar@/^3mm/[u]^{f_{1}} \\ar[ru]_{g} \\ar@/^3mm/[ru]^{g_{2}} & \n" \
+        "}\n"
+
+
+def test_XypicDiagramDrawer_cube():
+    # A cube diagram.
+    A1 = Object("A1")
+    A2 = Object("A2")
+    A3 = Object("A3")
+    A4 = Object("A4")
+    A5 = Object("A5")
+    A6 = Object("A6")
+    A7 = Object("A7")
+    A8 = Object("A8")
+
+    # The top face of the cube.
+    f1 = NamedMorphism(A1, A2, "f1")
+    f2 = NamedMorphism(A1, A3, "f2")
+    f3 = NamedMorphism(A2, A4, "f3")
+    f4 = NamedMorphism(A3, A4, "f3")
+
+    # The bottom face of the cube.
+    f5 = NamedMorphism(A5, A6, "f5")
+    f6 = NamedMorphism(A5, A7, "f6")
+    f7 = NamedMorphism(A6, A8, "f7")
+    f8 = NamedMorphism(A7, A8, "f8")
+
+    # The remaining morphisms.
+    f9 = NamedMorphism(A1, A5, "f9")
+    f10 = NamedMorphism(A2, A6, "f10")
+    f11 = NamedMorphism(A3, A7, "f11")
+    f12 = NamedMorphism(A4, A8, "f11")
+
+    d = Diagram([f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, f11, f12])
+    grid = DiagramGrid(d)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "& A_{5} \\ar[r]^{f_{5}} \\ar[ldd]_{f_{6}} & A_{6} \\ar[rdd]^{f_{7}} " \
+        "& \\\\\n" \
+        "& A_{1} \\ar[r]^{f_{1}} \\ar[d]^{f_{2}} \\ar[u]^{f_{9}} & A_{2} " \
+        "\\ar[d]^{f_{3}} \\ar[u]_{f_{10}} & \\\\\n" \
+        "A_{7} \\ar@/_3mm/[rrr]_{f_{8}} & A_{3} \\ar[r]^{f_{3}} \\ar[l]_{f_{11}} " \
+        "& A_{4} \\ar[r]^{f_{11}} & A_{8} \n" \
+        "}\n"
+
+    # The same diagram, transposed.
+    grid = DiagramGrid(d, transpose=True)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "& & A_{7} \\ar@/^3mm/[ddd]^{f_{8}} \\\\\n" \
+        "A_{5} \\ar[d]_{f_{5}} \\ar[rru]^{f_{6}} & A_{1} \\ar[d]^{f_{1}} " \
+        "\\ar[r]^{f_{2}} \\ar[l]^{f_{9}} & A_{3} \\ar[d]_{f_{3}} " \
+        "\\ar[u]^{f_{11}} \\\\\n" \
+        "A_{6} \\ar[rrd]_{f_{7}} & A_{2} \\ar[r]^{f_{3}} \\ar[l]^{f_{10}} " \
+        "& A_{4} \\ar[d]_{f_{11}} \\\\\n" \
+        "& & A_{8} \n" \
+        "}\n"
+
+
+def test_XypicDiagramDrawer_curved_and_loops():
+    # A simple diagram, with a curved arrow.
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    D = Object("D")
+
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    h = NamedMorphism(D, A, "h")
+    k = NamedMorphism(D, B, "k")
+    d = Diagram([f, g, h, k])
+    grid = DiagramGrid(d)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[r]_{f} & B \\ar[d]^{g} & D \\ar[l]^{k} \\ar@/_3mm/[ll]_{h} \\\\\n" \
+        "& C & \n" \
+        "}\n"
+
+    # The same diagram, transposed.
+    grid = DiagramGrid(d, transpose=True)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[d]^{f} & \\\\\n" \
+        "B \\ar[r]^{g} & C \\\\\n" \
+        "D \\ar[u]_{k} \\ar@/^3mm/[uu]^{h} & \n" \
+        "}\n"
+
+    # The same diagram, larger and rotated.
+    assert drawer.draw(d, grid, diagram_format="@+1cm@dr") == \
+        "\\xymatrix@+1cm@dr{\n" \
+        "A \\ar[d]^{f} & \\\\\n" \
+        "B \\ar[r]^{g} & C \\\\\n" \
+        "D \\ar[u]_{k} \\ar@/^3mm/[uu]^{h} & \n" \
+        "}\n"
+
+    # A simple diagram with three curved arrows.
+    h1 = NamedMorphism(D, A, "h1")
+    h2 = NamedMorphism(A, D, "h2")
+    k = NamedMorphism(D, B, "k")
+    d = Diagram([f, g, h, k, h1, h2])
+    grid = DiagramGrid(d)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[r]_{f} \\ar@/^3mm/[rr]^{h_{2}} & B \\ar[d]^{g} & D \\ar[l]^{k} " \
+        "\\ar@/_7mm/[ll]_{h} \\ar@/_11mm/[ll]_{h_{1}} \\\\\n" \
+        "& C & \n" \
+        "}\n"
+
+    # The same diagram, transposed.
+    grid = DiagramGrid(d, transpose=True)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[d]^{f} \\ar@/_3mm/[dd]_{h_{2}} & \\\\\n" \
+        "B \\ar[r]^{g} & C \\\\\n" \
+        "D \\ar[u]_{k} \\ar@/^7mm/[uu]^{h} \\ar@/^11mm/[uu]^{h_{1}} & \n" \
+        "}\n"
+
+    # The same diagram, with "loop" morphisms.
+    l_A = NamedMorphism(A, A, "l_A")
+    l_D = NamedMorphism(D, D, "l_D")
+    l_C = NamedMorphism(C, C, "l_C")
+    d = Diagram([f, g, h, k, h1, h2, l_A, l_D, l_C])
+    grid = DiagramGrid(d)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[r]_{f} \\ar@/^3mm/[rr]^{h_{2}} \\ar@(u,l)[]^{l_{A}} " \
+        "& B \\ar[d]^{g} & D \\ar[l]^{k} \\ar@/_7mm/[ll]_{h} " \
+        "\\ar@/_11mm/[ll]_{h_{1}} \\ar@(r,u)[]^{l_{D}} \\\\\n" \
+        "& C \\ar@(l,d)[]^{l_{C}} & \n" \
+        "}\n"
+
+    # The same diagram with "loop" morphisms, transposed.
+    grid = DiagramGrid(d, transpose=True)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[d]^{f} \\ar@/_3mm/[dd]_{h_{2}} \\ar@(r,u)[]^{l_{A}} & \\\\\n" \
+        "B \\ar[r]^{g} & C \\ar@(r,u)[]^{l_{C}} \\\\\n" \
+        "D \\ar[u]_{k} \\ar@/^7mm/[uu]^{h} \\ar@/^11mm/[uu]^{h_{1}} " \
+        "\\ar@(l,d)[]^{l_{D}} & \n" \
+        "}\n"
+
+    # The same diagram with two "loop" morphisms per object.
+    l_A_ = NamedMorphism(A, A, "n_A")
+    l_D_ = NamedMorphism(D, D, "n_D")
+    l_C_ = NamedMorphism(C, C, "n_C")
+    d = Diagram([f, g, h, k, h1, h2, l_A, l_D, l_C, l_A_, l_D_, l_C_])
+    grid = DiagramGrid(d)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[r]_{f} \\ar@/^3mm/[rr]^{h_{2}} \\ar@(u,l)[]^{l_{A}} " \
+        "\\ar@/^3mm/@(l,d)[]^{n_{A}} & B \\ar[d]^{g} & D \\ar[l]^{k} " \
+        "\\ar@/_7mm/[ll]_{h} \\ar@/_11mm/[ll]_{h_{1}} \\ar@(r,u)[]^{l_{D}} " \
+        "\\ar@/^3mm/@(d,r)[]^{n_{D}} \\\\\n" \
+        "& C \\ar@(l,d)[]^{l_{C}} \\ar@/^3mm/@(d,r)[]^{n_{C}} & \n" \
+        "}\n"
+
+    # The same diagram with two "loop" morphisms per object, transposed.
+    grid = DiagramGrid(d, transpose=True)
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == "\\xymatrix{\n" \
+        "A \\ar[d]^{f} \\ar@/_3mm/[dd]_{h_{2}} \\ar@(r,u)[]^{l_{A}} " \
+        "\\ar@/^3mm/@(u,l)[]^{n_{A}} & \\\\\n" \
+        "B \\ar[r]^{g} & C \\ar@(r,u)[]^{l_{C}} \\ar@/^3mm/@(d,r)[]^{n_{C}} \\\\\n" \
+        "D \\ar[u]_{k} \\ar@/^7mm/[uu]^{h} \\ar@/^11mm/[uu]^{h_{1}} " \
+        "\\ar@(l,d)[]^{l_{D}} \\ar@/^3mm/@(d,r)[]^{n_{D}} & \n" \
+        "}\n"
+
+
+def test_xypic_draw_diagram():
+    # A linear diagram.
+    A = Object("A")
+    B = Object("B")
+    C = Object("C")
+    D = Object("D")
+    E = Object("E")
+
+    f = NamedMorphism(A, B, "f")
+    g = NamedMorphism(B, C, "g")
+    h = NamedMorphism(C, D, "h")
+    i = NamedMorphism(D, E, "i")
+    d = Diagram([f, g, h, i])
+
+    grid = DiagramGrid(d, layout="sequential")
+    drawer = XypicDiagramDrawer()
+    assert drawer.draw(d, grid) == xypic_draw_diagram(d, layout="sequential")

llmeval-env/lib/python3.10/site-packages/sympy/plotting/__init__.py

@@ -0,0 +1,22 @@
+from .plot import plot_backends
+from .plot_implicit import plot_implicit
+from .textplot import textplot
+from .pygletplot import PygletPlot
+from .plot import PlotGrid
+from .plot import (plot, plot_parametric, plot3d, plot3d_parametric_surface,
+                  plot3d_parametric_line, plot_contour)
+
+__all__ = [
+    'plot_backends',
+
+    'plot_implicit',
+
+    'textplot',
+
+    'PygletPlot',
+
+    'PlotGrid',
+
+    'plot', 'plot_parametric', 'plot3d', 'plot3d_parametric_surface',
+    'plot3d_parametric_line', 'plot_contour'
+]

llmeval-env/lib/python3.10/site-packages/sympy/plotting/experimental_lambdify.py

@@ -0,0 +1,643 @@
+""" rewrite of lambdify - This stuff is not stable at all.
+
+It is for internal use in the new plotting module.
+It may (will! see the Q'n'A in the source) be rewritten.
+
+It's completely self contained. Especially it does not use lambdarepr.
+
+It does not aim to replace the current lambdify. Most importantly it will never
+ever support anything else than SymPy expressions (no Matrices, dictionaries
+and so on).
+"""
+
+
+import re
+from sympy.core.numbers import (I, NumberSymbol, oo, zoo)
+from sympy.core.symbol import Symbol
+from sympy.utilities.iterables import numbered_symbols
+
+#  We parse the expression string into a tree that identifies functions. Then
+# we translate the names of the functions and we translate also some strings
+# that are not names of functions (all this according to translation
+# dictionaries).
+#  If the translation goes to another module (like numpy) the
+# module is imported and 'func' is translated to 'module.func'.
+#  If a function can not be translated, the inner nodes of that part of the
+# tree are not translated. So if we have Integral(sqrt(x)), sqrt is not
+# translated to np.sqrt and the Integral does not crash.
+#  A namespace for all this is generated by crawling the (func, args) tree of
+# the expression. The creation of this namespace involves many ugly
+# workarounds.
+#  The namespace consists of all the names needed for the SymPy expression and
+# all the name of modules used for translation. Those modules are imported only
+# as a name (import numpy as np) in order to keep the namespace small and
+# manageable.
+
+#  Please, if there is a bug, do not try to fix it here! Rewrite this by using
+# the method proposed in the last Q'n'A below. That way the new function will
+# work just as well, be just as simple, but it wont need any new workarounds.
+#  If you insist on fixing it here, look at the workarounds in the function
+# sympy_expression_namespace and in lambdify.
+
+# Q: Why are you not using Python abstract syntax tree?
+# A: Because it is more complicated and not much more powerful in this case.
+
+# Q: What if I have Symbol('sin') or g=Function('f')?
+# A: You will break the algorithm. We should use srepr to defend against this?
+#  The problem with Symbol('sin') is that it will be printed as 'sin'. The
+# parser will distinguish it from the function 'sin' because functions are
+# detected thanks to the opening parenthesis, but the lambda expression won't
+# understand the difference if we have also the sin function.
+# The solution (complicated) is to use srepr and maybe ast.
+#  The problem with the g=Function('f') is that it will be printed as 'f' but in
+# the global namespace we have only 'g'. But as the same printer is used in the
+# constructor of the namespace there will be no problem.
+
+# Q: What if some of the printers are not printing as expected?
+# A: The algorithm wont work. You must use srepr for those cases. But even
+# srepr may not print well. All problems with printers should be considered
+# bugs.
+
+# Q: What about _imp_ functions?
+# A: Those are taken care for by evalf. A special case treatment will work
+# faster but it's not worth the code complexity.
+
+# Q: Will ast fix all possible problems?
+# A: No. You will always have to use some printer. Even srepr may not work in
+# some cases. But if the printer does not work, that should be considered a
+# bug.
+
+# Q: Is there same way to fix all possible problems?
+# A: Probably by constructing our strings ourself by traversing the (func,
+# args) tree and creating the namespace at the same time. That actually sounds
+# good.
+
+from sympy.external import import_module
+import warnings
+
+#TODO debugging output
+
+
+class vectorized_lambdify:
+    """ Return a sufficiently smart, vectorized and lambdified function.
+
+    Returns only reals.
+
+    Explanation
+    ===========
+
+    This function uses experimental_lambdify to created a lambdified
+    expression ready to be used with numpy. Many of the functions in SymPy
+    are not implemented in numpy so in some cases we resort to Python cmath or
+    even to evalf.
+
+    The following translations are tried:
+      only numpy complex
+      - on errors raised by SymPy trying to work with ndarray:
+          only Python cmath and then vectorize complex128
+
+    When using Python cmath there is no need for evalf or float/complex
+    because Python cmath calls those.
+
+    This function never tries to mix numpy directly with evalf because numpy
+    does not understand SymPy Float. If this is needed one can use the
+    float_wrap_evalf/complex_wrap_evalf options of experimental_lambdify or
+    better one can be explicit about the dtypes that numpy works with.
+    Check numpy bug http://projects.scipy.org/numpy/ticket/1013 to know what
+    types of errors to expect.
+    """
+    def __init__(self, args, expr):
+        self.args = args
+        self.expr = expr
+        self.np = import_module('numpy')
+
+        self.lambda_func_1 = experimental_lambdify(
+            args, expr, use_np=True)
+        self.vector_func_1 = self.lambda_func_1
+
+        self.lambda_func_2 = experimental_lambdify(
+            args, expr, use_python_cmath=True)
+        self.vector_func_2 = self.np.vectorize(
+            self.lambda_func_2, otypes=[complex])
+
+        self.vector_func = self.vector_func_1
+        self.failure = False
+
+    def __call__(self, *args):
+        np = self.np
+
+        try:
+            temp_args = (np.array(a, dtype=complex) for a in args)
+            results = self.vector_func(*temp_args)
+            results = np.ma.masked_where(
+                np.abs(results.imag) > 1e-7 * np.abs(results),
+                results.real, copy=False)
+            return results
+        except ValueError:
+            if self.failure:
+                raise
+
+            self.failure = True
+            self.vector_func = self.vector_func_2
+            warnings.warn(
+                'The evaluation of the expression is problematic. '
+                'We are trying a failback method that may still work. '
+                'Please report this as a bug.')
+            return self.__call__(*args)
+
+
+class lambdify:
+    """Returns the lambdified function.
+
+    Explanation
+    ===========
+
+    This function uses experimental_lambdify to create a lambdified
+    expression. It uses cmath to lambdify the expression. If the function
+    is not implemented in Python cmath, Python cmath calls evalf on those
+    functions.
+    """
+
+    def __init__(self, args, expr):
+        self.args = args
+        self.expr = expr
+        self.lambda_func_1 = experimental_lambdify(
+            args, expr, use_python_cmath=True, use_evalf=True)
+        self.lambda_func_2 = experimental_lambdify(
+            args, expr, use_python_math=True, use_evalf=True)
+        self.lambda_func_3 = experimental_lambdify(
+            args, expr, use_evalf=True, complex_wrap_evalf=True)
+        self.lambda_func = self.lambda_func_1
+        self.failure = False
+
+    def __call__(self, args):
+        try:
+            #The result can be sympy.Float. Hence wrap it with complex type.
+            result = complex(self.lambda_func(args))
+            if abs(result.imag) > 1e-7 * abs(result):
+                return None
+            return result.real
+        except (ZeroDivisionError, OverflowError):
+            return None
+        except TypeError as e:
+            if self.failure:
+                raise e
+
+            if self.lambda_func == self.lambda_func_1:
+                self.lambda_func = self.lambda_func_2
+                return self.__call__(args)
+
+            self.failure = True
+            self.lambda_func = self.lambda_func_3
+            warnings.warn(
+                'The evaluation of the expression is problematic. '
+                'We are trying a failback method that may still work. '
+                'Please report this as a bug.', stacklevel=2)
+            return self.__call__(args)
+
+
+def experimental_lambdify(*args, **kwargs):
+    l = Lambdifier(*args, **kwargs)
+    return l
+
+
+class Lambdifier:
+    def __init__(self, args, expr, print_lambda=False, use_evalf=False,
+                 float_wrap_evalf=False, complex_wrap_evalf=False,
+                 use_np=False, use_python_math=False, use_python_cmath=False,
+                 use_interval=False):
+
+        self.print_lambda = print_lambda
+        self.use_evalf = use_evalf
+        self.float_wrap_evalf = float_wrap_evalf
+        self.complex_wrap_evalf = complex_wrap_evalf
+        self.use_np = use_np
+        self.use_python_math = use_python_math
+        self.use_python_cmath = use_python_cmath
+        self.use_interval = use_interval
+
+        # Constructing the argument string
+        # - check
+        if not all(isinstance(a, Symbol) for a in args):
+            raise ValueError('The arguments must be Symbols.')
+        # - use numbered symbols
+        syms = numbered_symbols(exclude=expr.free_symbols)
+        newargs = [next(syms) for _ in args]
+        expr = expr.xreplace(dict(zip(args, newargs)))
+        argstr = ', '.join([str(a) for a in newargs])
+        del syms, newargs, args
+
+        # Constructing the translation dictionaries and making the translation
+        self.dict_str = self.get_dict_str()
+        self.dict_fun = self.get_dict_fun()
+        exprstr = str(expr)
+        newexpr = self.tree2str_translate(self.str2tree(exprstr))
+
+        # Constructing the namespaces
+        namespace = {}
+        namespace.update(self.sympy_atoms_namespace(expr))
+        namespace.update(self.sympy_expression_namespace(expr))
+        # XXX Workaround
+        # Ugly workaround because Pow(a,Half) prints as sqrt(a)
+        # and sympy_expression_namespace can not catch it.
+        from sympy.functions.elementary.miscellaneous import sqrt
+        namespace.update({'sqrt': sqrt})
+        namespace.update({'Eq': lambda x, y: x == y})
+        namespace.update({'Ne': lambda x, y: x != y})
+        # End workaround.
+        if use_python_math:
+            namespace.update({'math': __import__('math')})
+        if use_python_cmath:
+            namespace.update({'cmath': __import__('cmath')})
+        if use_np:
+            try:
+                namespace.update({'np': __import__('numpy')})
+            except ImportError:
+                raise ImportError(
+                    'experimental_lambdify failed to import numpy.')
+        if use_interval:
+            namespace.update({'imath': __import__(
+                'sympy.plotting.intervalmath', fromlist=['intervalmath'])})
+            namespace.update({'math': __import__('math')})
+
+        # Construct the lambda
+        if self.print_lambda:
+            print(newexpr)
+        eval_str = 'lambda %s : ( %s )' % (argstr, newexpr)
+        self.eval_str = eval_str
+        exec("MYNEWLAMBDA = %s" % eval_str, namespace)
+        self.lambda_func = namespace['MYNEWLAMBDA']
+
+    def __call__(self, *args, **kwargs):
+        return self.lambda_func(*args, **kwargs)
+
+
+    ##############################################################################
+    # Dicts for translating from SymPy to other modules
+    ##############################################################################
+    ###
+    # builtins
+    ###
+    # Functions with different names in builtins
+    builtin_functions_different = {
+        'Min': 'min',
+        'Max': 'max',
+        'Abs': 'abs',
+    }
+
+    # Strings that should be translated
+    builtin_not_functions = {
+        'I': '1j',
+#        'oo': '1e400',
+    }
+
+    ###
+    # numpy
+    ###
+
+    # Functions that are the same in numpy
+    numpy_functions_same = [
+        'sin', 'cos', 'tan', 'sinh', 'cosh', 'tanh', 'exp', 'log',
+        'sqrt', 'floor', 'conjugate',
+    ]
+
+    # Functions with different names in numpy
+    numpy_functions_different = {
+        "acos": "arccos",
+        "acosh": "arccosh",
+        "arg": "angle",
+        "asin": "arcsin",
+        "asinh": "arcsinh",
+        "atan": "arctan",
+        "atan2": "arctan2",
+        "atanh": "arctanh",
+        "ceiling": "ceil",
+        "im": "imag",
+        "ln": "log",
+        "Max": "amax",
+        "Min": "amin",
+        "re": "real",
+        "Abs": "abs",
+    }
+
+    # Strings that should be translated
+    numpy_not_functions = {
+        'pi': 'np.pi',
+        'oo': 'np.inf',
+        'E': 'np.e',
+    }
+
+    ###
+    # Python math
+    ###
+
+    # Functions that are the same in math
+    math_functions_same = [
+        'sin', 'cos', 'tan', 'asin', 'acos', 'atan', 'atan2',
+        'sinh', 'cosh', 'tanh', 'asinh', 'acosh', 'atanh',
+        'exp', 'log', 'erf', 'sqrt', 'floor', 'factorial', 'gamma',
+    ]
+
+    # Functions with different names in math
+    math_functions_different = {
+        'ceiling': 'ceil',
+        'ln': 'log',
+        'loggamma': 'lgamma'
+    }
+
+    # Strings that should be translated
+    math_not_functions = {
+        'pi': 'math.pi',
+        'E': 'math.e',
+    }
+
+    ###
+    # Python cmath
+    ###
+
+    # Functions that are the same in cmath
+    cmath_functions_same = [
+        'sin', 'cos', 'tan', 'asin', 'acos', 'atan',
+        'sinh', 'cosh', 'tanh', 'asinh', 'acosh', 'atanh',
+        'exp', 'log', 'sqrt',
+    ]
+
+    # Functions with different names in cmath
+    cmath_functions_different = {
+        'ln': 'log',
+        'arg': 'phase',
+    }
+
+    # Strings that should be translated
+    cmath_not_functions = {
+        'pi': 'cmath.pi',
+        'E': 'cmath.e',
+    }
+
+    ###
+    # intervalmath
+    ###
+
+    interval_not_functions = {
+        'pi': 'math.pi',
+        'E': 'math.e'
+    }
+
+    interval_functions_same = [
+        'sin', 'cos', 'exp', 'tan', 'atan', 'log',
+        'sqrt', 'cosh', 'sinh', 'tanh', 'floor',
+        'acos', 'asin', 'acosh', 'asinh', 'atanh',
+        'Abs', 'And', 'Or'
+    ]
+
+    interval_functions_different = {
+        'Min': 'imin',
+        'Max': 'imax',
+        'ceiling': 'ceil',
+
+    }
+
+    ###
+    # mpmath, etc
+    ###
+    #TODO
+
+    ###
+    # Create the final ordered tuples of dictionaries
+    ###
+
+    # For strings
+    def get_dict_str(self):
+        dict_str = dict(self.builtin_not_functions)
+        if self.use_np:
+            dict_str.update(self.numpy_not_functions)
+        if self.use_python_math:
+            dict_str.update(self.math_not_functions)
+        if self.use_python_cmath:
+            dict_str.update(self.cmath_not_functions)
+        if self.use_interval:
+            dict_str.update(self.interval_not_functions)
+        return dict_str
+
+    # For functions
+    def get_dict_fun(self):
+        dict_fun = dict(self.builtin_functions_different)
+        if self.use_np:
+            for s in self.numpy_functions_same:
+                dict_fun[s] = 'np.' + s
+            for k, v in self.numpy_functions_different.items():
+                dict_fun[k] = 'np.' + v
+        if self.use_python_math:
+            for s in self.math_functions_same:
+                dict_fun[s] = 'math.' + s
+            for k, v in self.math_functions_different.items():
+                dict_fun[k] = 'math.' + v
+        if self.use_python_cmath:
+            for s in self.cmath_functions_same:
+                dict_fun[s] = 'cmath.' + s
+            for k, v in self.cmath_functions_different.items():
+                dict_fun[k] = 'cmath.' + v
+        if self.use_interval:
+            for s in self.interval_functions_same:
+                dict_fun[s] = 'imath.' + s
+            for k, v in self.interval_functions_different.items():
+                dict_fun[k] = 'imath.' + v
+        return dict_fun
+
+    ##############################################################################
+    # The translator functions, tree parsers, etc.
+    ##############################################################################
+
+    def str2tree(self, exprstr):
+        """Converts an expression string to a tree.
+
+        Explanation
+        ===========
+
+        Functions are represented by ('func_name(', tree_of_arguments).
+        Other expressions are (head_string, mid_tree, tail_str).
+        Expressions that do not contain functions are directly returned.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x, y, z
+        >>> from sympy import Integral, sin
+        >>> from sympy.plotting.experimental_lambdify import Lambdifier
+        >>> str2tree = Lambdifier([x], x).str2tree
+
+        >>> str2tree(str(Integral(x, (x, 1, y))))
+        ('', ('Integral(', 'x, (x, 1, y)'), ')')
+        >>> str2tree(str(x+y))
+        'x + y'
+        >>> str2tree(str(x+y*sin(z)+1))
+        ('x + y*', ('sin(', 'z'), ') + 1')
+        >>> str2tree('sin(y*(y + 1.1) + (sin(y)))')
+        ('', ('sin(', ('y*(y + 1.1) + (', ('sin(', 'y'), '))')), ')')
+        """
+        #matches the first 'function_name('
+        first_par = re.search(r'(\w+\()', exprstr)
+        if first_par is None:
+            return exprstr
+        else:
+            start = first_par.start()
+            end = first_par.end()
+            head = exprstr[:start]
+            func = exprstr[start:end]
+            tail = exprstr[end:]
+            count = 0
+            for i, c in enumerate(tail):
+                if c == '(':
+                    count += 1
+                elif c == ')':
+                    count -= 1
+                if count == -1:
+                    break
+            func_tail = self.str2tree(tail[:i])
+            tail = self.str2tree(tail[i:])
+            return (head, (func, func_tail), tail)
+
+    @classmethod
+    def tree2str(cls, tree):
+        """Converts a tree to string without translations.
+
+        Examples
+        ========
+
+        >>> from sympy.abc import x, y, z
+        >>> from sympy import sin
+        >>> from sympy.plotting.experimental_lambdify import Lambdifier
+        >>> str2tree = Lambdifier([x], x).str2tree
+        >>> tree2str = Lambdifier([x], x).tree2str
+
+        >>> tree2str(str2tree(str(x+y*sin(z)+1)))
+        'x + y*sin(z) + 1'
+        """
+        if isinstance(tree, str):
+            return tree
+        else:
+            return ''.join(map(cls.tree2str, tree))
+
+    def tree2str_translate(self, tree):
+        """Converts a tree to string with translations.
+
+        Explanation
+        ===========
+
+        Function names are translated by translate_func.
+        Other strings are translated by translate_str.
+        """
+        if isinstance(tree, str):
+            return self.translate_str(tree)
+        elif isinstance(tree, tuple) and len(tree) == 2:
+            return self.translate_func(tree[0][:-1], tree[1])
+        else:
+            return ''.join([self.tree2str_translate(t) for t in tree])
+
+    def translate_str(self, estr):
+        """Translate substrings of estr using in order the dictionaries in
+        dict_tuple_str."""
+        for pattern, repl in self.dict_str.items():
+                estr = re.sub(pattern, repl, estr)
+        return estr
+
+    def translate_func(self, func_name, argtree):
+        """Translate function names and the tree of arguments.
+
+        Explanation
+        ===========
+
+        If the function name is not in the dictionaries of dict_tuple_fun then the
+        function is surrounded by a float((...).evalf()).
+
+        The use of float is necessary as np.<function>(sympy.Float(..)) raises an
+        error."""
+        if func_name in self.dict_fun:
+            new_name = self.dict_fun[func_name]
+            argstr = self.tree2str_translate(argtree)
+            return new_name + '(' + argstr
+        elif func_name in ['Eq', 'Ne']:
+            op = {'Eq': '==', 'Ne': '!='}
+            return "(lambda x, y: x {} y)({}".format(op[func_name], self.tree2str_translate(argtree))
+        else:
+            template = '(%s(%s)).evalf(' if self.use_evalf else '%s(%s'
+            if self.float_wrap_evalf:
+                template = 'float(%s)' % template
+            elif self.complex_wrap_evalf:
+                template = 'complex(%s)' % template
+
+            # Wrapping should only happen on the outermost expression, which
+            # is the only thing we know will be a number.
+            float_wrap_evalf = self.float_wrap_evalf
+            complex_wrap_evalf = self.complex_wrap_evalf
+            self.float_wrap_evalf = False
+            self.complex_wrap_evalf = False
+            ret =  template % (func_name, self.tree2str_translate(argtree))
+            self.float_wrap_evalf = float_wrap_evalf
+            self.complex_wrap_evalf = complex_wrap_evalf
+            return ret
+
+    ##############################################################################
+    # The namespace constructors
+    ##############################################################################
+
+    @classmethod
+    def sympy_expression_namespace(cls, expr):
+        """Traverses the (func, args) tree of an expression and creates a SymPy
+        namespace. All other modules are imported only as a module name. That way
+        the namespace is not polluted and rests quite small. It probably causes much
+        more variable lookups and so it takes more time, but there are no tests on
+        that for the moment."""
+        if expr is None:
+            return {}
+        else:
+            funcname = str(expr.func)
+            # XXX Workaround
+            # Here we add an ugly workaround because str(func(x))
+            # is not always the same as str(func). Eg
+            # >>> str(Integral(x))
+            # "Integral(x)"
+            # >>> str(Integral)
+            # "<class 'sympy.integrals.integrals.Integral'>"
+            # >>> str(sqrt(x))
+            # "sqrt(x)"
+            # >>> str(sqrt)
+            # "<function sqrt at 0x3d92de8>"
+            # >>> str(sin(x))
+            # "sin(x)"
+            # >>> str(sin)
+            # "sin"
+            # Either one of those can be used but not all at the same time.
+            # The code considers the sin example as the right one.
+            regexlist = [
+                r'<class \'sympy[\w.]*?.([\w]*)\'>$',
+                # the example Integral
+                r'<function ([\w]*) at 0x[\w]*>$',    # the example sqrt
+            ]
+            for r in regexlist:
+                m = re.match(r, funcname)
+                if m is not None:
+                    funcname = m.groups()[0]
+            # End of the workaround
+            # XXX debug: print funcname
+            args_dict = {}
+            for a in expr.args:
+                if (isinstance(a, Symbol) or
+                    isinstance(a, NumberSymbol) or
+                        a in [I, zoo, oo]):
+                    continue
+                else:
+                    args_dict.update(cls.sympy_expression_namespace(a))
+            args_dict.update({funcname: expr.func})
+            return args_dict
+
+    @staticmethod
+    def sympy_atoms_namespace(expr):
+        """For no real reason this function is separated from
+        sympy_expression_namespace. It can be moved to it."""
+        atoms = expr.atoms(Symbol, NumberSymbol, I, zoo, oo)
+        d = {}
+        for a in atoms:
+            # XXX debug: print 'atom:' + str(a)
+            d[str(a)] = a
+        return d

llmeval-env/lib/python3.10/site-packages/sympy/plotting/intervalmath/__init__.py

@@ -0,0 +1,12 @@
+from .interval_arithmetic import interval
+from .lib_interval import (Abs, exp, log, log10, sin, cos, tan, sqrt,
+                          imin, imax, sinh, cosh, tanh, acosh, asinh, atanh,
+                          asin, acos, atan, ceil, floor, And, Or)
+
+__all__ = [
+    'interval',
+
+    'Abs', 'exp', 'log', 'log10', 'sin', 'cos', 'tan', 'sqrt', 'imin', 'imax',
+    'sinh', 'cosh', 'tanh', 'acosh', 'asinh', 'atanh', 'asin', 'acos', 'atan',
+    'ceil', 'floor', 'And', 'Or',
+]

llmeval-env/lib/python3.10/site-packages/sympy/plotting/intervalmath/interval_membership.py

@@ -0,0 +1,78 @@
+from sympy.core.logic import fuzzy_and, fuzzy_or, fuzzy_not, fuzzy_xor
+
+
+class intervalMembership:
+    """Represents a boolean expression returned by the comparison of
+    the interval object.
+
+    Parameters
+    ==========
+
+    (a, b) : (bool, bool)
+        The first value determines the comparison as follows:
+        - True: If the comparison is True throughout the intervals.
+        - False: If the comparison is False throughout the intervals.
+        - None: If the comparison is True for some part of the intervals.
+
+        The second value is determined as follows:
+        - True: If both the intervals in comparison are valid.
+        - False: If at least one of the intervals is False, else
+        - None
+    """
+    def __init__(self, a, b):
+        self._wrapped = (a, b)
+
+    def __getitem__(self, i):
+        try:
+            return self._wrapped[i]
+        except IndexError:
+            raise IndexError(
+                "{} must be a valid indexing for the 2-tuple."
+                .format(i))
+
+    def __len__(self):
+        return 2
+
+    def __iter__(self):
+        return iter(self._wrapped)
+
+    def __str__(self):
+        return "intervalMembership({}, {})".format(*self)
+    __repr__ = __str__
+
+    def __and__(self, other):
+        if not isinstance(other, intervalMembership):
+            raise ValueError(
+                "The comparison is not supported for {}.".format(other))
+
+        a1, b1 = self
+        a2, b2 = other
+        return intervalMembership(fuzzy_and([a1, a2]), fuzzy_and([b1, b2]))
+
+    def __or__(self, other):
+        if not isinstance(other, intervalMembership):
+            raise ValueError(
+                "The comparison is not supported for {}.".format(other))
+
+        a1, b1 = self
+        a2, b2 = other
+        return intervalMembership(fuzzy_or([a1, a2]), fuzzy_and([b1, b2]))
+
+    def __invert__(self):
+        a, b = self
+        return intervalMembership(fuzzy_not(a), b)
+
+    def __xor__(self, other):
+        if not isinstance(other, intervalMembership):
+            raise ValueError(
+                "The comparison is not supported for {}.".format(other))
+
+        a1, b1 = self
+        a2, b2 = other
+        return intervalMembership(fuzzy_xor([a1, a2]), fuzzy_and([b1, b2]))
+
+    def __eq__(self, other):
+        return self._wrapped == other
+
+    def __ne__(self, other):
+        return self._wrapped != other

llmeval-env/lib/python3.10/site-packages/sympy/plotting/intervalmath/lib_interval.py

@@ -0,0 +1,452 @@
+""" The module contains implemented functions for interval arithmetic."""
+from functools import reduce
+
+from sympy.plotting.intervalmath import interval
+from sympy.external import import_module
+
+
+def Abs(x):
+    if isinstance(x, (int, float)):
+        return interval(abs(x))
+    elif isinstance(x, interval):
+        if x.start < 0 and x.end > 0:
+            return interval(0, max(abs(x.start), abs(x.end)), is_valid=x.is_valid)
+        else:
+            return interval(abs(x.start), abs(x.end))
+    else:
+        raise NotImplementedError
+
+#Monotonic
+
+
+def exp(x):
+    """evaluates the exponential of an interval"""
+    np = import_module('numpy')
+    if isinstance(x, (int, float)):
+        return interval(np.exp(x), np.exp(x))
+    elif isinstance(x, interval):
+        return interval(np.exp(x.start), np.exp(x.end), is_valid=x.is_valid)
+    else:
+        raise NotImplementedError
+
+
+#Monotonic
+def log(x):
+    """evaluates the natural logarithm of an interval"""
+    np = import_module('numpy')
+    if isinstance(x, (int, float)):
+        if x <= 0:
+            return interval(-np.inf, np.inf, is_valid=False)
+        else:
+            return interval(np.log(x))
+    elif isinstance(x, interval):
+        if not x.is_valid:
+            return interval(-np.inf, np.inf, is_valid=x.is_valid)
+        elif x.end <= 0:
+            return interval(-np.inf, np.inf, is_valid=False)
+        elif x.start <= 0:
+            return interval(-np.inf, np.inf, is_valid=None)
+
+        return interval(np.log(x.start), np.log(x.end))
+    else:
+        raise NotImplementedError
+
+
+#Monotonic
+def log10(x):
+    """evaluates the logarithm to the base 10 of an interval"""
+    np = import_module('numpy')
+    if isinstance(x, (int, float)):
+        if x <= 0:
+            return interval(-np.inf, np.inf, is_valid=False)
+        else:
+            return interval(np.log10(x))
+    elif isinstance(x, interval):
+        if not x.is_valid:
+            return interval(-np.inf, np.inf, is_valid=x.is_valid)
+        elif x.end <= 0:
+            return interval(-np.inf, np.inf, is_valid=False)
+        elif x.start <= 0:
+            return interval(-np.inf, np.inf, is_valid=None)
+        return interval(np.log10(x.start), np.log10(x.end))
+    else:
+        raise NotImplementedError
+
+
+#Monotonic
+def atan(x):
+    """evaluates the tan inverse of an interval"""
+    np = import_module('numpy')
+    if isinstance(x, (int, float)):
+        return interval(np.arctan(x))
+    elif isinstance(x, interval):
+        start = np.arctan(x.start)
+        end = np.arctan(x.end)
+        return interval(start, end, is_valid=x.is_valid)
+    else:
+        raise NotImplementedError
+
+
+#periodic
+def sin(x):
+    """evaluates the sine of an interval"""
+    np = import_module('numpy')
+    if isinstance(x, (int, float)):
+        return interval(np.sin(x))
+    elif isinstance(x, interval):
+        if not x.is_valid:
+            return interval(-1, 1, is_valid=x.is_valid)
+        na, __ = divmod(x.start, np.pi / 2.0)
+        nb, __ = divmod(x.end, np.pi / 2.0)
+        start = min(np.sin(x.start), np.sin(x.end))
+        end = max(np.sin(x.start), np.sin(x.end))
+        if nb - na > 4:
+            return interval(-1, 1, is_valid=x.is_valid)
+        elif na == nb:
+            return interval(start, end, is_valid=x.is_valid)
+        else:
+            if (na - 1) // 4 != (nb - 1) // 4:
+                #sin has max
+                end = 1
+            if (na - 3) // 4 != (nb - 3) // 4:
+                #sin has min
+                start = -1
+            return interval(start, end)
+    else:
+        raise NotImplementedError
+
+
+#periodic
+def cos(x):
+    """Evaluates the cos of an interval"""
+    np = import_module('numpy')
+    if isinstance(x, (int, float)):
+        return interval(np.sin(x))
+    elif isinstance(x, interval):
+        if not (np.isfinite(x.start) and np.isfinite(x.end)):
+            return interval(-1, 1, is_valid=x.is_valid)
+        na, __ = divmod(x.start, np.pi / 2.0)
+        nb, __ = divmod(x.end, np.pi / 2.0)
+        start = min(np.cos(x.start), np.cos(x.end))
+        end = max(np.cos(x.start), np.cos(x.end))
+        if nb - na > 4:
+            #differ more than 2*pi
+            return interval(-1, 1, is_valid=x.is_valid)
+        elif na == nb:
+            #in the same quadarant
+            return interval(start, end, is_valid=x.is_valid)
+        else:
+            if (na) // 4 != (nb) // 4:
+                #cos has max
+                end = 1
+            if (na - 2) // 4 != (nb - 2) // 4:
+                #cos has min
+                start = -1
+            return interval(start, end, is_valid=x.is_valid)
+    else:
+        raise NotImplementedError
+
+
+def tan(x):
+    """Evaluates the tan of an interval"""
+    return sin(x) / cos(x)
+
+
+#Monotonic
+def sqrt(x):
+    """Evaluates the square root of an interval"""
+    np = import_module('numpy')
+    if isinstance(x, (int, float)):
+        if x > 0:
+            return interval(np.sqrt(x))
+        else:
+            return interval(-np.inf, np.inf, is_valid=False)
+    elif isinstance(x, interval):
+        #Outside the domain
+        if x.end < 0:
+            return interval(-np.inf, np.inf, is_valid=False)
+        #Partially outside the domain
+        elif x.start < 0:
+            return interval(-np.inf, np.inf, is_valid=None)
+        else:
+            return interval(np.sqrt(x.start), np.sqrt(x.end),
+                    is_valid=x.is_valid)
+    else:
+        raise NotImplementedError
+
+
+def imin(*args):
+    """Evaluates the minimum of a list of intervals"""
+    np = import_module('numpy')
+    if not all(isinstance(arg, (int, float, interval)) for arg in args):
+        return NotImplementedError
+    else:
+        new_args = [a for a in args if isinstance(a, (int, float))
+                    or a.is_valid]
+        if len(new_args) == 0:
+            if all(a.is_valid is False for a in args):
+                return interval(-np.inf, np.inf, is_valid=False)
+            else:
+                return interval(-np.inf, np.inf, is_valid=None)
+        start_array = [a if isinstance(a, (int, float)) else a.start
+                       for a in new_args]
+
+        end_array = [a if isinstance(a, (int, float)) else a.end
+                     for a in new_args]
+        return interval(min(start_array), min(end_array))
+
+
+def imax(*args):
+    """Evaluates the maximum of a list of intervals"""
+    np = import_module('numpy')
+    if not all(isinstance(arg, (int, float, interval)) for arg in args):
+        return NotImplementedError
+    else:
+        new_args = [a for a in args if isinstance(a, (int, float))
+                    or a.is_valid]
+        if len(new_args) == 0:
+            if all(a.is_valid is False for a in args):
+                return interval(-np.inf, np.inf, is_valid=False)
+            else:
+                return interval(-np.inf, np.inf, is_valid=None)
+        start_array = [a if isinstance(a, (int, float)) else a.start
+                       for a in new_args]
+
+        end_array = [a if isinstance(a, (int, float)) else a.end
+                     for a in new_args]
+
+        return interval(max(start_array), max(end_array))
+
+
+#Monotonic
+def sinh(x):
+    """Evaluates the hyperbolic sine of an interval"""
+    np = import_module('numpy')
+    if isinstance(x, (int, float)):
+        return interval(np.sinh(x), np.sinh(x))
+    elif isinstance(x, interval):
+        return interval(np.sinh(x.start), np.sinh(x.end), is_valid=x.is_valid)
+    else:
+        raise NotImplementedError
+
+
+def cosh(x):
+    """Evaluates the hyperbolic cos of an interval"""
+    np = import_module('numpy')
+    if isinstance(x, (int, float)):
+        return interval(np.cosh(x), np.cosh(x))
+    elif isinstance(x, interval):
+        #both signs
+        if x.start < 0 and x.end > 0:
+            end = max(np.cosh(x.start), np.cosh(x.end))
+            return interval(1, end, is_valid=x.is_valid)
+        else:
+            #Monotonic
+            start = np.cosh(x.start)
+            end = np.cosh(x.end)
+            return interval(start, end, is_valid=x.is_valid)
+    else:
+        raise NotImplementedError
+
+
+#Monotonic
+def tanh(x):
+    """Evaluates the hyperbolic tan of an interval"""
+    np = import_module('numpy')
+    if isinstance(x, (int, float)):
+        return interval(np.tanh(x), np.tanh(x))
+    elif isinstance(x, interval):
+        return interval(np.tanh(x.start), np.tanh(x.end), is_valid=x.is_valid)
+    else:
+        raise NotImplementedError
+
+
+def asin(x):
+    """Evaluates the inverse sine of an interval"""
+    np = import_module('numpy')
+    if isinstance(x, (int, float)):
+        #Outside the domain
+        if abs(x) > 1:
+            return interval(-np.inf, np.inf, is_valid=False)
+        else:
+            return interval(np.arcsin(x), np.arcsin(x))
+    elif isinstance(x, interval):
+        #Outside the domain
+        if x.is_valid is False or x.start > 1 or x.end < -1:
+            return interval(-np.inf, np.inf, is_valid=False)
+        #Partially outside the domain
+        elif x.start < -1 or x.end > 1:
+            return interval(-np.inf, np.inf, is_valid=None)
+        else:
+            start = np.arcsin(x.start)
+            end = np.arcsin(x.end)
+            return interval(start, end, is_valid=x.is_valid)
+
+
+def acos(x):
+    """Evaluates the inverse cos of an interval"""
+    np = import_module('numpy')
+    if isinstance(x, (int, float)):
+        if abs(x) > 1:
+            #Outside the domain
+            return interval(-np.inf, np.inf, is_valid=False)
+        else:
+            return interval(np.arccos(x), np.arccos(x))
+    elif isinstance(x, interval):
+        #Outside the domain
+        if x.is_valid is False or x.start > 1 or x.end < -1:
+            return interval(-np.inf, np.inf, is_valid=False)
+        #Partially outside the domain
+        elif x.start < -1 or x.end > 1:
+            return interval(-np.inf, np.inf, is_valid=None)
+        else:
+            start = np.arccos(x.start)
+            end = np.arccos(x.end)
+            return interval(start, end, is_valid=x.is_valid)
+
+
+def ceil(x):
+    """Evaluates the ceiling of an interval"""
+    np = import_module('numpy')
+    if isinstance(x, (int, float)):
+        return interval(np.ceil(x))
+    elif isinstance(x, interval):
+        if x.is_valid is False:
+            return interval(-np.inf, np.inf, is_valid=False)
+        else:
+            start = np.ceil(x.start)
+            end = np.ceil(x.end)
+            #Continuous over the interval
+            if start == end:
+                return interval(start, end, is_valid=x.is_valid)
+            else:
+                #Not continuous over the interval
+                return interval(start, end, is_valid=None)
+    else:
+        return NotImplementedError
+
+
+def floor(x):
+    """Evaluates the floor of an interval"""
+    np = import_module('numpy')
+    if isinstance(x, (int, float)):
+        return interval(np.floor(x))
+    elif isinstance(x, interval):
+        if x.is_valid is False:
+            return interval(-np.inf, np.inf, is_valid=False)
+        else:
+            start = np.floor(x.start)
+            end = np.floor(x.end)
+            #continuous over the argument
+            if start == end:
+                return interval(start, end, is_valid=x.is_valid)
+            else:
+                #not continuous over the interval
+                return interval(start, end, is_valid=None)
+    else:
+        return NotImplementedError
+
+
+def acosh(x):
+    """Evaluates the inverse hyperbolic cosine of an interval"""
+    np = import_module('numpy')
+    if isinstance(x, (int, float)):
+        #Outside the domain
+        if x < 1:
+            return interval(-np.inf, np.inf, is_valid=False)
+        else:
+            return interval(np.arccosh(x))
+    elif isinstance(x, interval):
+        #Outside the domain
+        if x.end < 1:
+            return interval(-np.inf, np.inf, is_valid=False)
+        #Partly outside the domain
+        elif x.start < 1:
+            return interval(-np.inf, np.inf, is_valid=None)
+        else:
+            start = np.arccosh(x.start)
+            end = np.arccosh(x.end)
+            return interval(start, end, is_valid=x.is_valid)
+    else:
+        return NotImplementedError
+
+
+#Monotonic
+def asinh(x):
+    """Evaluates the inverse hyperbolic sine of an interval"""
+    np = import_module('numpy')
+    if isinstance(x, (int, float)):
+        return interval(np.arcsinh(x))
+    elif isinstance(x, interval):
+        start = np.arcsinh(x.start)
+        end = np.arcsinh(x.end)
+        return interval(start, end, is_valid=x.is_valid)
+    else:
+        return NotImplementedError
+
+
+def atanh(x):
+    """Evaluates the inverse hyperbolic tangent of an interval"""
+    np = import_module('numpy')
+    if isinstance(x, (int, float)):
+        #Outside the domain
+        if abs(x) >= 1:
+            return interval(-np.inf, np.inf, is_valid=False)
+        else:
+            return interval(np.arctanh(x))
+    elif isinstance(x, interval):
+        #outside the domain
+        if x.is_valid is False or x.start >= 1 or x.end <= -1:
+            return interval(-np.inf, np.inf, is_valid=False)
+        #partly outside the domain
+        elif x.start <= -1 or x.end >= 1:
+            return interval(-np.inf, np.inf, is_valid=None)
+        else:
+            start = np.arctanh(x.start)
+            end = np.arctanh(x.end)
+            return interval(start, end, is_valid=x.is_valid)
+    else:
+        return NotImplementedError
+
+
+#Three valued logic for interval plotting.
+
+def And(*args):
+    """Defines the three valued ``And`` behaviour for a 2-tuple of
+     three valued logic values"""
+    def reduce_and(cmp_intervala, cmp_intervalb):
+        if cmp_intervala[0] is False or cmp_intervalb[0] is False:
+            first = False
+        elif cmp_intervala[0] is None or cmp_intervalb[0] is None:
+            first = None
+        else:
+            first = True
+        if cmp_intervala[1] is False or cmp_intervalb[1] is False:
+            second = False
+        elif cmp_intervala[1] is None or cmp_intervalb[1] is None:
+            second = None
+        else:
+            second = True
+        return (first, second)
+    return reduce(reduce_and, args)
+
+
+def Or(*args):
+    """Defines the three valued ``Or`` behaviour for a 2-tuple of
+     three valued logic values"""
+    def reduce_or(cmp_intervala, cmp_intervalb):
+        if cmp_intervala[0] is True or cmp_intervalb[0] is True:
+            first = True
+        elif cmp_intervala[0] is None or cmp_intervalb[0] is None:
+            first = None
+        else:
+            first = False
+
+        if cmp_intervala[1] is True or cmp_intervalb[1] is True:
+            second = True
+        elif cmp_intervala[1] is None or cmp_intervalb[1] is None:
+            second = None
+        else:
+            second = False
+        return (first, second)
+    return reduce(reduce_or, args)

llmeval-env/lib/python3.10/site-packages/sympy/plotting/plot.py

@@ -0,0 +1,2637 @@
+"""Plotting module for SymPy.
+
+A plot is represented by the ``Plot`` class that contains a reference to the
+backend and a list of the data series to be plotted. The data series are
+instances of classes meant to simplify getting points and meshes from SymPy
+expressions. ``plot_backends`` is a dictionary with all the backends.
+
+This module gives only the essential. For all the fancy stuff use directly
+the backend. You can get the backend wrapper for every plot from the
+``_backend`` attribute. Moreover the data series classes have various useful
+methods like ``get_points``, ``get_meshes``, etc, that may
+be useful if you wish to use another plotting library.
+
+Especially if you need publication ready graphs and this module is not enough
+for you - just get the ``_backend`` attribute and add whatever you want
+directly to it. In the case of matplotlib (the common way to graph data in
+python) just copy ``_backend.fig`` which is the figure and ``_backend.ax``
+which is the axis and work on them as you would on any other matplotlib object.
+
+Simplicity of code takes much greater importance than performance. Do not use it
+if you care at all about performance. A new backend instance is initialized
+every time you call ``show()`` and the old one is left to the garbage collector.
+"""
+
+
+from collections.abc import Callable
+
+
+from sympy.core.basic import Basic
+from sympy.core.containers import Tuple
+from sympy.core.expr import Expr
+from sympy.core.function import arity, Function
+from sympy.core.symbol import (Dummy, Symbol)
+from sympy.core.sympify import sympify
+from sympy.external import import_module
+from sympy.printing.latex import latex
+from sympy.utilities.exceptions import sympy_deprecation_warning
+from sympy.utilities.iterables import is_sequence
+from .experimental_lambdify import (vectorized_lambdify, lambdify)
+
+# N.B.
+# When changing the minimum module version for matplotlib, please change
+# the same in the `SymPyDocTestFinder`` in `sympy/testing/runtests.py`
+
+# Backend specific imports - textplot
+from sympy.plotting.textplot import textplot
+
+# Global variable
+# Set to False when running tests / doctests so that the plots don't show.
+_show = True
+
+
+def unset_show():
+    """
+    Disable show(). For use in the tests.
+    """
+    global _show
+    _show = False
+
+def _str_or_latex(label):
+    if isinstance(label, Basic):
+        return latex(label, mode='inline')
+    return str(label)
+
+##############################################################################
+# The public interface
+##############################################################################
+
+
+class Plot:
+    """The central class of the plotting module.
+
+    Explanation
+    ===========
+
+    For interactive work the function :func:`plot()` is better suited.
+
+    This class permits the plotting of SymPy expressions using numerous
+    backends (:external:mod:`matplotlib`, textplot, the old pyglet module for SymPy, Google
+    charts api, etc).
+
+    The figure can contain an arbitrary number of plots of SymPy expressions,
+    lists of coordinates of points, etc. Plot has a private attribute _series that
+    contains all data series to be plotted (expressions for lines or surfaces,
+    lists of points, etc (all subclasses of BaseSeries)). Those data series are
+    instances of classes not imported by ``from sympy import *``.
+
+    The customization of the figure is on two levels. Global options that
+    concern the figure as a whole (e.g. title, xlabel, scale, etc) and
+    per-data series options (e.g. name) and aesthetics (e.g. color, point shape,
+    line type, etc.).
+
+    The difference between options and aesthetics is that an aesthetic can be
+    a function of the coordinates (or parameters in a parametric plot). The
+    supported values for an aesthetic are:
+
+    - None (the backend uses default values)
+    - a constant
+    - a function of one variable (the first coordinate or parameter)
+    - a function of two variables (the first and second coordinate or parameters)
+    - a function of three variables (only in nonparametric 3D plots)
+
+    Their implementation depends on the backend so they may not work in some
+    backends.
+
+    If the plot is parametric and the arity of the aesthetic function permits
+    it the aesthetic is calculated over parameters and not over coordinates.
+    If the arity does not permit calculation over parameters the calculation is
+    done over coordinates.
+
+    Only cartesian coordinates are supported for the moment, but you can use
+    the parametric plots to plot in polar, spherical and cylindrical
+    coordinates.
+
+    The arguments for the constructor Plot must be subclasses of BaseSeries.
+
+    Any global option can be specified as a keyword argument.
+
+    The global options for a figure are:
+
+    - title : str
+    - xlabel : str or Symbol
+    - ylabel : str or Symbol
+    - zlabel : str or Symbol
+    - legend : bool
+    - xscale : {'linear', 'log'}
+    - yscale : {'linear', 'log'}
+    - axis : bool
+    - axis_center : tuple of two floats or {'center', 'auto'}
+    - xlim : tuple of two floats
+    - ylim : tuple of two floats
+    - aspect_ratio : tuple of two floats or {'auto'}
+    - autoscale : bool
+    - margin : float in [0, 1]
+    - backend : {'default', 'matplotlib', 'text'} or a subclass of BaseBackend
+    - size : optional tuple of two floats, (width, height); default: None
+
+    The per data series options and aesthetics are:
+    There are none in the base series. See below for options for subclasses.
+
+    Some data series support additional aesthetics or options:
+
+    :class:`~.LineOver1DRangeSeries`, :class:`~.Parametric2DLineSeries`, and
+    :class:`~.Parametric3DLineSeries` support the following:
+
+    Aesthetics:
+
+    - line_color : string, or float, or function, optional
+        Specifies the color for the plot, which depends on the backend being
+        used.
+
+        For example, if ``MatplotlibBackend`` is being used, then
+        Matplotlib string colors are acceptable (``"red"``, ``"r"``,
+        ``"cyan"``, ``"c"``, ...).
+        Alternatively, we can use a float number, 0 < color < 1, wrapped in a
+        string (for example, ``line_color="0.5"``) to specify grayscale colors.
+        Alternatively, We can specify a function returning a single
+        float value: this will be used to apply a color-loop (for example,
+        ``line_color=lambda x: math.cos(x)``).
+
+        Note that by setting line_color, it would be applied simultaneously
+        to all the series.
+
+    Options:
+
+    - label : str
+    - steps : bool
+    - integers_only : bool
+
+    :class:`~.SurfaceOver2DRangeSeries` and :class:`~.ParametricSurfaceSeries`
+    support the following:
+
+    Aesthetics:
+
+    - surface_color : function which returns a float.
+    """
+
+    def __init__(self, *args,
+        title=None, xlabel=None, ylabel=None, zlabel=None, aspect_ratio='auto',
+        xlim=None, ylim=None, axis_center='auto', axis=True,
+        xscale='linear', yscale='linear', legend=False, autoscale=True,
+        margin=0, annotations=None, markers=None, rectangles=None,
+        fill=None, backend='default', size=None, **kwargs):
+        super().__init__()
+
+        # Options for the graph as a whole.
+        # The possible values for each option are described in the docstring of
+        # Plot. They are based purely on convention, no checking is done.
+        self.title = title
+        self.xlabel = xlabel
+        self.ylabel = ylabel
+        self.zlabel = zlabel
+        self.aspect_ratio = aspect_ratio
+        self.axis_center = axis_center
+        self.axis = axis
+        self.xscale = xscale
+        self.yscale = yscale
+        self.legend = legend
+        self.autoscale = autoscale
+        self.margin = margin
+        self.annotations = annotations
+        self.markers = markers
+        self.rectangles = rectangles
+        self.fill = fill
+
+        # Contains the data objects to be plotted. The backend should be smart
+        # enough to iterate over this list.
+        self._series = []
+        self._series.extend(args)
+
+        # The backend type. On every show() a new backend instance is created
+        # in self._backend which is tightly coupled to the Plot instance
+        # (thanks to the parent attribute of the backend).
+        if isinstance(backend, str):
+            self.backend = plot_backends[backend]
+        elif (type(backend) == type) and issubclass(backend, BaseBackend):
+            self.backend = backend
+        else:
+            raise TypeError(
+                "backend must be either a string or a subclass of BaseBackend")
+
+        is_real = \
+            lambda lim: all(getattr(i, 'is_real', True) for i in lim)
+        is_finite = \
+            lambda lim: all(getattr(i, 'is_finite', True) for i in lim)
+
+        # reduce code repetition
+        def check_and_set(t_name, t):
+            if t:
+                if not is_real(t):
+                    raise ValueError(
+                    "All numbers from {}={} must be real".format(t_name, t))
+                if not is_finite(t):
+                    raise ValueError(
+                    "All numbers from {}={} must be finite".format(t_name, t))
+                setattr(self, t_name, (float(t[0]), float(t[1])))
+
+        self.xlim = None
+        check_and_set("xlim", xlim)
+        self.ylim = None
+        check_and_set("ylim", ylim)
+        self.size = None
+        check_and_set("size", size)
+
+
+    def show(self):
+        # TODO move this to the backend (also for save)
+        if hasattr(self, '_backend'):
+            self._backend.close()
+        self._backend = self.backend(self)
+        self._backend.show()
+
+    def save(self, path):
+        if hasattr(self, '_backend'):
+            self._backend.close()
+        self._backend = self.backend(self)
+        self._backend.save(path)
+
+    def __str__(self):
+        series_strs = [('[%d]: ' % i) + str(s)
+                       for i, s in enumerate(self._series)]
+        return 'Plot object containing:\n' + '\n'.join(series_strs)
+
+    def __getitem__(self, index):
+        return self._series[index]
+
+    def __setitem__(self, index, *args):
+        if len(args) == 1 and isinstance(args[0], BaseSeries):
+            self._series[index] = args
+
+    def __delitem__(self, index):
+        del self._series[index]
+
+    def append(self, arg):
+        """Adds an element from a plot's series to an existing plot.
+
+        Examples
+        ========
+
+        Consider two ``Plot`` objects, ``p1`` and ``p2``. To add the
+        second plot's first series object to the first, use the
+        ``append`` method, like so:
+
+        .. plot::
+           :format: doctest
+           :include-source: True
+
+           >>> from sympy import symbols
+           >>> from sympy.plotting import plot
+           >>> x = symbols('x')
+           >>> p1 = plot(x*x, show=False)
+           >>> p2 = plot(x, show=False)
+           >>> p1.append(p2[0])
+           >>> p1
+           Plot object containing:
+           [0]: cartesian line: x**2 for x over (-10.0, 10.0)
+           [1]: cartesian line: x for x over (-10.0, 10.0)
+           >>> p1.show()
+
+        See Also
+        ========
+
+        extend
+
+        """
+        if isinstance(arg, BaseSeries):
+            self._series.append(arg)
+        else:
+            raise TypeError('Must specify element of plot to append.')
+
+    def extend(self, arg):
+        """Adds all series from another plot.
+
+        Examples
+        ========
+
+        Consider two ``Plot`` objects, ``p1`` and ``p2``. To add the
+        second plot to the first, use the ``extend`` method, like so:
+
+        .. plot::
+           :format: doctest
+           :include-source: True
+
+           >>> from sympy import symbols
+           >>> from sympy.plotting import plot
+           >>> x = symbols('x')
+           >>> p1 = plot(x**2, show=False)
+           >>> p2 = plot(x, -x, show=False)
+           >>> p1.extend(p2)
+           >>> p1
+           Plot object containing:
+           [0]: cartesian line: x**2 for x over (-10.0, 10.0)
+           [1]: cartesian line: x for x over (-10.0, 10.0)
+           [2]: cartesian line: -x for x over (-10.0, 10.0)
+           >>> p1.show()
+
+        """
+        if isinstance(arg, Plot):
+            self._series.extend(arg._series)
+        elif is_sequence(arg):
+            self._series.extend(arg)
+        else:
+            raise TypeError('Expecting Plot or sequence of BaseSeries')
+
+
+class PlotGrid:
+    """This class helps to plot subplots from already created SymPy plots
+    in a single figure.
+
+    Examples
+    ========
+
+    .. plot::
+       :context: close-figs
+       :format: doctest
+       :include-source: True
+
+        >>> from sympy import symbols
+        >>> from sympy.plotting import plot, plot3d, PlotGrid
+        >>> x, y = symbols('x, y')
+        >>> p1 = plot(x, x**2, x**3, (x, -5, 5))
+        >>> p2 = plot((x**2, (x, -6, 6)), (x, (x, -5, 5)))
+        >>> p3 = plot(x**3, (x, -5, 5))
+        >>> p4 = plot3d(x*y, (x, -5, 5), (y, -5, 5))
+
+    Plotting vertically in a single line:
+
+    .. plot::
+       :context: close-figs
+       :format: doctest
+       :include-source: True
+
+        >>> PlotGrid(2, 1, p1, p2)
+        PlotGrid object containing:
+        Plot[0]:Plot object containing:
+        [0]: cartesian line: x for x over (-5.0, 5.0)
+        [1]: cartesian line: x**2 for x over (-5.0, 5.0)
+        [2]: cartesian line: x**3 for x over (-5.0, 5.0)
+        Plot[1]:Plot object containing:
+        [0]: cartesian line: x**2 for x over (-6.0, 6.0)
+        [1]: cartesian line: x for x over (-5.0, 5.0)
+
+    Plotting horizontally in a single line:
+
+    .. plot::
+       :context: close-figs
+       :format: doctest
+       :include-source: True
+
+        >>> PlotGrid(1, 3, p2, p3, p4)
+        PlotGrid object containing:
+        Plot[0]:Plot object containing:
+        [0]: cartesian line: x**2 for x over (-6.0, 6.0)
+        [1]: cartesian line: x for x over (-5.0, 5.0)
+        Plot[1]:Plot object containing:
+        [0]: cartesian line: x**3 for x over (-5.0, 5.0)
+        Plot[2]:Plot object containing:
+        [0]: cartesian surface: x*y for x over (-5.0, 5.0) and y over (-5.0, 5.0)
+
+    Plotting in a grid form:
+
+    .. plot::
+       :context: close-figs
+       :format: doctest
+       :include-source: True
+
+        >>> PlotGrid(2, 2, p1, p2, p3, p4)
+        PlotGrid object containing:
+        Plot[0]:Plot object containing:
+        [0]: cartesian line: x for x over (-5.0, 5.0)
+        [1]: cartesian line: x**2 for x over (-5.0, 5.0)
+        [2]: cartesian line: x**3 for x over (-5.0, 5.0)
+        Plot[1]:Plot object containing:
+        [0]: cartesian line: x**2 for x over (-6.0, 6.0)
+        [1]: cartesian line: x for x over (-5.0, 5.0)
+        Plot[2]:Plot object containing:
+        [0]: cartesian line: x**3 for x over (-5.0, 5.0)
+        Plot[3]:Plot object containing:
+        [0]: cartesian surface: x*y for x over (-5.0, 5.0) and y over (-5.0, 5.0)
+
+    """
+    def __init__(self, nrows, ncolumns, *args, show=True, size=None, **kwargs):
+        """
+        Parameters
+        ==========
+
+        nrows :
+            The number of rows that should be in the grid of the
+            required subplot.
+        ncolumns :
+            The number of columns that should be in the grid
+            of the required subplot.
+
+        nrows and ncolumns together define the required grid.
+
+        Arguments
+        =========
+
+        A list of predefined plot objects entered in a row-wise sequence
+        i.e. plot objects which are to be in the top row of the required
+        grid are written first, then the second row objects and so on
+
+        Keyword arguments
+        =================
+
+        show : Boolean
+            The default value is set to ``True``. Set show to ``False`` and
+            the function will not display the subplot. The returned instance
+            of the ``PlotGrid`` class can then be used to save or display the
+            plot by calling the ``save()`` and ``show()`` methods
+            respectively.
+        size : (float, float), optional
+            A tuple in the form (width, height) in inches to specify the size of
+            the overall figure. The default value is set to ``None``, meaning
+            the size will be set by the default backend.
+        """
+        self.nrows = nrows
+        self.ncolumns = ncolumns
+        self._series = []
+        self.args = args
+        for arg in args:
+            self._series.append(arg._series)
+        self.backend = DefaultBackend
+        self.size = size
+        if show:
+            self.show()
+
+    def show(self):
+        if hasattr(self, '_backend'):
+            self._backend.close()
+        self._backend = self.backend(self)
+        self._backend.show()
+
+    def save(self, path):
+        if hasattr(self, '_backend'):
+            self._backend.close()
+        self._backend = self.backend(self)
+        self._backend.save(path)
+
+    def __str__(self):
+        plot_strs = [('Plot[%d]:' % i) + str(plot)
+                      for i, plot in enumerate(self.args)]
+
+        return 'PlotGrid object containing:\n' + '\n'.join(plot_strs)
+
+
+##############################################################################
+# Data Series
+##############################################################################
+#TODO more general way to calculate aesthetics (see get_color_array)
+
+### The base class for all series
+class BaseSeries:
+    """Base class for the data objects containing stuff to be plotted.
+
+    Explanation
+    ===========
+
+    The backend should check if it supports the data series that is given.
+    (e.g. TextBackend supports only LineOver1DRangeSeries).
+    It is the backend responsibility to know how to use the class of
+    data series that is given.
+
+    Some data series classes are grouped (using a class attribute like is_2Dline)
+    according to the api they present (based only on convention). The backend is
+    not obliged to use that api (e.g. LineOver1DRangeSeries belongs to the
+    is_2Dline group and presents the get_points method, but the
+    TextBackend does not use the get_points method).
+    """
+
+    # Some flags follow. The rationale for using flags instead of checking base
+    # classes is that setting multiple flags is simpler than multiple
+    # inheritance.
+
+    is_2Dline = False
+    # Some of the backends expect:
+    #  - get_points returning 1D np.arrays list_x, list_y
+    #  - get_color_array returning 1D np.array (done in Line2DBaseSeries)
+    # with the colors calculated at the points from get_points
+
+    is_3Dline = False
+    # Some of the backends expect:
+    #  - get_points returning 1D np.arrays list_x, list_y, list_y
+    #  - get_color_array returning 1D np.array (done in Line2DBaseSeries)
+    # with the colors calculated at the points from get_points
+
+    is_3Dsurface = False
+    # Some of the backends expect:
+    #   - get_meshes returning mesh_x, mesh_y, mesh_z (2D np.arrays)
+    #   - get_points an alias for get_meshes
+
+    is_contour = False
+    # Some of the backends expect:
+    #   - get_meshes returning mesh_x, mesh_y, mesh_z (2D np.arrays)
+    #   - get_points an alias for get_meshes
+
+    is_implicit = False
+    # Some of the backends expect:
+    #   - get_meshes returning mesh_x (1D array), mesh_y(1D array,
+    #     mesh_z (2D np.arrays)
+    #   - get_points an alias for get_meshes
+    # Different from is_contour as the colormap in backend will be
+    # different
+
+    is_parametric = False
+    # The calculation of aesthetics expects:
+    #   - get_parameter_points returning one or two np.arrays (1D or 2D)
+    # used for calculation aesthetics
+
+    def __init__(self):
+        super().__init__()
+
+    @property
+    def is_3D(self):
+        flags3D = [
+            self.is_3Dline,
+            self.is_3Dsurface
+        ]
+        return any(flags3D)
+
+    @property
+    def is_line(self):
+        flagslines = [
+            self.is_2Dline,
+            self.is_3Dline
+        ]
+        return any(flagslines)
+
+
+### 2D lines
+class Line2DBaseSeries(BaseSeries):
+    """A base class for 2D lines.
+
+    - adding the label, steps and only_integers options
+    - making is_2Dline true
+    - defining get_segments and get_color_array
+    """
+
+    is_2Dline = True
+
+    _dim = 2
+
+    def __init__(self):
+        super().__init__()
+        self.label = None
+        self.steps = False
+        self.only_integers = False
+        self.line_color = None
+
+    def get_data(self):
+        """ Return lists of coordinates for plotting the line.
+
+        Returns
+        =======
+            x : list
+                List of x-coordinates
+
+            y : list
+                List of y-coordinates
+
+            z : list
+                List of z-coordinates in case of Parametric3DLineSeries
+        """
+        np = import_module('numpy')
+        points = self.get_points()
+        if self.steps is True:
+            if len(points) == 2:
+                x = np.array((points[0], points[0])).T.flatten()[1:]
+                y = np.array((points[1], points[1])).T.flatten()[:-1]
+                points = (x, y)
+            else:
+                x = np.repeat(points[0], 3)[2:]
+                y = np.repeat(points[1], 3)[:-2]
+                z = np.repeat(points[2], 3)[1:-1]
+                points = (x, y, z)
+        return points
+
+    def get_segments(self):
+        sympy_deprecation_warning(
+            """
+            The Line2DBaseSeries.get_segments() method is deprecated.
+
+            Instead, use the MatplotlibBackend.get_segments() method, or use
+            The get_points() or get_data() methods.
+            """,
+            deprecated_since_version="1.9",
+            active_deprecations_target="deprecated-get-segments")
+
+        np = import_module('numpy')
+        points = type(self).get_data(self)
+        points = np.ma.array(points).T.reshape(-1, 1, self._dim)
+        return np.ma.concatenate([points[:-1], points[1:]], axis=1)
+
+    def get_color_array(self):
+        np = import_module('numpy')
+        c = self.line_color
+        if hasattr(c, '__call__'):
+            f = np.vectorize(c)
+            nargs = arity(c)
+            if nargs == 1 and self.is_parametric:
+                x = self.get_parameter_points()
+                return f(centers_of_segments(x))
+            else:
+                variables = list(map(centers_of_segments, self.get_points()))
+                if nargs == 1:
+                    return f(variables[0])
+                elif nargs == 2:
+                    return f(*variables[:2])
+                else:  # only if the line is 3D (otherwise raises an error)
+                    return f(*variables)
+        else:
+            return c*np.ones(self.nb_of_points)
+
+
+class List2DSeries(Line2DBaseSeries):
+    """Representation for a line consisting of list of points."""
+
+    def __init__(self, list_x, list_y):
+        np = import_module('numpy')
+        super().__init__()
+        self.list_x = np.array(list_x)
+        self.list_y = np.array(list_y)
+        self.label = 'list'
+
+    def __str__(self):
+        return 'list plot'
+
+    def get_points(self):
+        return (self.list_x, self.list_y)
+
+
+class LineOver1DRangeSeries(Line2DBaseSeries):
+    """Representation for a line consisting of a SymPy expression over a range."""
+
+    def __init__(self, expr, var_start_end, **kwargs):
+        super().__init__()
+        self.expr = sympify(expr)
+        self.label = kwargs.get('label', None) or self.expr
+        self.var = sympify(var_start_end[0])
+        self.start = float(var_start_end[1])
+        self.end = float(var_start_end[2])
+        self.nb_of_points = kwargs.get('nb_of_points', 300)
+        self.adaptive = kwargs.get('adaptive', True)
+        self.depth = kwargs.get('depth', 12)
+        self.line_color = kwargs.get('line_color', None)
+        self.xscale = kwargs.get('xscale', 'linear')
+
+    def __str__(self):
+        return 'cartesian line: %s for %s over %s' % (
+            str(self.expr), str(self.var), str((self.start, self.end)))
+
+    def get_points(self):
+        """ Return lists of coordinates for plotting. Depending on the
+        ``adaptive`` option, this function will either use an adaptive algorithm
+        or it will uniformly sample the expression over the provided range.
+
+        Returns
+        =======
+            x : list
+                List of x-coordinates
+
+            y : list
+                List of y-coordinates
+
+
+        Explanation
+        ===========
+
+        The adaptive sampling is done by recursively checking if three
+        points are almost collinear. If they are not collinear, then more
+        points are added between those points.
+
+        References
+        ==========
+
+        .. [1] Adaptive polygonal approximation of parametric curves,
+               Luiz Henrique de Figueiredo.
+
+        """
+        if self.only_integers or not self.adaptive:
+            return self._uniform_sampling()
+        else:
+            f = lambdify([self.var], self.expr)
+            x_coords = []
+            y_coords = []
+            np = import_module('numpy')
+            def sample(p, q, depth):
+                """ Samples recursively if three points are almost collinear.
+                For depth < 6, points are added irrespective of whether they
+                satisfy the collinearity condition or not. The maximum depth
+                allowed is 12.
+                """
+                # Randomly sample to avoid aliasing.
+                random = 0.45 + np.random.rand() * 0.1
+                if self.xscale == 'log':
+                    xnew = 10**(np.log10(p[0]) + random * (np.log10(q[0]) -
+                                                           np.log10(p[0])))
+                else:
+                    xnew = p[0] + random * (q[0] - p[0])
+                ynew = f(xnew)
+                new_point = np.array([xnew, ynew])
+
+                # Maximum depth
+                if depth > self.depth:
+                    x_coords.append(q[0])
+                    y_coords.append(q[1])
+
+                # Sample irrespective of whether the line is flat till the
+                # depth of 6. We are not using linspace to avoid aliasing.
+                elif depth < 6:
+                    sample(p, new_point, depth + 1)
+                    sample(new_point, q, depth + 1)
+
+                # Sample ten points if complex values are encountered
+                # at both ends. If there is a real value in between, then
+                # sample those points further.
+                elif p[1] is None and q[1] is None:
+                    if self.xscale == 'log':
+                        xarray = np.logspace(p[0], q[0], 10)
+                    else:
+                        xarray = np.linspace(p[0], q[0], 10)
+                    yarray = list(map(f, xarray))
+                    if not all(y is None for y in yarray):
+                        for i in range(len(yarray) - 1):
+                            if not (yarray[i] is None and yarray[i + 1] is None):
+                                sample([xarray[i], yarray[i]],
+                                    [xarray[i + 1], yarray[i + 1]], depth + 1)
+
+                # Sample further if one of the end points in None (i.e. a
+                # complex value) or the three points are not almost collinear.
+                elif (p[1] is None or q[1] is None or new_point[1] is None
+                        or not flat(p, new_point, q)):
+                    sample(p, new_point, depth + 1)
+                    sample(new_point, q, depth + 1)
+                else:
+                    x_coords.append(q[0])
+                    y_coords.append(q[1])
+
+            f_start = f(self.start)
+            f_end = f(self.end)
+            x_coords.append(self.start)
+            y_coords.append(f_start)
+            sample(np.array([self.start, f_start]),
+                   np.array([self.end, f_end]), 0)
+
+        return (x_coords, y_coords)
+
+    def _uniform_sampling(self):
+        np = import_module('numpy')
+        if self.only_integers is True:
+            if self.xscale == 'log':
+                list_x = np.logspace(int(self.start), int(self.end),
+                        num=int(self.end) - int(self.start) + 1)
+            else:
+                list_x = np.linspace(int(self.start), int(self.end),
+                    num=int(self.end) - int(self.start) + 1)
+        else:
+            if self.xscale == 'log':
+                list_x = np.logspace(self.start, self.end, num=self.nb_of_points)
+            else:
+                list_x = np.linspace(self.start, self.end, num=self.nb_of_points)
+        f = vectorized_lambdify([self.var], self.expr)
+        list_y = f(list_x)
+        return (list_x, list_y)
+
+
+class Parametric2DLineSeries(Line2DBaseSeries):
+    """Representation for a line consisting of two parametric SymPy expressions
+    over a range."""
+
+    is_parametric = True
+
+    def __init__(self, expr_x, expr_y, var_start_end, **kwargs):
+        super().__init__()
+        self.expr_x = sympify(expr_x)
+        self.expr_y = sympify(expr_y)
+        self.label = kwargs.get('label', None) or \
+                            Tuple(self.expr_x, self.expr_y)
+        self.var = sympify(var_start_end[0])
+        self.start = float(var_start_end[1])
+        self.end = float(var_start_end[2])
+        self.nb_of_points = kwargs.get('nb_of_points', 300)
+        self.adaptive = kwargs.get('adaptive', True)
+        self.depth = kwargs.get('depth', 12)
+        self.line_color = kwargs.get('line_color', None)
+
+    def __str__(self):
+        return 'parametric cartesian line: (%s, %s) for %s over %s' % (
+            str(self.expr_x), str(self.expr_y), str(self.var),
+            str((self.start, self.end)))
+
+    def get_parameter_points(self):
+        np = import_module('numpy')
+        return np.linspace(self.start, self.end, num=self.nb_of_points)
+
+    def _uniform_sampling(self):
+        param = self.get_parameter_points()
+        fx = vectorized_lambdify([self.var], self.expr_x)
+        fy = vectorized_lambdify([self.var], self.expr_y)
+        list_x = fx(param)
+        list_y = fy(param)
+        return (list_x, list_y)
+
+    def get_points(self):
+        """ Return lists of coordinates for plotting. Depending on the
+        ``adaptive`` option, this function will either use an adaptive algorithm
+        or it will uniformly sample the expression over the provided range.
+
+        Returns
+        =======
+            x : list
+                List of x-coordinates
+
+            y : list
+                List of y-coordinates
+
+
+        Explanation
+        ===========
+
+        The adaptive sampling is done by recursively checking if three
+        points are almost collinear. If they are not collinear, then more
+        points are added between those points.
+
+        References
+        ==========
+
+        .. [1] Adaptive polygonal approximation of parametric curves,
+            Luiz Henrique de Figueiredo.
+
+        """
+        if not self.adaptive:
+            return self._uniform_sampling()
+
+        f_x = lambdify([self.var], self.expr_x)
+        f_y = lambdify([self.var], self.expr_y)
+        x_coords = []
+        y_coords = []
+
+        def sample(param_p, param_q, p, q, depth):
+            """ Samples recursively if three points are almost collinear.
+            For depth < 6, points are added irrespective of whether they
+            satisfy the collinearity condition or not. The maximum depth
+            allowed is 12.
+            """
+            # Randomly sample to avoid aliasing.
+            np = import_module('numpy')
+            random = 0.45 + np.random.rand() * 0.1
+            param_new = param_p + random * (param_q - param_p)
+            xnew = f_x(param_new)
+            ynew = f_y(param_new)
+            new_point = np.array([xnew, ynew])
+
+            # Maximum depth
+            if depth > self.depth:
+                x_coords.append(q[0])
+                y_coords.append(q[1])
+
+            # Sample irrespective of whether the line is flat till the
+            # depth of 6. We are not using linspace to avoid aliasing.
+            elif depth < 6:
+                sample(param_p, param_new, p, new_point, depth + 1)
+                sample(param_new, param_q, new_point, q, depth + 1)
+
+            # Sample ten points if complex values are encountered
+            # at both ends. If there is a real value in between, then
+            # sample those points further.
+            elif ((p[0] is None and q[1] is None) or
+                    (p[1] is None and q[1] is None)):
+                param_array = np.linspace(param_p, param_q, 10)
+                x_array = list(map(f_x, param_array))
+                y_array = list(map(f_y, param_array))
+                if not all(x is None and y is None
+                           for x, y in zip(x_array, y_array)):
+                    for i in range(len(y_array) - 1):
+                        if ((x_array[i] is not None and y_array[i] is not None) or
+                                (x_array[i + 1] is not None and y_array[i + 1] is not None)):
+                            point_a = [x_array[i], y_array[i]]
+                            point_b = [x_array[i + 1], y_array[i + 1]]
+                            sample(param_array[i], param_array[i], point_a,
+                                   point_b, depth + 1)
+
+            # Sample further if one of the end points in None (i.e. a complex
+            # value) or the three points are not almost collinear.
+            elif (p[0] is None or p[1] is None
+                    or q[1] is None or q[0] is None
+                    or not flat(p, new_point, q)):
+                sample(param_p, param_new, p, new_point, depth + 1)
+                sample(param_new, param_q, new_point, q, depth + 1)
+            else:
+                x_coords.append(q[0])
+                y_coords.append(q[1])
+
+        f_start_x = f_x(self.start)
+        f_start_y = f_y(self.start)
+        start = [f_start_x, f_start_y]
+        f_end_x = f_x(self.end)
+        f_end_y = f_y(self.end)
+        end = [f_end_x, f_end_y]
+        x_coords.append(f_start_x)
+        y_coords.append(f_start_y)
+        sample(self.start, self.end, start, end, 0)
+
+        return x_coords, y_coords
+
+
+### 3D lines
+class Line3DBaseSeries(Line2DBaseSeries):
+    """A base class for 3D lines.
+
+    Most of the stuff is derived from Line2DBaseSeries."""
+
+    is_2Dline = False
+    is_3Dline = True
+    _dim = 3
+
+    def __init__(self):
+        super().__init__()
+
+
+class Parametric3DLineSeries(Line3DBaseSeries):
+    """Representation for a 3D line consisting of three parametric SymPy
+    expressions and a range."""
+
+    is_parametric = True
+
+    def __init__(self, expr_x, expr_y, expr_z, var_start_end, **kwargs):
+        super().__init__()
+        self.expr_x = sympify(expr_x)
+        self.expr_y = sympify(expr_y)
+        self.expr_z = sympify(expr_z)
+        self.label = kwargs.get('label', None) or \
+                        Tuple(self.expr_x, self.expr_y)
+        self.var = sympify(var_start_end[0])
+        self.start = float(var_start_end[1])
+        self.end = float(var_start_end[2])
+        self.nb_of_points = kwargs.get('nb_of_points', 300)
+        self.line_color = kwargs.get('line_color', None)
+        self._xlim = None
+        self._ylim = None
+        self._zlim = None
+
+    def __str__(self):
+        return '3D parametric cartesian line: (%s, %s, %s) for %s over %s' % (
+            str(self.expr_x), str(self.expr_y), str(self.expr_z),
+            str(self.var), str((self.start, self.end)))
+
+    def get_parameter_points(self):
+        np = import_module('numpy')
+        return np.linspace(self.start, self.end, num=self.nb_of_points)
+
+    def get_points(self):
+        np = import_module('numpy')
+        param = self.get_parameter_points()
+        fx = vectorized_lambdify([self.var], self.expr_x)
+        fy = vectorized_lambdify([self.var], self.expr_y)
+        fz = vectorized_lambdify([self.var], self.expr_z)
+
+        list_x = fx(param)
+        list_y = fy(param)
+        list_z = fz(param)
+
+        list_x = np.array(list_x, dtype=np.float64)
+        list_y = np.array(list_y, dtype=np.float64)
+        list_z = np.array(list_z, dtype=np.float64)
+
+        list_x = np.ma.masked_invalid(list_x)
+        list_y = np.ma.masked_invalid(list_y)
+        list_z = np.ma.masked_invalid(list_z)
+
+        self._xlim = (np.amin(list_x), np.amax(list_x))
+        self._ylim = (np.amin(list_y), np.amax(list_y))
+        self._zlim = (np.amin(list_z), np.amax(list_z))
+        return list_x, list_y, list_z
+
+
+### Surfaces
+class SurfaceBaseSeries(BaseSeries):
+    """A base class for 3D surfaces."""
+
+    is_3Dsurface = True
+
+    def __init__(self):
+        super().__init__()
+        self.surface_color = None
+
+    def get_color_array(self):
+        np = import_module('numpy')
+        c = self.surface_color
+        if isinstance(c, Callable):
+            f = np.vectorize(c)
+            nargs = arity(c)
+            if self.is_parametric:
+                variables = list(map(centers_of_faces, self.get_parameter_meshes()))
+                if nargs == 1:
+                    return f(variables[0])
+                elif nargs == 2:
+                    return f(*variables)
+            variables = list(map(centers_of_faces, self.get_meshes()))
+            if nargs == 1:
+                return f(variables[0])
+            elif nargs == 2:
+                return f(*variables[:2])
+            else:
+                return f(*variables)
+        else:
+            if isinstance(self, SurfaceOver2DRangeSeries):
+                return c*np.ones(min(self.nb_of_points_x, self.nb_of_points_y))
+            else:
+                return c*np.ones(min(self.nb_of_points_u, self.nb_of_points_v))
+
+
+class SurfaceOver2DRangeSeries(SurfaceBaseSeries):
+    """Representation for a 3D surface consisting of a SymPy expression and 2D
+    range."""
+    def __init__(self, expr, var_start_end_x, var_start_end_y, **kwargs):
+        super().__init__()
+        self.expr = sympify(expr)
+        self.var_x = sympify(var_start_end_x[0])
+        self.start_x = float(var_start_end_x[1])
+        self.end_x = float(var_start_end_x[2])
+        self.var_y = sympify(var_start_end_y[0])
+        self.start_y = float(var_start_end_y[1])
+        self.end_y = float(var_start_end_y[2])
+        self.nb_of_points_x = kwargs.get('nb_of_points_x', 50)
+        self.nb_of_points_y = kwargs.get('nb_of_points_y', 50)
+        self.surface_color = kwargs.get('surface_color', None)
+
+        self._xlim = (self.start_x, self.end_x)
+        self._ylim = (self.start_y, self.end_y)
+
+    def __str__(self):
+        return ('cartesian surface: %s for'
+                ' %s over %s and %s over %s') % (
+                    str(self.expr),
+                    str(self.var_x),
+                    str((self.start_x, self.end_x)),
+                    str(self.var_y),
+                    str((self.start_y, self.end_y)))
+
+    def get_meshes(self):
+        np = import_module('numpy')
+        mesh_x, mesh_y = np.meshgrid(np.linspace(self.start_x, self.end_x,
+                                                 num=self.nb_of_points_x),
+                                     np.linspace(self.start_y, self.end_y,
+                                                 num=self.nb_of_points_y))
+        f = vectorized_lambdify((self.var_x, self.var_y), self.expr)
+        mesh_z = f(mesh_x, mesh_y)
+        mesh_z = np.array(mesh_z, dtype=np.float64)
+        mesh_z = np.ma.masked_invalid(mesh_z)
+        self._zlim = (np.amin(mesh_z), np.amax(mesh_z))
+        return mesh_x, mesh_y, mesh_z
+
+
+class ParametricSurfaceSeries(SurfaceBaseSeries):
+    """Representation for a 3D surface consisting of three parametric SymPy
+    expressions and a range."""
+
+    is_parametric = True
+
+    def __init__(
+        self, expr_x, expr_y, expr_z, var_start_end_u, var_start_end_v,
+            **kwargs):
+        super().__init__()
+        self.expr_x = sympify(expr_x)
+        self.expr_y = sympify(expr_y)
+        self.expr_z = sympify(expr_z)
+        self.var_u = sympify(var_start_end_u[0])
+        self.start_u = float(var_start_end_u[1])
+        self.end_u = float(var_start_end_u[2])
+        self.var_v = sympify(var_start_end_v[0])
+        self.start_v = float(var_start_end_v[1])
+        self.end_v = float(var_start_end_v[2])
+        self.nb_of_points_u = kwargs.get('nb_of_points_u', 50)
+        self.nb_of_points_v = kwargs.get('nb_of_points_v', 50)
+        self.surface_color = kwargs.get('surface_color', None)
+
+    def __str__(self):
+        return ('parametric cartesian surface: (%s, %s, %s) for'
+                ' %s over %s and %s over %s') % (
+                    str(self.expr_x),
+                    str(self.expr_y),
+                    str(self.expr_z),
+                    str(self.var_u),
+                    str((self.start_u, self.end_u)),
+                    str(self.var_v),
+                    str((self.start_v, self.end_v)))
+
+    def get_parameter_meshes(self):
+        np = import_module('numpy')
+        return np.meshgrid(np.linspace(self.start_u, self.end_u,
+                                       num=self.nb_of_points_u),
+                           np.linspace(self.start_v, self.end_v,
+                                       num=self.nb_of_points_v))
+
+    def get_meshes(self):
+        np = import_module('numpy')
+
+        mesh_u, mesh_v = self.get_parameter_meshes()
+        fx = vectorized_lambdify((self.var_u, self.var_v), self.expr_x)
+        fy = vectorized_lambdify((self.var_u, self.var_v), self.expr_y)
+        fz = vectorized_lambdify((self.var_u, self.var_v), self.expr_z)
+
+        mesh_x = fx(mesh_u, mesh_v)
+        mesh_y = fy(mesh_u, mesh_v)
+        mesh_z = fz(mesh_u, mesh_v)
+
+        mesh_x = np.array(mesh_x, dtype=np.float64)
+        mesh_y = np.array(mesh_y, dtype=np.float64)
+        mesh_z = np.array(mesh_z, dtype=np.float64)
+
+        mesh_x = np.ma.masked_invalid(mesh_x)
+        mesh_y = np.ma.masked_invalid(mesh_y)
+        mesh_z = np.ma.masked_invalid(mesh_z)
+
+        self._xlim = (np.amin(mesh_x), np.amax(mesh_x))
+        self._ylim = (np.amin(mesh_y), np.amax(mesh_y))
+        self._zlim = (np.amin(mesh_z), np.amax(mesh_z))
+
+        return mesh_x, mesh_y, mesh_z
+
+
+### Contours
+class ContourSeries(BaseSeries):
+    """Representation for a contour plot."""
+    # The code is mostly repetition of SurfaceOver2DRange.
+    # Presently used in contour_plot function
+
+    is_contour = True
+
+    def __init__(self, expr, var_start_end_x, var_start_end_y):
+        super().__init__()
+        self.nb_of_points_x = 50
+        self.nb_of_points_y = 50
+        self.expr = sympify(expr)
+        self.var_x = sympify(var_start_end_x[0])
+        self.start_x = float(var_start_end_x[1])
+        self.end_x = float(var_start_end_x[2])
+        self.var_y = sympify(var_start_end_y[0])
+        self.start_y = float(var_start_end_y[1])
+        self.end_y = float(var_start_end_y[2])
+
+        self.get_points = self.get_meshes
+
+        self._xlim = (self.start_x, self.end_x)
+        self._ylim = (self.start_y, self.end_y)
+
+    def __str__(self):
+        return ('contour: %s for '
+                '%s over %s and %s over %s') % (
+                    str(self.expr),
+                    str(self.var_x),
+                    str((self.start_x, self.end_x)),
+                    str(self.var_y),
+                    str((self.start_y, self.end_y)))
+
+    def get_meshes(self):
+        np = import_module('numpy')
+        mesh_x, mesh_y = np.meshgrid(np.linspace(self.start_x, self.end_x,
+                                                 num=self.nb_of_points_x),
+                                     np.linspace(self.start_y, self.end_y,
+                                                 num=self.nb_of_points_y))
+        f = vectorized_lambdify((self.var_x, self.var_y), self.expr)
+        return (mesh_x, mesh_y, f(mesh_x, mesh_y))
+
+
+##############################################################################
+# Backends
+##############################################################################
+
+class BaseBackend:
+    """Base class for all backends. A backend represents the plotting library,
+    which implements the necessary functionalities in order to use SymPy
+    plotting functions.
+
+    How the plotting module works:
+
+    1. Whenever a plotting function is called, the provided expressions are
+        processed and a list of instances of the :class:`BaseSeries` class is
+        created, containing the necessary information to plot the expressions
+        (e.g. the expression, ranges, series name, ...). Eventually, these
+        objects will generate the numerical data to be plotted.
+    2. A :class:`~.Plot` object is instantiated, which stores the list of
+        series and the main attributes of the plot (e.g. axis labels, title, ...).
+    3. When the ``show`` command is executed, a new backend is instantiated,
+        which loops through each series object to generate and plot the
+        numerical data. The backend is also going to set the axis labels, title,
+        ..., according to the values stored in the Plot instance.
+
+    The backend should check if it supports the data series that it is given
+    (e.g. :class:`TextBackend` supports only :class:`LineOver1DRangeSeries`).
+
+    It is the backend responsibility to know how to use the class of data series
+    that it's given. Note that the current implementation of the ``*Series``
+    classes is "matplotlib-centric": the numerical data returned by the
+    ``get_points`` and ``get_meshes`` methods is meant to be used directly by
+    Matplotlib. Therefore, the new backend will have to pre-process the
+    numerical data to make it compatible with the chosen plotting library.
+    Keep in mind that future SymPy versions may improve the ``*Series`` classes
+    in order to return numerical data "non-matplotlib-centric", hence if you code
+    a new backend you have the responsibility to check if its working on each
+    SymPy release.
+
+    Please explore the :class:`MatplotlibBackend` source code to understand how a
+    backend should be coded.
+
+    Methods
+    =======
+
+    In order to be used by SymPy plotting functions, a backend must implement
+    the following methods:
+
+    * show(self): used to loop over the data series, generate the numerical
+        data, plot it and set the axis labels, title, ...
+    * save(self, path): used to save the current plot to the specified file
+        path.
+    * close(self): used to close the current plot backend (note: some plotting
+        library does not support this functionality. In that case, just raise a
+        warning).
+
+    See also
+    ========
+
+    MatplotlibBackend
+    """
+    def __init__(self, parent):
+        super().__init__()
+        self.parent = parent
+
+    def show(self):
+        raise NotImplementedError
+
+    def save(self, path):
+        raise NotImplementedError
+
+    def close(self):
+        raise NotImplementedError
+
+
+# Don't have to check for the success of importing matplotlib in each case;
+# we will only be using this backend if we can successfully import matploblib
+class MatplotlibBackend(BaseBackend):
+    """ This class implements the functionalities to use Matplotlib with SymPy
+    plotting functions.
+    """
+    def __init__(self, parent):
+        super().__init__(parent)
+        self.matplotlib = import_module('matplotlib',
+            import_kwargs={'fromlist': ['pyplot', 'cm', 'collections']},
+            min_module_version='1.1.0', catch=(RuntimeError,))
+        self.plt = self.matplotlib.pyplot
+        self.cm = self.matplotlib.cm
+        self.LineCollection = self.matplotlib.collections.LineCollection
+        aspect = getattr(self.parent, 'aspect_ratio', 'auto')
+        if aspect != 'auto':
+            aspect = float(aspect[1]) / aspect[0]
+
+        if isinstance(self.parent, Plot):
+            nrows, ncolumns = 1, 1
+            series_list = [self.parent._series]
+        elif isinstance(self.parent, PlotGrid):
+            nrows, ncolumns = self.parent.nrows, self.parent.ncolumns
+            series_list = self.parent._series
+
+        self.ax = []
+        self.fig = self.plt.figure(figsize=parent.size)
+
+        for i, series in enumerate(series_list):
+            are_3D = [s.is_3D for s in series]
+
+            if any(are_3D) and not all(are_3D):
+                raise ValueError('The matplotlib backend cannot mix 2D and 3D.')
+            elif all(are_3D):
+                # mpl_toolkits.mplot3d is necessary for
+                # projection='3d'
+                mpl_toolkits = import_module('mpl_toolkits', # noqa
+                                     import_kwargs={'fromlist': ['mplot3d']})
+                self.ax.append(self.fig.add_subplot(nrows, ncolumns, i + 1, projection='3d', aspect=aspect))
+
+            elif not any(are_3D):
+                self.ax.append(self.fig.add_subplot(nrows, ncolumns, i + 1, aspect=aspect))
+                self.ax[i].spines['left'].set_position('zero')
+                self.ax[i].spines['right'].set_color('none')
+                self.ax[i].spines['bottom'].set_position('zero')
+                self.ax[i].spines['top'].set_color('none')
+                self.ax[i].xaxis.set_ticks_position('bottom')
+                self.ax[i].yaxis.set_ticks_position('left')
+
+    @staticmethod
+    def get_segments(x, y, z=None):
+        """ Convert two list of coordinates to a list of segments to be used
+        with Matplotlib's :external:class:`~matplotlib.collections.LineCollection`.
+
+        Parameters
+        ==========
+            x : list
+                List of x-coordinates
+
+            y : list
+                List of y-coordinates
+
+            z : list
+                List of z-coordinates for a 3D line.
+        """
+        np = import_module('numpy')
+        if z is not None:
+            dim = 3
+            points = (x, y, z)
+        else:
+            dim = 2
+            points = (x, y)
+        points = np.ma.array(points).T.reshape(-1, 1, dim)
+        return np.ma.concatenate([points[:-1], points[1:]], axis=1)
+
+    def _process_series(self, series, ax, parent):
+        np = import_module('numpy')
+        mpl_toolkits = import_module(
+            'mpl_toolkits', import_kwargs={'fromlist': ['mplot3d']})
+
+        # XXX Workaround for matplotlib issue
+        # https://github.com/matplotlib/matplotlib/issues/17130
+        xlims, ylims, zlims = [], [], []
+
+        for s in series:
+            # Create the collections
+            if s.is_2Dline:
+                x, y = s.get_data()
+                if (isinstance(s.line_color, (int, float)) or
+                        callable(s.line_color)):
+                    segments = self.get_segments(x, y)
+                    collection = self.LineCollection(segments)
+                    collection.set_array(s.get_color_array())
+                    ax.add_collection(collection)
+                else:
+                    lbl = _str_or_latex(s.label)
+                    line, = ax.plot(x, y, label=lbl, color=s.line_color)
+            elif s.is_contour:
+                ax.contour(*s.get_meshes())
+            elif s.is_3Dline:
+                x, y, z = s.get_data()
+                if (isinstance(s.line_color, (int, float)) or
+                        callable(s.line_color)):
+                    art3d = mpl_toolkits.mplot3d.art3d
+                    segments = self.get_segments(x, y, z)
+                    collection = art3d.Line3DCollection(segments)
+                    collection.set_array(s.get_color_array())
+                    ax.add_collection(collection)
+                else:
+                    lbl = _str_or_latex(s.label)
+                    ax.plot(x, y, z, label=lbl, color=s.line_color)
+
+                xlims.append(s._xlim)
+                ylims.append(s._ylim)
+                zlims.append(s._zlim)
+            elif s.is_3Dsurface:
+                x, y, z = s.get_meshes()
+                collection = ax.plot_surface(x, y, z,
+                    cmap=getattr(self.cm, 'viridis', self.cm.jet),
+                    rstride=1, cstride=1, linewidth=0.1)
+                if isinstance(s.surface_color, (float, int, Callable)):
+                    color_array = s.get_color_array()
+                    color_array = color_array.reshape(color_array.size)
+                    collection.set_array(color_array)
+                else:
+                    collection.set_color(s.surface_color)
+
+                xlims.append(s._xlim)
+                ylims.append(s._ylim)
+                zlims.append(s._zlim)
+            elif s.is_implicit:
+                points = s.get_raster()
+                if len(points) == 2:
+                    # interval math plotting
+                    x, y = _matplotlib_list(points[0])
+                    ax.fill(x, y, facecolor=s.line_color, edgecolor='None')
+                else:
+                    # use contourf or contour depending on whether it is
+                    # an inequality or equality.
+                    # XXX: ``contour`` plots multiple lines. Should be fixed.
+                    ListedColormap = self.matplotlib.colors.ListedColormap
+                    colormap = ListedColormap(["white", s.line_color])
+                    xarray, yarray, zarray, plot_type = points
+                    if plot_type == 'contour':
+                        ax.contour(xarray, yarray, zarray, cmap=colormap)
+                    else:
+                        ax.contourf(xarray, yarray, zarray, cmap=colormap)
+            else:
+                raise NotImplementedError(
+                    '{} is not supported in the SymPy plotting module '
+                    'with matplotlib backend. Please report this issue.'
+                    .format(ax))
+
+        Axes3D = mpl_toolkits.mplot3d.Axes3D
+        if not isinstance(ax, Axes3D):
+            ax.autoscale_view(
+                scalex=ax.get_autoscalex_on(),
+                scaley=ax.get_autoscaley_on())
+        else:
+            # XXX Workaround for matplotlib issue
+            # https://github.com/matplotlib/matplotlib/issues/17130
+            if xlims:
+                xlims = np.array(xlims)
+                xlim = (np.amin(xlims[:, 0]), np.amax(xlims[:, 1]))
+                ax.set_xlim(xlim)
+            else:
+                ax.set_xlim([0, 1])
+
+            if ylims:
+                ylims = np.array(ylims)
+                ylim = (np.amin(ylims[:, 0]), np.amax(ylims[:, 1]))
+                ax.set_ylim(ylim)
+            else:
+                ax.set_ylim([0, 1])
+
+            if zlims:
+                zlims = np.array(zlims)
+                zlim = (np.amin(zlims[:, 0]), np.amax(zlims[:, 1]))
+                ax.set_zlim(zlim)
+            else:
+                ax.set_zlim([0, 1])
+
+        # Set global options.
+        # TODO The 3D stuff
+        # XXX The order of those is important.
+        if parent.xscale and not isinstance(ax, Axes3D):
+            ax.set_xscale(parent.xscale)
+        if parent.yscale and not isinstance(ax, Axes3D):
+            ax.set_yscale(parent.yscale)
+        if not isinstance(ax, Axes3D) or self.matplotlib.__version__ >= '1.2.0':  # XXX in the distant future remove this check
+            ax.set_autoscale_on(parent.autoscale)
+        if parent.axis_center:
+            val = parent.axis_center
+            if isinstance(ax, Axes3D):
+                pass
+            elif val == 'center':
+                ax.spines['left'].set_position('center')
+                ax.spines['bottom'].set_position('center')
+            elif val == 'auto':
+                xl, xh = ax.get_xlim()
+                yl, yh = ax.get_ylim()
+                pos_left = ('data', 0) if xl*xh <= 0 else 'center'
+                pos_bottom = ('data', 0) if yl*yh <= 0 else 'center'
+                ax.spines['left'].set_position(pos_left)
+                ax.spines['bottom'].set_position(pos_bottom)
+            else:
+                ax.spines['left'].set_position(('data', val[0]))
+                ax.spines['bottom'].set_position(('data', val[1]))
+        if not parent.axis:
+            ax.set_axis_off()
+        if parent.legend:
+            if ax.legend():
+                ax.legend_.set_visible(parent.legend)
+        if parent.margin:
+            ax.set_xmargin(parent.margin)
+            ax.set_ymargin(parent.margin)
+        if parent.title:
+            ax.set_title(parent.title)
+        if parent.xlabel:
+            xlbl = _str_or_latex(parent.xlabel)
+            ax.set_xlabel(xlbl, position=(1, 0))
+        if parent.ylabel:
+            ylbl = _str_or_latex(parent.ylabel)
+            ax.set_ylabel(ylbl, position=(0, 1))
+        if isinstance(ax, Axes3D) and parent.zlabel:
+            zlbl = _str_or_latex(parent.zlabel)
+            ax.set_zlabel(zlbl, position=(0, 1))
+        if parent.annotations:
+            for a in parent.annotations:
+                ax.annotate(**a)
+        if parent.markers:
+            for marker in parent.markers:
+                # make a copy of the marker dictionary
+                # so that it doesn't get altered
+                m = marker.copy()
+                args = m.pop('args')
+                ax.plot(*args, **m)
+        if parent.rectangles:
+            for r in parent.rectangles:
+                rect = self.matplotlib.patches.Rectangle(**r)
+                ax.add_patch(rect)
+        if parent.fill:
+            ax.fill_between(**parent.fill)
+
+        # xlim and ylim should always be set at last so that plot limits
+        # doesn't get altered during the process.
+        if parent.xlim:
+            ax.set_xlim(parent.xlim)
+        if parent.ylim:
+            ax.set_ylim(parent.ylim)
+
+
+    def process_series(self):
+        """
+        Iterates over every ``Plot`` object and further calls
+        _process_series()
+        """
+        parent = self.parent
+        if isinstance(parent, Plot):
+            series_list = [parent._series]
+        else:
+            series_list = parent._series
+
+        for i, (series, ax) in enumerate(zip(series_list, self.ax)):
+            if isinstance(self.parent, PlotGrid):
+                parent = self.parent.args[i]
+            self._process_series(series, ax, parent)
+
+    def show(self):
+        self.process_series()
+        #TODO after fixing https://github.com/ipython/ipython/issues/1255
+        # you can uncomment the next line and remove the pyplot.show() call
+        #self.fig.show()
+        if _show:
+            self.fig.tight_layout()
+            self.plt.show()
+        else:
+            self.close()
+
+    def save(self, path):
+        self.process_series()
+        self.fig.savefig(path)
+
+    def close(self):
+        self.plt.close(self.fig)
+
+
+class TextBackend(BaseBackend):
+    def __init__(self, parent):
+        super().__init__(parent)
+
+    def show(self):
+        if not _show:
+            return
+        if len(self.parent._series) != 1:
+            raise ValueError(
+                'The TextBackend supports only one graph per Plot.')
+        elif not isinstance(self.parent._series[0], LineOver1DRangeSeries):
+            raise ValueError(
+                'The TextBackend supports only expressions over a 1D range')
+        else:
+            ser = self.parent._series[0]
+            textplot(ser.expr, ser.start, ser.end)
+
+    def close(self):
+        pass
+
+
+class DefaultBackend(BaseBackend):
+    def __new__(cls, parent):
+        matplotlib = import_module('matplotlib', min_module_version='1.1.0', catch=(RuntimeError,))
+        if matplotlib:
+            return MatplotlibBackend(parent)
+        else:
+            return TextBackend(parent)
+
+
+plot_backends = {
+    'matplotlib': MatplotlibBackend,
+    'text': TextBackend,
+    'default': DefaultBackend
+}
+
+
+##############################################################################
+# Finding the centers of line segments or mesh faces
+##############################################################################
+
+def centers_of_segments(array):
+    np = import_module('numpy')
+    return np.mean(np.vstack((array[:-1], array[1:])), 0)
+
+
+def centers_of_faces(array):
+    np = import_module('numpy')
+    return np.mean(np.dstack((array[:-1, :-1],
+                             array[1:, :-1],
+                             array[:-1, 1:],
+                             array[:-1, :-1],
+                             )), 2)
+
+
+def flat(x, y, z, eps=1e-3):
+    """Checks whether three points are almost collinear"""
+    np = import_module('numpy')
+    # Workaround plotting piecewise (#8577):
+    #   workaround for `lambdify` in `.experimental_lambdify` fails
+    #   to return numerical values in some cases. Lower-level fix
+    #   in `lambdify` is possible.
+    vector_a = (x - y).astype(np.float64)
+    vector_b = (z - y).astype(np.float64)
+    dot_product = np.dot(vector_a, vector_b)
+    vector_a_norm = np.linalg.norm(vector_a)
+    vector_b_norm = np.linalg.norm(vector_b)
+    cos_theta = dot_product / (vector_a_norm * vector_b_norm)
+    return abs(cos_theta + 1) < eps
+
+
+def _matplotlib_list(interval_list):
+    """
+    Returns lists for matplotlib ``fill`` command from a list of bounding
+    rectangular intervals
+    """
+    xlist = []
+    ylist = []
+    if len(interval_list):
+        for intervals in interval_list:
+            intervalx = intervals[0]
+            intervaly = intervals[1]
+            xlist.extend([intervalx.start, intervalx.start,
+                          intervalx.end, intervalx.end, None])
+            ylist.extend([intervaly.start, intervaly.end,
+                          intervaly.end, intervaly.start, None])
+    else:
+        #XXX Ugly hack. Matplotlib does not accept empty lists for ``fill``
+        xlist.extend((None, None, None, None))
+        ylist.extend((None, None, None, None))
+    return xlist, ylist
+
+
+####New API for plotting module ####
+
+# TODO: Add color arrays for plots.
+# TODO: Add more plotting options for 3d plots.
+# TODO: Adaptive sampling for 3D plots.
+
+def plot(*args, show=True, **kwargs):
+    """Plots a function of a single variable as a curve.
+
+    Parameters
+    ==========
+
+    args :
+        The first argument is the expression representing the function
+        of single variable to be plotted.
+
+        The last argument is a 3-tuple denoting the range of the free
+        variable. e.g. ``(x, 0, 5)``
+
+        Typical usage examples are in the following:
+
+        - Plotting a single expression with a single range.
+            ``plot(expr, range, **kwargs)``
+        - Plotting a single expression with the default range (-10, 10).
+            ``plot(expr, **kwargs)``
+        - Plotting multiple expressions with a single range.
+            ``plot(expr1, expr2, ..., range, **kwargs)``
+        - Plotting multiple expressions with multiple ranges.
+            ``plot((expr1, range1), (expr2, range2), ..., **kwargs)``
+
+        It is best practice to specify range explicitly because default
+        range may change in the future if a more advanced default range
+        detection algorithm is implemented.
+
+    show : bool, optional
+        The default value is set to ``True``. Set show to ``False`` and
+        the function will not display the plot. The returned instance of
+        the ``Plot`` class can then be used to save or display the plot
+        by calling the ``save()`` and ``show()`` methods respectively.
+
+    line_color : string, or float, or function, optional
+        Specifies the color for the plot.
+        See ``Plot`` to see how to set color for the plots.
+        Note that by setting ``line_color``, it would be applied simultaneously
+        to all the series.
+
+    title : str, optional
+        Title of the plot. It is set to the latex representation of
+        the expression, if the plot has only one expression.
+
+    label : str, optional
+        The label of the expression in the plot. It will be used when
+        called with ``legend``. Default is the name of the expression.
+        e.g. ``sin(x)``
+
+    xlabel : str or expression, optional
+        Label for the x-axis.
+
+    ylabel : str or expression, optional
+        Label for the y-axis.
+
+    xscale : 'linear' or 'log', optional
+        Sets the scaling of the x-axis.
+
+    yscale : 'linear' or 'log', optional
+        Sets the scaling of the y-axis.
+
+    axis_center : (float, float), optional
+        Tuple of two floats denoting the coordinates of the center or
+        {'center', 'auto'}
+
+    xlim : (float, float), optional
+        Denotes the x-axis limits, ``(min, max)```.
+
+    ylim : (float, float), optional
+        Denotes the y-axis limits, ``(min, max)```.
+
+    annotations : list, optional
+        A list of dictionaries specifying the type of annotation
+        required. The keys in the dictionary should be equivalent
+        to the arguments of the :external:mod:`matplotlib`'s
+        :external:meth:`~matplotlib.axes.Axes.annotate` method.
+
+    markers : list, optional
+        A list of dictionaries specifying the type the markers required.
+        The keys in the dictionary should be equivalent to the arguments
+        of the :external:mod:`matplotlib`'s :external:func:`~matplotlib.pyplot.plot()` function
+        along with the marker related keyworded arguments.
+
+    rectangles : list, optional
+        A list of dictionaries specifying the dimensions of the
+        rectangles to be plotted. The keys in the dictionary should be
+        equivalent to the arguments of the :external:mod:`matplotlib`'s
+        :external:class:`~matplotlib.patches.Rectangle` class.
+
+    fill : dict, optional
+        A dictionary specifying the type of color filling required in
+        the plot. The keys in the dictionary should be equivalent to the
+        arguments of the :external:mod:`matplotlib`'s
+        :external:meth:`~matplotlib.axes.Axes.fill_between` method.
+
+    adaptive : bool, optional
+        The default value is set to ``True``. Set adaptive to ``False``
+        and specify ``nb_of_points`` if uniform sampling is required.
+
+        The plotting uses an adaptive algorithm which samples
+        recursively to accurately plot. The adaptive algorithm uses a
+        random point near the midpoint of two points that has to be
+        further sampled. Hence the same plots can appear slightly
+        different.
+
+    depth : int, optional
+        Recursion depth of the adaptive algorithm. A depth of value
+        `n` samples a maximum of `2^{n}` points.
+
+        If the ``adaptive`` flag is set to ``False``, this will be
+        ignored.
+
+    nb_of_points : int, optional
+        Used when the ``adaptive`` is set to ``False``. The function
+        is uniformly sampled at ``nb_of_points`` number of points.
+
+        If the ``adaptive`` flag is set to ``True``, this will be
+        ignored.
+
+    size : (float, float), optional
+        A tuple in the form (width, height) in inches to specify the size of
+        the overall figure. The default value is set to ``None``, meaning
+        the size will be set by the default backend.
+
+    Examples
+    ========
+
+    .. plot::
+       :context: close-figs
+       :format: doctest
+       :include-source: True
+
+       >>> from sympy import symbols
+       >>> from sympy.plotting import plot
+       >>> x = symbols('x')
+
+    Single Plot
+
+    .. plot::
+       :context: close-figs
+       :format: doctest
+       :include-source: True
+
+       >>> plot(x**2, (x, -5, 5))
+       Plot object containing:
+       [0]: cartesian line: x**2 for x over (-5.0, 5.0)
+
+    Multiple plots with single range.
+
+    .. plot::
+       :context: close-figs
+       :format: doctest
+       :include-source: True
+
+       >>> plot(x, x**2, x**3, (x, -5, 5))
+       Plot object containing:
+       [0]: cartesian line: x for x over (-5.0, 5.0)
+       [1]: cartesian line: x**2 for x over (-5.0, 5.0)
+       [2]: cartesian line: x**3 for x over (-5.0, 5.0)
+
+    Multiple plots with different ranges.
+
+    .. plot::
+       :context: close-figs
+       :format: doctest
+       :include-source: True
+
+       >>> plot((x**2, (x, -6, 6)), (x, (x, -5, 5)))
+       Plot object containing:
+       [0]: cartesian line: x**2 for x over (-6.0, 6.0)
+       [1]: cartesian line: x for x over (-5.0, 5.0)
+
+    No adaptive sampling.
+
+    .. plot::
+       :context: close-figs
+       :format: doctest
+       :include-source: True
+
+       >>> plot(x**2, adaptive=False, nb_of_points=400)
+       Plot object containing:
+       [0]: cartesian line: x**2 for x over (-10.0, 10.0)
+
+    See Also
+    ========
+
+    Plot, LineOver1DRangeSeries
+
+    """
+    args = list(map(sympify, args))
+    free = set()
+    for a in args:
+        if isinstance(a, Expr):
+            free |= a.free_symbols
+            if len(free) > 1:
+                raise ValueError(
+                    'The same variable should be used in all '
+                    'univariate expressions being plotted.')
+    x = free.pop() if free else Symbol('x')
+    kwargs.setdefault('xlabel', x)
+    kwargs.setdefault('ylabel', Function('f')(x))
+    series = []
+    plot_expr = check_arguments(args, 1, 1)
+    series = [LineOver1DRangeSeries(*arg, **kwargs) for arg in plot_expr]
+
+    plots = Plot(*series, **kwargs)
+    if show:
+        plots.show()
+    return plots
+
+
+def plot_parametric(*args, show=True, **kwargs):
+    """
+    Plots a 2D parametric curve.
+
+    Parameters
+    ==========
+
+    args
+        Common specifications are:
+
+        - Plotting a single parametric curve with a range
+            ``plot_parametric((expr_x, expr_y), range)``
+        - Plotting multiple parametric curves with the same range
+            ``plot_parametric((expr_x, expr_y), ..., range)``
+        - Plotting multiple parametric curves with different ranges
+            ``plot_parametric((expr_x, expr_y, range), ...)``
+
+        ``expr_x`` is the expression representing $x$ component of the
+        parametric function.
+
+        ``expr_y`` is the expression representing $y$ component of the
+        parametric function.
+
+        ``range`` is a 3-tuple denoting the parameter symbol, start and
+        stop. For example, ``(u, 0, 5)``.
+
+        If the range is not specified, then a default range of (-10, 10)
+        is used.
+
+        However, if the arguments are specified as
+        ``(expr_x, expr_y, range), ...``, you must specify the ranges
+        for each expressions manually.
+
+        Default range may change in the future if a more advanced
+        algorithm is implemented.
+
+    adaptive : bool, optional
+        Specifies whether to use the adaptive sampling or not.
+
+        The default value is set to ``True``. Set adaptive to ``False``
+        and specify ``nb_of_points`` if uniform sampling is required.
+
+    depth :  int, optional
+        The recursion depth of the adaptive algorithm. A depth of
+        value $n$ samples a maximum of $2^n$ points.
+
+    nb_of_points : int, optional
+        Used when the ``adaptive`` flag is set to ``False``.
+
+        Specifies the number of the points used for the uniform
+        sampling.
+
+    line_color : string, or float, or function, optional
+        Specifies the color for the plot.
+        See ``Plot`` to see how to set color for the plots.
+        Note that by setting ``line_color``, it would be applied simultaneously
+        to all the series.
+
+    label : str, optional
+        The label of the expression in the plot. It will be used when
+        called with ``legend``. Default is the name of the expression.
+        e.g. ``sin(x)``
+
+    xlabel : str, optional
+        Label for the x-axis.
+
+    ylabel : str, optional
+        Label for the y-axis.
+
+    xscale : 'linear' or 'log', optional
+        Sets the scaling of the x-axis.
+
+    yscale : 'linear' or 'log', optional
+        Sets the scaling of the y-axis.
+
+    axis_center : (float, float), optional
+        Tuple of two floats denoting the coordinates of the center or
+        {'center', 'auto'}
+
+    xlim : (float, float), optional
+        Denotes the x-axis limits, ``(min, max)```.
+
+    ylim : (float, float), optional
+        Denotes the y-axis limits, ``(min, max)```.
+
+    size : (float, float), optional
+        A tuple in the form (width, height) in inches to specify the size of
+        the overall figure. The default value is set to ``None``, meaning
+        the size will be set by the default backend.
+
+    Examples
+    ========
+
+    .. plot::
+       :context: reset
+       :format: doctest
+       :include-source: True
+
+       >>> from sympy import plot_parametric, symbols, cos, sin
+       >>> u = symbols('u')
+
+    A parametric plot with a single expression:
+
+    .. plot::
+       :context: close-figs
+       :format: doctest
+       :include-source: True
+
+       >>> plot_parametric((cos(u), sin(u)), (u, -5, 5))
+       Plot object containing:
+       [0]: parametric cartesian line: (cos(u), sin(u)) for u over (-5.0, 5.0)
+
+    A parametric plot with multiple expressions with the same range:
+
+    .. plot::
+       :context: close-figs
+       :format: doctest
+       :include-source: True
+
+       >>> plot_parametric((cos(u), sin(u)), (u, cos(u)), (u, -10, 10))
+       Plot object containing:
+       [0]: parametric cartesian line: (cos(u), sin(u)) for u over (-10.0, 10.0)
+       [1]: parametric cartesian line: (u, cos(u)) for u over (-10.0, 10.0)
+
+    A parametric plot with multiple expressions with different ranges
+    for each curve:
+
+    .. plot::
+       :context: close-figs
+       :format: doctest
+       :include-source: True
+
+       >>> plot_parametric((cos(u), sin(u), (u, -5, 5)),
+       ...     (cos(u), u, (u, -5, 5)))
+       Plot object containing:
+       [0]: parametric cartesian line: (cos(u), sin(u)) for u over (-5.0, 5.0)
+       [1]: parametric cartesian line: (cos(u), u) for u over (-5.0, 5.0)
+
+    Notes
+    =====
+
+    The plotting uses an adaptive algorithm which samples recursively to
+    accurately plot the curve. The adaptive algorithm uses a random point
+    near the midpoint of two points that has to be further sampled.
+    Hence, repeating the same plot command can give slightly different
+    results because of the random sampling.
+
+    If there are multiple plots, then the same optional arguments are
+    applied to all the plots drawn in the same canvas. If you want to
+    set these options separately, you can index the returned ``Plot``
+    object and set it.
+
+    For example, when you specify ``line_color`` once, it would be
+    applied simultaneously to both series.
+
+    .. plot::
+       :context: close-figs
+       :format: doctest
+       :include-source: True
+
+        >>> from sympy import pi
+        >>> expr1 = (u, cos(2*pi*u)/2 + 1/2)
+        >>> expr2 = (u, sin(2*pi*u)/2 + 1/2)
+        >>> p = plot_parametric(expr1, expr2, (u, 0, 1), line_color='blue')
+
+    If you want to specify the line color for the specific series, you
+    should index each item and apply the property manually.
+
+    .. plot::
+       :context: close-figs
+       :format: doctest
+       :include-source: True
+
+        >>> p[0].line_color = 'red'
+        >>> p.show()
+
+    See Also
+    ========
+
+    Plot, Parametric2DLineSeries
+    """
+    args = list(map(sympify, args))
+    series = []
+    plot_expr = check_arguments(args, 2, 1)
+    series = [Parametric2DLineSeries(*arg, **kwargs) for arg in plot_expr]
+    plots = Plot(*series, **kwargs)
+    if show:
+        plots.show()
+    return plots
+
+
+def plot3d_parametric_line(*args, show=True, **kwargs):
+    """
+    Plots a 3D parametric line plot.
+
+    Usage
+    =====
+
+    Single plot:
+
+    ``plot3d_parametric_line(expr_x, expr_y, expr_z, range, **kwargs)``
+
+    If the range is not specified, then a default range of (-10, 10) is used.
+
+    Multiple plots.
+
+    ``plot3d_parametric_line((expr_x, expr_y, expr_z, range), ..., **kwargs)``
+
+    Ranges have to be specified for every expression.
+
+    Default range may change in the future if a more advanced default range
+    detection algorithm is implemented.
+
+    Arguments
+    =========
+
+    expr_x : Expression representing the function along x.
+
+    expr_y : Expression representing the function along y.
+
+    expr_z : Expression representing the function along z.
+
+    range : (:class:`~.Symbol`, float, float)
+        A 3-tuple denoting the range of the parameter variable, e.g., (u, 0, 5).
+
+    Keyword Arguments
+    =================
+
+    Arguments for ``Parametric3DLineSeries`` class.
+
+    nb_of_points : The range is uniformly sampled at ``nb_of_points``
+    number of points.
+
+    Aesthetics:
+
+    line_color : string, or float, or function, optional
+        Specifies the color for the plot.
+        See ``Plot`` to see how to set color for the plots.
+        Note that by setting ``line_color``, it would be applied simultaneously
+        to all the series.
+
+    label : str
+        The label to the plot. It will be used when called with ``legend=True``
+        to denote the function with the given label in the plot.
+
+    If there are multiple plots, then the same series arguments are applied to
+    all the plots. If you want to set these options separately, you can index
+    the returned ``Plot`` object and set it.
+
+    Arguments for ``Plot`` class.
+
+    title : str
+        Title of the plot.
+
+    size : (float, float), optional
+        A tuple in the form (width, height) in inches to specify the size of
+        the overall figure. The default value is set to ``None``, meaning
+        the size will be set by the default backend.
+
+    Examples
+    ========
+
+    .. plot::
+       :context: reset
+       :format: doctest
+       :include-source: True
+
+       >>> from sympy import symbols, cos, sin
+       >>> from sympy.plotting import plot3d_parametric_line
+       >>> u = symbols('u')
+
+    Single plot.
+
+    .. plot::
+       :context: close-figs
+       :format: doctest
+       :include-source: True
+
+       >>> plot3d_parametric_line(cos(u), sin(u), u, (u, -5, 5))
+       Plot object containing:
+       [0]: 3D parametric cartesian line: (cos(u), sin(u), u) for u over (-5.0, 5.0)
+
+
+    Multiple plots.
+
+    .. plot::
+       :context: close-figs
+       :format: doctest
+       :include-source: True
+
+       >>> plot3d_parametric_line((cos(u), sin(u), u, (u, -5, 5)),
+       ...     (sin(u), u**2, u, (u, -5, 5)))
+       Plot object containing:
+       [0]: 3D parametric cartesian line: (cos(u), sin(u), u) for u over (-5.0, 5.0)
+       [1]: 3D parametric cartesian line: (sin(u), u**2, u) for u over (-5.0, 5.0)
+
+
+    See Also
+    ========
+
+    Plot, Parametric3DLineSeries
+
+    """
+    args = list(map(sympify, args))
+    series = []
+    plot_expr = check_arguments(args, 3, 1)
+    series = [Parametric3DLineSeries(*arg, **kwargs) for arg in plot_expr]
+    kwargs.setdefault("xlabel", "x")
+    kwargs.setdefault("ylabel", "y")
+    kwargs.setdefault("zlabel", "z")
+    plots = Plot(*series, **kwargs)
+    if show:
+        plots.show()
+    return plots
+
+
+def plot3d(*args, show=True, **kwargs):
+    """
+    Plots a 3D surface plot.
+
+    Usage
+    =====
+
+    Single plot
+
+    ``plot3d(expr, range_x, range_y, **kwargs)``
+
+    If the ranges are not specified, then a default range of (-10, 10) is used.
+
+    Multiple plot with the same range.
+
+    ``plot3d(expr1, expr2, range_x, range_y, **kwargs)``
+
+    If the ranges are not specified, then a default range of (-10, 10) is used.
+
+    Multiple plots with different ranges.
+
+    ``plot3d((expr1, range_x, range_y), (expr2, range_x, range_y), ..., **kwargs)``
+
+    Ranges have to be specified for every expression.
+
+    Default range may change in the future if a more advanced default range
+    detection algorithm is implemented.
+
+    Arguments
+    =========
+
+    expr : Expression representing the function along x.
+
+    range_x : (:class:`~.Symbol`, float, float)
+        A 3-tuple denoting the range of the x variable, e.g. (x, 0, 5).
+
+    range_y : (:class:`~.Symbol`, float, float)
+        A 3-tuple denoting the range of the y variable, e.g. (y, 0, 5).
+
+    Keyword Arguments
+    =================
+
+    Arguments for ``SurfaceOver2DRangeSeries`` class:
+
+    nb_of_points_x : int
+        The x range is sampled uniformly at ``nb_of_points_x`` of points.
+
+    nb_of_points_y : int
+        The y range is sampled uniformly at ``nb_of_points_y`` of points.
+
+    Aesthetics:
+
+    surface_color : Function which returns a float
+        Specifies the color for the surface of the plot.
+        See :class:`~.Plot` for more details.
+
+    If there are multiple plots, then the same series arguments are applied to
+    all the plots. If you want to set these options separately, you can index
+    the returned ``Plot`` object and set it.
+
+    Arguments for ``Plot`` class:
+
+    title : str
+        Title of the plot.
+
+    size : (float, float), optional
+        A tuple in the form (width, height) in inches to specify the size of the
+        overall figure. The default value is set to ``None``, meaning the size will
+        be set by the default backend.
+
+    Examples
+    ========
+
+    .. plot::
+       :context: reset
+       :format: doctest
+       :include-source: True
+
+       >>> from sympy import symbols
+       >>> from sympy.plotting import plot3d
+       >>> x, y = symbols('x y')
+
+    Single plot
+
+    .. plot::
+       :context: close-figs
+       :format: doctest
+       :include-source: True
+
+       >>> plot3d(x*y, (x, -5, 5), (y, -5, 5))
+       Plot object containing:
+       [0]: cartesian surface: x*y for x over (-5.0, 5.0) and y over (-5.0, 5.0)
+
+
+    Multiple plots with same range
+
+    .. plot::
+       :context: close-figs
+       :format: doctest
+       :include-source: True
+
+       >>> plot3d(x*y, -x*y, (x, -5, 5), (y, -5, 5))
+       Plot object containing:
+       [0]: cartesian surface: x*y for x over (-5.0, 5.0) and y over (-5.0, 5.0)
+       [1]: cartesian surface: -x*y for x over (-5.0, 5.0) and y over (-5.0, 5.0)
+
+
+    Multiple plots with different ranges.
+
+    .. plot::
+       :context: close-figs
+       :format: doctest
+       :include-source: True
+
+       >>> plot3d((x**2 + y**2, (x, -5, 5), (y, -5, 5)),
+       ...     (x*y, (x, -3, 3), (y, -3, 3)))
+       Plot object containing:
+       [0]: cartesian surface: x**2 + y**2 for x over (-5.0, 5.0) and y over (-5.0, 5.0)
+       [1]: cartesian surface: x*y for x over (-3.0, 3.0) and y over (-3.0, 3.0)
+
+
+    See Also
+    ========
+
+    Plot, SurfaceOver2DRangeSeries
+
+    """
+
+    args = list(map(sympify, args))
+    series = []
+    plot_expr = check_arguments(args, 1, 2)
+    series = [SurfaceOver2DRangeSeries(*arg, **kwargs) for arg in plot_expr]
+    kwargs.setdefault("xlabel", series[0].var_x)
+    kwargs.setdefault("ylabel", series[0].var_y)
+    kwargs.setdefault("zlabel", Function('f')(series[0].var_x, series[0].var_y))
+    plots = Plot(*series, **kwargs)
+    if show:
+        plots.show()
+    return plots
+
+
+def plot3d_parametric_surface(*args, show=True, **kwargs):
+    """
+    Plots a 3D parametric surface plot.
+
+    Explanation
+    ===========
+
+    Single plot.
+
+    ``plot3d_parametric_surface(expr_x, expr_y, expr_z, range_u, range_v, **kwargs)``
+
+    If the ranges is not specified, then a default range of (-10, 10) is used.
+
+    Multiple plots.
+
+    ``plot3d_parametric_surface((expr_x, expr_y, expr_z, range_u, range_v), ..., **kwargs)``
+
+    Ranges have to be specified for every expression.
+
+    Default range may change in the future if a more advanced default range
+    detection algorithm is implemented.
+
+    Arguments
+    =========
+
+    expr_x : Expression representing the function along ``x``.
+
+    expr_y : Expression representing the function along ``y``.
+
+    expr_z : Expression representing the function along ``z``.
+
+    range_u : (:class:`~.Symbol`, float, float)
+        A 3-tuple denoting the range of the u variable, e.g. (u, 0, 5).
+
+    range_v : (:class:`~.Symbol`, float, float)
+        A 3-tuple denoting the range of the v variable, e.g. (v, 0, 5).
+
+    Keyword Arguments
+    =================
+
+    Arguments for ``ParametricSurfaceSeries`` class:
+
+    nb_of_points_u : int
+        The ``u`` range is sampled uniformly at ``nb_of_points_v`` of points
+
+    nb_of_points_y : int
+        The ``v`` range is sampled uniformly at ``nb_of_points_y`` of points
+
+    Aesthetics:
+
+    surface_color : Function which returns a float
+        Specifies the color for the surface of the plot. See
+        :class:`~Plot` for more details.
+
+    If there are multiple plots, then the same series arguments are applied for
+    all the plots. If you want to set these options separately, you can index
+    the returned ``Plot`` object and set it.
+
+
+    Arguments for ``Plot`` class:
+
+    title : str
+        Title of the plot.
+
+    size : (float, float), optional
+        A tuple in the form (width, height) in inches to specify the size of the
+        overall figure. The default value is set to ``None``, meaning the size will
+        be set by the default backend.
+
+    Examples
+    ========
+
+    .. plot::
+       :context: reset
+       :format: doctest
+       :include-source: True
+
+       >>> from sympy import symbols, cos, sin
+       >>> from sympy.plotting import plot3d_parametric_surface
+       >>> u, v = symbols('u v')
+
+    Single plot.
+
+    .. plot::
+       :context: close-figs
+       :format: doctest
+       :include-source: True
+
+       >>> plot3d_parametric_surface(cos(u + v), sin(u - v), u - v,
+       ...     (u, -5, 5), (v, -5, 5))
+       Plot object containing:
+       [0]: parametric cartesian surface: (cos(u + v), sin(u - v), u - v) for u over (-5.0, 5.0) and v over (-5.0, 5.0)
+
+
+    See Also
+    ========
+
+    Plot, ParametricSurfaceSeries
+
+    """
+
+    args = list(map(sympify, args))
+    series = []
+    plot_expr = check_arguments(args, 3, 2)
+    series = [ParametricSurfaceSeries(*arg, **kwargs) for arg in plot_expr]
+    kwargs.setdefault("xlabel", "x")
+    kwargs.setdefault("ylabel", "y")
+    kwargs.setdefault("zlabel", "z")
+    plots = Plot(*series, **kwargs)
+    if show:
+        plots.show()
+    return plots
+
+def plot_contour(*args, show=True, **kwargs):
+    """
+    Draws contour plot of a function
+
+    Usage
+    =====
+
+    Single plot
+
+    ``plot_contour(expr, range_x, range_y, **kwargs)``
+
+    If the ranges are not specified, then a default range of (-10, 10) is used.
+
+    Multiple plot with the same range.
+
+    ``plot_contour(expr1, expr2, range_x, range_y, **kwargs)``
+
+    If the ranges are not specified, then a default range of (-10, 10) is used.
+
+    Multiple plots with different ranges.
+
+    ``plot_contour((expr1, range_x, range_y), (expr2, range_x, range_y), ..., **kwargs)``
+
+    Ranges have to be specified for every expression.
+
+    Default range may change in the future if a more advanced default range
+    detection algorithm is implemented.
+
+    Arguments
+    =========
+
+    expr : Expression representing the function along x.
+
+    range_x : (:class:`Symbol`, float, float)
+        A 3-tuple denoting the range of the x variable, e.g. (x, 0, 5).
+
+    range_y : (:class:`Symbol`, float, float)
+        A 3-tuple denoting the range of the y variable, e.g. (y, 0, 5).
+
+    Keyword Arguments
+    =================
+
+    Arguments for ``ContourSeries`` class:
+
+    nb_of_points_x : int
+        The x range is sampled uniformly at ``nb_of_points_x`` of points.
+
+    nb_of_points_y : int
+        The y range is sampled uniformly at ``nb_of_points_y`` of points.
+
+    Aesthetics:
+
+    surface_color : Function which returns a float
+        Specifies the color for the surface of the plot. See
+        :class:`sympy.plotting.Plot` for more details.
+
+    If there are multiple plots, then the same series arguments are applied to
+    all the plots. If you want to set these options separately, you can index
+    the returned ``Plot`` object and set it.
+
+    Arguments for ``Plot`` class:
+
+    title : str
+        Title of the plot.
+
+    size : (float, float), optional
+        A tuple in the form (width, height) in inches to specify the size of
+        the overall figure. The default value is set to ``None``, meaning
+        the size will be set by the default backend.
+
+    See Also
+    ========
+
+    Plot, ContourSeries
+
+    """
+
+    args = list(map(sympify, args))
+    plot_expr = check_arguments(args, 1, 2)
+    series = [ContourSeries(*arg) for arg in plot_expr]
+    plot_contours = Plot(*series, **kwargs)
+    if len(plot_expr[0].free_symbols) > 2:
+        raise ValueError('Contour Plot cannot Plot for more than two variables.')
+    if show:
+        plot_contours.show()
+    return plot_contours
+
+def check_arguments(args, expr_len, nb_of_free_symbols):
+    """
+    Checks the arguments and converts into tuples of the
+    form (exprs, ranges).
+
+    Examples
+    ========
+
+    .. plot::
+       :context: reset
+       :format: doctest
+       :include-source: True
+
+       >>> from sympy import cos, sin, symbols
+       >>> from sympy.plotting.plot import check_arguments
+       >>> x = symbols('x')
+       >>> check_arguments([cos(x), sin(x)], 2, 1)
+           [(cos(x), sin(x), (x, -10, 10))]
+
+       >>> check_arguments([x, x**2], 1, 1)
+           [(x, (x, -10, 10)), (x**2, (x, -10, 10))]
+    """
+    if not args:
+        return []
+    if expr_len > 1 and isinstance(args[0], Expr):
+        # Multiple expressions same range.
+        # The arguments are tuples when the expression length is
+        # greater than 1.
+        if len(args) < expr_len:
+            raise ValueError("len(args) should not be less than expr_len")
+        for i in range(len(args)):
+            if isinstance(args[i], Tuple):
+                break
+        else:
+            i = len(args) + 1
+
+        exprs = Tuple(*args[:i])
+        free_symbols = list(set().union(*[e.free_symbols for e in exprs]))
+        if len(args) == expr_len + nb_of_free_symbols:
+            #Ranges given
+            plots = [exprs + Tuple(*args[expr_len:])]
+        else:
+            default_range = Tuple(-10, 10)
+            ranges = []
+            for symbol in free_symbols:
+                ranges.append(Tuple(symbol) + default_range)
+
+            for i in range(len(free_symbols) - nb_of_free_symbols):
+                ranges.append(Tuple(Dummy()) + default_range)
+            plots = [exprs + Tuple(*ranges)]
+        return plots
+
+    if isinstance(args[0], Expr) or (isinstance(args[0], Tuple) and
+                                     len(args[0]) == expr_len and
+                                     expr_len != 3):
+        # Cannot handle expressions with number of expression = 3. It is
+        # not possible to differentiate between expressions and ranges.
+        #Series of plots with same range
+        for i in range(len(args)):
+            if isinstance(args[i], Tuple) and len(args[i]) != expr_len:
+                break
+            if not isinstance(args[i], Tuple):
+                args[i] = Tuple(args[i])
+        else:
+            i = len(args) + 1
+
+        exprs = args[:i]
+        assert all(isinstance(e, Expr) for expr in exprs for e in expr)
+        free_symbols = list(set().union(*[e.free_symbols for expr in exprs
+                                        for e in expr]))
+
+        if len(free_symbols) > nb_of_free_symbols:
+            raise ValueError("The number of free_symbols in the expression "
+                             "is greater than %d" % nb_of_free_symbols)
+        if len(args) == i + nb_of_free_symbols and isinstance(args[i], Tuple):
+            ranges = Tuple(*list(args[
+                           i:i + nb_of_free_symbols]))
+            plots = [expr + ranges for expr in exprs]
+            return plots
+        else:
+            # Use default ranges.
+            default_range = Tuple(-10, 10)
+            ranges = []
+            for symbol in free_symbols:
+                ranges.append(Tuple(symbol) + default_range)
+
+            for i in range(nb_of_free_symbols - len(free_symbols)):
+                ranges.append(Tuple(Dummy()) + default_range)
+            ranges = Tuple(*ranges)
+            plots = [expr + ranges for expr in exprs]
+            return plots
+
+    elif isinstance(args[0], Tuple) and len(args[0]) == expr_len + nb_of_free_symbols:
+        # Multiple plots with different ranges.
+        for arg in args:
+            for i in range(expr_len):
+                if not isinstance(arg[i], Expr):
+                    raise ValueError("Expected an expression, given %s" %
+                                     str(arg[i]))
+            for i in range(nb_of_free_symbols):
+                if not len(arg[i + expr_len]) == 3:
+                    raise ValueError("The ranges should be a tuple of "
+                                     "length 3, got %s" % str(arg[i + expr_len]))
+        return args

llmeval-env/lib/python3.10/site-packages/sympy/plotting/plot_implicit.py

@@ -0,0 +1,432 @@
+"""Implicit plotting module for SymPy.
+
+Explanation
+===========
+
+The module implements a data series called ImplicitSeries which is used by
+``Plot`` class to plot implicit plots for different backends. The module,
+by default, implements plotting using interval arithmetic. It switches to a
+fall back algorithm if the expression cannot be plotted using interval arithmetic.
+It is also possible to specify to use the fall back algorithm for all plots.
+
+Boolean combinations of expressions cannot be plotted by the fall back
+algorithm.
+
+See Also
+========
+
+sympy.plotting.plot
+
+References
+==========
+
+.. [1] Jeffrey Allen Tupper. Reliable Two-Dimensional Graphing Methods for
+Mathematical Formulae with Two Free Variables.
+
+.. [2] Jeffrey Allen Tupper. Graphing Equations with Generalized Interval
+Arithmetic. Master's thesis. University of Toronto, 1996
+
+"""
+
+
+from .plot import BaseSeries, Plot
+from .experimental_lambdify import experimental_lambdify, vectorized_lambdify
+from .intervalmath import interval
+from sympy.core.relational import (Equality, GreaterThan, LessThan,
+                Relational, StrictLessThan, StrictGreaterThan)
+from sympy.core.containers import Tuple
+from sympy.core.relational import Eq
+from sympy.core.symbol import (Dummy, Symbol)
+from sympy.core.sympify import sympify
+from sympy.external import import_module
+from sympy.logic.boolalg import BooleanFunction
+from sympy.polys.polyutils import _sort_gens
+from sympy.utilities.decorator import doctest_depends_on
+from sympy.utilities.iterables import flatten
+import warnings
+
+
+class ImplicitSeries(BaseSeries):
+    """ Representation for Implicit plot """
+    is_implicit = True
+
+    def __init__(self, expr, var_start_end_x, var_start_end_y,
+            has_equality, use_interval_math, depth, nb_of_points,
+            line_color):
+        super().__init__()
+        self.expr = sympify(expr)
+        self.label = self.expr
+        self.var_x = sympify(var_start_end_x[0])
+        self.start_x = float(var_start_end_x[1])
+        self.end_x = float(var_start_end_x[2])
+        self.var_y = sympify(var_start_end_y[0])
+        self.start_y = float(var_start_end_y[1])
+        self.end_y = float(var_start_end_y[2])
+        self.get_points = self.get_raster
+        self.has_equality = has_equality  # If the expression has equality, i.e.
+                                         #Eq, Greaterthan, LessThan.
+        self.nb_of_points = nb_of_points
+        self.use_interval_math = use_interval_math
+        self.depth = 4 + depth
+        self.line_color = line_color
+
+    def __str__(self):
+        return ('Implicit equation: %s for '
+                '%s over %s and %s over %s') % (
+                    str(self.expr),
+                    str(self.var_x),
+                    str((self.start_x, self.end_x)),
+                    str(self.var_y),
+                    str((self.start_y, self.end_y)))
+
+    def get_raster(self):
+        func = experimental_lambdify((self.var_x, self.var_y), self.expr,
+                                    use_interval=True)
+        xinterval = interval(self.start_x, self.end_x)
+        yinterval = interval(self.start_y, self.end_y)
+        try:
+            func(xinterval, yinterval)
+        except AttributeError:
+            # XXX: AttributeError("'list' object has no attribute 'is_real'")
+            # That needs fixing somehow - we shouldn't be catching
+            # AttributeError here.
+            if self.use_interval_math:
+                warnings.warn("Adaptive meshing could not be applied to the"
+                            " expression. Using uniform meshing.", stacklevel=7)
+            self.use_interval_math = False
+
+        if self.use_interval_math:
+            return self._get_raster_interval(func)
+        else:
+            return self._get_meshes_grid()
+
+    def _get_raster_interval(self, func):
+        """ Uses interval math to adaptively mesh and obtain the plot"""
+        k = self.depth
+        interval_list = []
+        #Create initial 32 divisions
+        np = import_module('numpy')
+        xsample = np.linspace(self.start_x, self.end_x, 33)
+        ysample = np.linspace(self.start_y, self.end_y, 33)
+
+        #Add a small jitter so that there are no false positives for equality.
+        # Ex: y==x becomes True for x interval(1, 2) and y interval(1, 2)
+        #which will draw a rectangle.
+        jitterx = (np.random.rand(
+            len(xsample)) * 2 - 1) * (self.end_x - self.start_x) / 2**20
+        jittery = (np.random.rand(
+            len(ysample)) * 2 - 1) * (self.end_y - self.start_y) / 2**20
+        xsample += jitterx
+        ysample += jittery
+
+        xinter = [interval(x1, x2) for x1, x2 in zip(xsample[:-1],
+                           xsample[1:])]
+        yinter = [interval(y1, y2) for y1, y2 in zip(ysample[:-1],
+                           ysample[1:])]
+        interval_list = [[x, y] for x in xinter for y in yinter]
+        plot_list = []
+
+        #recursive call refinepixels which subdivides the intervals which are
+        #neither True nor False according to the expression.
+        def refine_pixels(interval_list):
+            """ Evaluates the intervals and subdivides the interval if the
+            expression is partially satisfied."""
+            temp_interval_list = []
+            plot_list = []
+            for intervals in interval_list:
+
+                #Convert the array indices to x and y values
+                intervalx = intervals[0]
+                intervaly = intervals[1]
+                func_eval = func(intervalx, intervaly)
+                #The expression is valid in the interval. Change the contour
+                #array values to 1.
+                if func_eval[1] is False or func_eval[0] is False:
+                    pass
+                elif func_eval == (True, True):
+                    plot_list.append([intervalx, intervaly])
+                elif func_eval[1] is None or func_eval[0] is None:
+                    #Subdivide
+                    avgx = intervalx.mid
+                    avgy = intervaly.mid
+                    a = interval(intervalx.start, avgx)
+                    b = interval(avgx, intervalx.end)
+                    c = interval(intervaly.start, avgy)
+                    d = interval(avgy, intervaly.end)
+                    temp_interval_list.append([a, c])
+                    temp_interval_list.append([a, d])
+                    temp_interval_list.append([b, c])
+                    temp_interval_list.append([b, d])
+            return temp_interval_list, plot_list
+
+        while k >= 0 and len(interval_list):
+            interval_list, plot_list_temp = refine_pixels(interval_list)
+            plot_list.extend(plot_list_temp)
+            k = k - 1
+        #Check whether the expression represents an equality
+        #If it represents an equality, then none of the intervals
+        #would have satisfied the expression due to floating point
+        #differences. Add all the undecided values to the plot.
+        if self.has_equality:
+            for intervals in interval_list:
+                intervalx = intervals[0]
+                intervaly = intervals[1]
+                func_eval = func(intervalx, intervaly)
+                if func_eval[1] and func_eval[0] is not False:
+                    plot_list.append([intervalx, intervaly])
+        return plot_list, 'fill'
+
+    def _get_meshes_grid(self):
+        """Generates the mesh for generating a contour.
+
+        In the case of equality, ``contour`` function of matplotlib can
+        be used. In other cases, matplotlib's ``contourf`` is used.
+        """
+        equal = False
+        if isinstance(self.expr, Equality):
+            expr = self.expr.lhs - self.expr.rhs
+            equal = True
+
+        elif isinstance(self.expr, (GreaterThan, StrictGreaterThan)):
+            expr = self.expr.lhs - self.expr.rhs
+
+        elif isinstance(self.expr, (LessThan, StrictLessThan)):
+            expr = self.expr.rhs - self.expr.lhs
+        else:
+            raise NotImplementedError("The expression is not supported for "
+                                    "plotting in uniform meshed plot.")
+        np = import_module('numpy')
+        xarray = np.linspace(self.start_x, self.end_x, self.nb_of_points)
+        yarray = np.linspace(self.start_y, self.end_y, self.nb_of_points)
+        x_grid, y_grid = np.meshgrid(xarray, yarray)
+
+        func = vectorized_lambdify((self.var_x, self.var_y), expr)
+        z_grid = func(x_grid, y_grid)
+        z_grid[np.ma.where(z_grid < 0)] = -1
+        z_grid[np.ma.where(z_grid > 0)] = 1
+        if equal:
+            return xarray, yarray, z_grid, 'contour'
+        else:
+            return xarray, yarray, z_grid, 'contourf'
+
+
+@doctest_depends_on(modules=('matplotlib',))
+def plot_implicit(expr, x_var=None, y_var=None, adaptive=True, depth=0,
+                  points=300, line_color="blue", show=True, **kwargs):
+    """A plot function to plot implicit equations / inequalities.
+
+    Arguments
+    =========
+
+    - expr : The equation / inequality that is to be plotted.
+    - x_var (optional) : symbol to plot on x-axis or tuple giving symbol
+      and range as ``(symbol, xmin, xmax)``
+    - y_var (optional) : symbol to plot on y-axis or tuple giving symbol
+      and range as ``(symbol, ymin, ymax)``
+
+    If neither ``x_var`` nor ``y_var`` are given then the free symbols in the
+    expression will be assigned in the order they are sorted.
+
+    The following keyword arguments can also be used:
+
+    - ``adaptive`` Boolean. The default value is set to True. It has to be
+        set to False if you want to use a mesh grid.
+
+    - ``depth`` integer. The depth of recursion for adaptive mesh grid.
+        Default value is 0. Takes value in the range (0, 4).
+
+    - ``points`` integer. The number of points if adaptive mesh grid is not
+        used. Default value is 300.
+
+    - ``show`` Boolean. Default value is True. If set to False, the plot will
+        not be shown. See ``Plot`` for further information.
+
+    - ``title`` string. The title for the plot.
+
+    - ``xlabel`` string. The label for the x-axis
+
+    - ``ylabel`` string. The label for the y-axis
+
+    Aesthetics options:
+
+    - ``line_color``: float or string. Specifies the color for the plot.
+        See ``Plot`` to see how to set color for the plots.
+        Default value is "Blue"
+
+    plot_implicit, by default, uses interval arithmetic to plot functions. If
+    the expression cannot be plotted using interval arithmetic, it defaults to
+    a generating a contour using a mesh grid of fixed number of points. By
+    setting adaptive to False, you can force plot_implicit to use the mesh
+    grid. The mesh grid method can be effective when adaptive plotting using
+    interval arithmetic, fails to plot with small line width.
+
+    Examples
+    ========
+
+    Plot expressions:
+
+    .. plot::
+        :context: reset
+        :format: doctest
+        :include-source: True
+
+        >>> from sympy import plot_implicit, symbols, Eq, And
+        >>> x, y = symbols('x y')
+
+    Without any ranges for the symbols in the expression:
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> p1 = plot_implicit(Eq(x**2 + y**2, 5))
+
+    With the range for the symbols:
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> p2 = plot_implicit(
+        ...     Eq(x**2 + y**2, 3), (x, -3, 3), (y, -3, 3))
+
+    With depth of recursion as argument:
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> p3 = plot_implicit(
+        ...     Eq(x**2 + y**2, 5), (x, -4, 4), (y, -4, 4), depth = 2)
+
+    Using mesh grid and not using adaptive meshing:
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> p4 = plot_implicit(
+        ...     Eq(x**2 + y**2, 5), (x, -5, 5), (y, -2, 2),
+        ...     adaptive=False)
+
+    Using mesh grid without using adaptive meshing with number of points
+    specified:
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> p5 = plot_implicit(
+        ...     Eq(x**2 + y**2, 5), (x, -5, 5), (y, -2, 2),
+        ...     adaptive=False, points=400)
+
+    Plotting regions:
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> p6 = plot_implicit(y > x**2)
+
+    Plotting Using boolean conjunctions:
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> p7 = plot_implicit(And(y > x, y > -x))
+
+    When plotting an expression with a single variable (y - 1, for example),
+    specify the x or the y variable explicitly:
+
+    .. plot::
+        :context: close-figs
+        :format: doctest
+        :include-source: True
+
+        >>> p8 = plot_implicit(y - 1, y_var=y)
+        >>> p9 = plot_implicit(x - 1, x_var=x)
+    """
+    has_equality = False  # Represents whether the expression contains an Equality,
+                     #GreaterThan or LessThan
+
+    def arg_expand(bool_expr):
+        """
+        Recursively expands the arguments of an Boolean Function
+        """
+        for arg in bool_expr.args:
+            if isinstance(arg, BooleanFunction):
+                arg_expand(arg)
+            elif isinstance(arg, Relational):
+                arg_list.append(arg)
+
+    arg_list = []
+    if isinstance(expr, BooleanFunction):
+        arg_expand(expr)
+
+    #Check whether there is an equality in the expression provided.
+        if any(isinstance(e, (Equality, GreaterThan, LessThan))
+               for e in arg_list):
+            has_equality = True
+
+    elif not isinstance(expr, Relational):
+        expr = Eq(expr, 0)
+        has_equality = True
+    elif isinstance(expr, (Equality, GreaterThan, LessThan)):
+        has_equality = True
+
+    xyvar = [i for i in (x_var, y_var) if i is not None]
+    free_symbols = expr.free_symbols
+    range_symbols = Tuple(*flatten(xyvar)).free_symbols
+    undeclared = free_symbols - range_symbols
+    if len(free_symbols & range_symbols) > 2:
+        raise NotImplementedError("Implicit plotting is not implemented for "
+                                  "more than 2 variables")
+
+    #Create default ranges if the range is not provided.
+    default_range = Tuple(-5, 5)
+    def _range_tuple(s):
+        if isinstance(s, Symbol):
+            return Tuple(s) + default_range
+        if len(s) == 3:
+            return Tuple(*s)
+        raise ValueError('symbol or `(symbol, min, max)` expected but got %s' % s)
+
+    if len(xyvar) == 0:
+        xyvar = list(_sort_gens(free_symbols))
+    var_start_end_x = _range_tuple(xyvar[0])
+    x = var_start_end_x[0]
+    if len(xyvar) != 2:
+        if x in undeclared or not undeclared:
+            xyvar.append(Dummy('f(%s)' % x.name))
+        else:
+            xyvar.append(undeclared.pop())
+    var_start_end_y = _range_tuple(xyvar[1])
+
+    #Check whether the depth is greater than 4 or less than 0.
+    if depth > 4:
+        depth = 4
+    elif depth < 0:
+        depth = 0
+
+    series_argument = ImplicitSeries(expr, var_start_end_x, var_start_end_y,
+                                    has_equality, adaptive, depth,
+                                    points, line_color)
+
+    #set the x and y limits
+    kwargs['xlim'] = tuple(float(x) for x in var_start_end_x[1:])
+    kwargs['ylim'] = tuple(float(y) for y in var_start_end_y[1:])
+    # set the x and y labels
+    kwargs.setdefault('xlabel', var_start_end_x[0])
+    kwargs.setdefault('ylabel', var_start_end_y[0])
+    p = Plot(series_argument, **kwargs)
+    if show:
+        p.show()
+    return p

llmeval-env/lib/python3.10/site-packages/sympy/plotting/pygletplot/__init__.py

@@ -0,0 +1,138 @@
+"""Plotting module that can plot 2D and 3D functions
+"""
+
+from sympy.utilities.decorator import doctest_depends_on
+
+@doctest_depends_on(modules=('pyglet',))
+def PygletPlot(*args, **kwargs):
+    """
+
+    Plot Examples
+    =============
+
+    See examples/advanced/pyglet_plotting.py for many more examples.
+
+    >>> from sympy.plotting.pygletplot import PygletPlot as Plot
+    >>> from sympy.abc import x, y, z
+
+    >>> Plot(x*y**3-y*x**3)
+    [0]: -x**3*y + x*y**3, 'mode=cartesian'
+
+    >>> p = Plot()
+    >>> p[1] = x*y
+    >>> p[1].color = z, (0.4,0.4,0.9), (0.9,0.4,0.4)
+
+    >>> p = Plot()
+    >>> p[1] =  x**2+y**2
+    >>> p[2] = -x**2-y**2
+
+
+    Variable Intervals
+    ==================
+
+    The basic format is [var, min, max, steps], but the
+    syntax is flexible and arguments left out are taken
+    from the defaults for the current coordinate mode:
+
+    >>> Plot(x**2) # implies [x,-5,5,100]
+    [0]: x**2, 'mode=cartesian'
+
+    >>> Plot(x**2, [], []) # [x,-1,1,40], [y,-1,1,40]
+    [0]: x**2, 'mode=cartesian'
+    >>> Plot(x**2-y**2, [100], [100]) # [x,-1,1,100], [y,-1,1,100]
+    [0]: x**2 - y**2, 'mode=cartesian'
+    >>> Plot(x**2, [x,-13,13,100])
+    [0]: x**2, 'mode=cartesian'
+    >>> Plot(x**2, [-13,13]) # [x,-13,13,100]
+    [0]: x**2, 'mode=cartesian'
+    >>> Plot(x**2, [x,-13,13]) # [x,-13,13,100]
+    [0]: x**2, 'mode=cartesian'
+    >>> Plot(1*x, [], [x], mode='cylindrical')
+    ... # [unbound_theta,0,2*Pi,40], [x,-1,1,20]
+    [0]: x, 'mode=cartesian'
+
+
+    Coordinate Modes
+    ================
+
+    Plot supports several curvilinear coordinate modes, and
+    they independent for each plotted function. You can specify
+    a coordinate mode explicitly with the 'mode' named argument,
+    but it can be automatically determined for Cartesian or
+    parametric plots, and therefore must only be specified for
+    polar, cylindrical, and spherical modes.
+
+    Specifically, Plot(function arguments) and Plot[n] =
+    (function arguments) will interpret your arguments as a
+    Cartesian plot if you provide one function and a parametric
+    plot if you provide two or three functions. Similarly, the
+    arguments will be interpreted as a curve if one variable is
+    used, and a surface if two are used.
+
+    Supported mode names by number of variables:
+
+    1: parametric, cartesian, polar
+    2: parametric, cartesian, cylindrical = polar, spherical
+
+    >>> Plot(1, mode='spherical')
+
+
+    Calculator-like Interface
+    =========================
+
+    >>> p = Plot(visible=False)
+    >>> f = x**2
+    >>> p[1] = f
+    >>> p[2] = f.diff(x)
+    >>> p[3] = f.diff(x).diff(x)
+    >>> p
+    [1]: x**2, 'mode=cartesian'
+    [2]: 2*x, 'mode=cartesian'
+    [3]: 2, 'mode=cartesian'
+    >>> p.show()
+    >>> p.clear()
+    >>> p
+    <blank plot>
+    >>> p[1] =  x**2+y**2
+    >>> p[1].style = 'solid'
+    >>> p[2] = -x**2-y**2
+    >>> p[2].style = 'wireframe'
+    >>> p[1].color = z, (0.4,0.4,0.9), (0.9,0.4,0.4)
+    >>> p[1].style = 'both'
+    >>> p[2].style = 'both'
+    >>> p.close()
+
+
+    Plot Window Keyboard Controls
+    =============================
+
+    Screen Rotation:
+        X,Y axis      Arrow Keys, A,S,D,W, Numpad 4,6,8,2
+        Z axis        Q,E, Numpad 7,9
+
+    Model Rotation:
+        Z axis        Z,C, Numpad 1,3
+
+    Zoom:             R,F, PgUp,PgDn, Numpad +,-
+
+    Reset Camera:     X, Numpad 5
+
+    Camera Presets:
+        XY            F1
+        XZ            F2
+        YZ            F3
+        Perspective   F4
+
+    Sensitivity Modifier: SHIFT
+
+    Axes Toggle:
+        Visible       F5
+        Colors        F6
+
+    Close Window:     ESCAPE
+
+    =============================
+    """
+
+    from sympy.plotting.pygletplot.plot import PygletPlot
+    return PygletPlot(*args, **kwargs)

llmeval-env/lib/python3.10/site-packages/sympy/plotting/pygletplot/color_scheme.py

@@ -0,0 +1,336 @@
+from sympy.core.basic import Basic
+from sympy.core.symbol import (Symbol, symbols)
+from sympy.utilities.lambdify import lambdify
+from .util import interpolate, rinterpolate, create_bounds, update_bounds
+from sympy.utilities.iterables import sift
+
+
+class ColorGradient:
+    colors = [0.4, 0.4, 0.4], [0.9, 0.9, 0.9]
+    intervals = 0.0, 1.0
+
+    def __init__(self, *args):
+        if len(args) == 2:
+            self.colors = list(args)
+            self.intervals = [0.0, 1.0]
+        elif len(args) > 0:
+            if len(args) % 2 != 0:
+                raise ValueError("len(args) should be even")
+            self.colors = [args[i] for i in range(1, len(args), 2)]
+            self.intervals = [args[i] for i in range(0, len(args), 2)]
+        assert len(self.colors) == len(self.intervals)
+
+    def copy(self):
+        c = ColorGradient()
+        c.colors = [e[::] for e in self.colors]
+        c.intervals = self.intervals[::]
+        return c
+
+    def _find_interval(self, v):
+        m = len(self.intervals)
+        i = 0
+        while i < m - 1 and self.intervals[i] <= v:
+            i += 1
+        return i
+
+    def _interpolate_axis(self, axis, v):
+        i = self._find_interval(v)
+        v = rinterpolate(self.intervals[i - 1], self.intervals[i], v)
+        return interpolate(self.colors[i - 1][axis], self.colors[i][axis], v)
+
+    def __call__(self, r, g, b):
+        c = self._interpolate_axis
+        return c(0, r), c(1, g), c(2, b)
+
+default_color_schemes = {}  # defined at the bottom of this file
+
+
+class ColorScheme:
+
+    def __init__(self, *args, **kwargs):
+        self.args = args
+        self.f, self.gradient = None, ColorGradient()
+
+        if len(args) == 1 and not isinstance(args[0], Basic) and callable(args[0]):
+            self.f = args[0]
+        elif len(args) == 1 and isinstance(args[0], str):
+            if args[0] in default_color_schemes:
+                cs = default_color_schemes[args[0]]
+                self.f, self.gradient = cs.f, cs.gradient.copy()
+            else:
+                self.f = lambdify('x,y,z,u,v', args[0])
+        else:
+            self.f, self.gradient = self._interpret_args(args)
+        self._test_color_function()
+        if not isinstance(self.gradient, ColorGradient):
+            raise ValueError("Color gradient not properly initialized. "
+                             "(Not a ColorGradient instance.)")
+
+    def _interpret_args(self, args):
+        f, gradient = None, self.gradient
+        atoms, lists = self._sort_args(args)
+        s = self._pop_symbol_list(lists)
+        s = self._fill_in_vars(s)
+
+        # prepare the error message for lambdification failure
+        f_str = ', '.join(str(fa) for fa in atoms)
+        s_str = (str(sa) for sa in s)
+        s_str = ', '.join(sa for sa in s_str if sa.find('unbound') < 0)
+        f_error = ValueError("Could not interpret arguments "
+                             "%s as functions of %s." % (f_str, s_str))
+
+        # try to lambdify args
+        if len(atoms) == 1:
+            fv = atoms[0]
+            try:
+                f = lambdify(s, [fv, fv, fv])
+            except TypeError:
+                raise f_error
+
+        elif len(atoms) == 3:
+            fr, fg, fb = atoms
+            try:
+                f = lambdify(s, [fr, fg, fb])
+            except TypeError:
+                raise f_error
+
+        else:
+            raise ValueError("A ColorScheme must provide 1 or 3 "
+                             "functions in x, y, z, u, and/or v.")
+
+        # try to intrepret any given color information
+        if len(lists) == 0:
+            gargs = []
+
+        elif len(lists) == 1:
+            gargs = lists[0]
+
+        elif len(lists) == 2:
+            try:
+                (r1, g1, b1), (r2, g2, b2) = lists
+            except TypeError:
+                raise ValueError("If two color arguments are given, "
+                                 "they must be given in the format "
+                                 "(r1, g1, b1), (r2, g2, b2).")
+            gargs = lists
+
+        elif len(lists) == 3:
+            try:
+                (r1, r2), (g1, g2), (b1, b2) = lists
+            except Exception:
+                raise ValueError("If three color arguments are given, "
+                                 "they must be given in the format "
+                                 "(r1, r2), (g1, g2), (b1, b2). To create "
+                                 "a multi-step gradient, use the syntax "
+                                 "[0, colorStart, step1, color1, ..., 1, "
+                                 "colorEnd].")
+            gargs = [[r1, g1, b1], [r2, g2, b2]]
+
+        else:
+            raise ValueError("Don't know what to do with collection "
+                             "arguments %s." % (', '.join(str(l) for l in lists)))
+
+        if gargs:
+            try:
+                gradient = ColorGradient(*gargs)
+            except Exception as ex:
+                raise ValueError(("Could not initialize a gradient "
+                                  "with arguments %s. Inner "
+                                  "exception: %s") % (gargs, str(ex)))
+
+        return f, gradient
+
+    def _pop_symbol_list(self, lists):
+        symbol_lists = []
+        for l in lists:
+            mark = True
+            for s in l:
+                if s is not None and not isinstance(s, Symbol):
+                    mark = False
+                    break
+            if mark:
+                lists.remove(l)
+                symbol_lists.append(l)
+        if len(symbol_lists) == 1:
+            return symbol_lists[0]
+        elif len(symbol_lists) == 0:
+            return []
+        else:
+            raise ValueError("Only one list of Symbols "
+                             "can be given for a color scheme.")
+
+    def _fill_in_vars(self, args):
+        defaults = symbols('x,y,z,u,v')
+        v_error = ValueError("Could not find what to plot.")
+        if len(args) == 0:
+            return defaults
+        if not isinstance(args, (tuple, list)):
+            raise v_error
+        if len(args) == 0:
+            return defaults
+        for s in args:
+            if s is not None and not isinstance(s, Symbol):
+                raise v_error
+        # when vars are given explicitly, any vars
+        # not given are marked 'unbound' as to not
+        # be accidentally used in an expression
+        vars = [Symbol('unbound%i' % (i)) for i in range(1, 6)]
+        # interpret as t
+        if len(args) == 1:
+            vars[3] = args[0]
+        # interpret as u,v
+        elif len(args) == 2:
+            if args[0] is not None:
+                vars[3] = args[0]
+            if args[1] is not None:
+                vars[4] = args[1]
+        # interpret as x,y,z
+        elif len(args) >= 3:
+            # allow some of x,y,z to be
+            # left unbound if not given
+            if args[0] is not None:
+                vars[0] = args[0]
+            if args[1] is not None:
+                vars[1] = args[1]
+            if args[2] is not None:
+                vars[2] = args[2]
+            # interpret the rest as t
+            if len(args) >= 4:
+                vars[3] = args[3]
+                # ...or u,v
+                if len(args) >= 5:
+                    vars[4] = args[4]
+        return vars
+
+    def _sort_args(self, args):
+        lists, atoms = sift(args,
+            lambda a: isinstance(a, (tuple, list)), binary=True)
+        return atoms, lists
+
+    def _test_color_function(self):
+        if not callable(self.f):
+            raise ValueError("Color function is not callable.")
+        try:
+            result = self.f(0, 0, 0, 0, 0)
+            if len(result) != 3:
+                raise ValueError("length should be equal to 3")
+        except TypeError:
+            raise ValueError("Color function needs to accept x,y,z,u,v, "
+                             "as arguments even if it doesn't use all of them.")
+        except AssertionError:
+            raise ValueError("Color function needs to return 3-tuple r,g,b.")
+        except Exception:
+            pass  # color function probably not valid at 0,0,0,0,0
+
+    def __call__(self, x, y, z, u, v):
+        try:
+            return self.f(x, y, z, u, v)
+        except Exception:
+            return None
+
+    def apply_to_curve(self, verts, u_set, set_len=None, inc_pos=None):
+        """
+        Apply this color scheme to a
+        set of vertices over a single
+        independent variable u.
+        """
+        bounds = create_bounds()
+        cverts = []
+        if callable(set_len):
+            set_len(len(u_set)*2)
+        # calculate f() = r,g,b for each vert
+        # and find the min and max for r,g,b
+        for _u in range(len(u_set)):
+            if verts[_u] is None:
+                cverts.append(None)
+            else:
+                x, y, z = verts[_u]
+                u, v = u_set[_u], None
+                c = self(x, y, z, u, v)
+                if c is not None:
+                    c = list(c)
+                    update_bounds(bounds, c)
+                cverts.append(c)
+            if callable(inc_pos):
+                inc_pos()
+        # scale and apply gradient
+        for _u in range(len(u_set)):
+            if cverts[_u] is not None:
+                for _c in range(3):
+                    # scale from [f_min, f_max] to [0,1]
+                    cverts[_u][_c] = rinterpolate(bounds[_c][0], bounds[_c][1],
+                                                  cverts[_u][_c])
+                # apply gradient
+                cverts[_u] = self.gradient(*cverts[_u])
+            if callable(inc_pos):
+                inc_pos()
+        return cverts
+
+    def apply_to_surface(self, verts, u_set, v_set, set_len=None, inc_pos=None):
+        """
+        Apply this color scheme to a
+        set of vertices over two
+        independent variables u and v.
+        """
+        bounds = create_bounds()
+        cverts = []
+        if callable(set_len):
+            set_len(len(u_set)*len(v_set)*2)
+        # calculate f() = r,g,b for each vert
+        # and find the min and max for r,g,b
+        for _u in range(len(u_set)):
+            column = []
+            for _v in range(len(v_set)):
+                if verts[_u][_v] is None:
+                    column.append(None)
+                else:
+                    x, y, z = verts[_u][_v]
+                    u, v = u_set[_u], v_set[_v]
+                    c = self(x, y, z, u, v)
+                    if c is not None:
+                        c = list(c)
+                        update_bounds(bounds, c)
+                    column.append(c)
+                if callable(inc_pos):
+                    inc_pos()
+            cverts.append(column)
+        # scale and apply gradient
+        for _u in range(len(u_set)):
+            for _v in range(len(v_set)):
+                if cverts[_u][_v] is not None:
+                    # scale from [f_min, f_max] to [0,1]
+                    for _c in range(3):
+                        cverts[_u][_v][_c] = rinterpolate(bounds[_c][0],
+                                             bounds[_c][1], cverts[_u][_v][_c])
+                    # apply gradient
+                    cverts[_u][_v] = self.gradient(*cverts[_u][_v])
+                if callable(inc_pos):
+                    inc_pos()
+        return cverts
+
+    def str_base(self):
+        return ", ".join(str(a) for a in self.args)
+
+    def __repr__(self):
+        return "%s" % (self.str_base())
+
+
+x, y, z, t, u, v = symbols('x,y,z,t,u,v')
+
+default_color_schemes['rainbow'] = ColorScheme(z, y, x)
+default_color_schemes['zfade'] = ColorScheme(z, (0.4, 0.4, 0.97),
+                                             (0.97, 0.4, 0.4), (None, None, z))
+default_color_schemes['zfade3'] = ColorScheme(z, (None, None, z),
+                                              [0.00, (0.2, 0.2, 1.0),
+                                               0.35, (0.2, 0.8, 0.4),
+                                               0.50, (0.3, 0.9, 0.3),
+                                               0.65, (0.4, 0.8, 0.2),
+                                               1.00, (1.0, 0.2, 0.2)])
+
+default_color_schemes['zfade4'] = ColorScheme(z, (None, None, z),
+                                              [0.0, (0.3, 0.3, 1.0),
+                                               0.30, (0.3, 1.0, 0.3),
+                                               0.55, (0.95, 1.0, 0.2),
+                                               0.65, (1.0, 0.95, 0.2),
+                                               0.85, (1.0, 0.7, 0.2),
+                                               1.0, (1.0, 0.3, 0.2)])

llmeval-env/lib/python3.10/site-packages/sympy/plotting/pygletplot/managed_window.py

@@ -0,0 +1,106 @@
+from pyglet.window import Window
+from pyglet.clock import Clock
+
+from threading import Thread, Lock
+
+gl_lock = Lock()
+
+
+class ManagedWindow(Window):
+    """
+    A pyglet window with an event loop which executes automatically
+    in a separate thread. Behavior is added by creating a subclass
+    which overrides setup, update, and/or draw.
+    """
+    fps_limit = 30
+    default_win_args = {"width": 600,
+                            "height": 500,
+                            "vsync": False,
+                            "resizable": True}
+
+    def __init__(self, **win_args):
+        """
+        It is best not to override this function in the child
+        class, unless you need to take additional arguments.
+        Do any OpenGL initialization calls in setup().
+        """
+
+        # check if this is run from the doctester
+        if win_args.get('runfromdoctester', False):
+            return
+
+        self.win_args = dict(self.default_win_args, **win_args)
+        self.Thread = Thread(target=self.__event_loop__)
+        self.Thread.start()
+
+    def __event_loop__(self, **win_args):
+        """
+        The event loop thread function. Do not override or call
+        directly (it is called by __init__).
+        """
+        gl_lock.acquire()
+        try:
+            try:
+                super().__init__(**self.win_args)
+                self.switch_to()
+                self.setup()
+            except Exception as e:
+                print("Window initialization failed: %s" % (str(e)))
+                self.has_exit = True
+        finally:
+            gl_lock.release()
+
+        clock = Clock()
+        clock.fps_limit = self.fps_limit
+        while not self.has_exit:
+            dt = clock.tick()
+            gl_lock.acquire()
+            try:
+                try:
+                    self.switch_to()
+                    self.dispatch_events()
+                    self.clear()
+                    self.update(dt)
+                    self.draw()
+                    self.flip()
+                except Exception as e:
+                    print("Uncaught exception in event loop: %s" % str(e))
+                    self.has_exit = True
+            finally:
+                gl_lock.release()
+        super().close()
+
+    def close(self):
+        """
+        Closes the window.
+        """
+        self.has_exit = True
+
+    def setup(self):
+        """
+        Called once before the event loop begins.
+        Override this method in a child class. This
+        is the best place to put things like OpenGL
+        initialization calls.
+        """
+        pass
+
+    def update(self, dt):
+        """
+        Called before draw during each iteration of
+        the event loop. dt is the elapsed time in
+        seconds since the last update. OpenGL rendering
+        calls are best put in draw() rather than here.
+        """
+        pass
+
+    def draw(self):
+        """
+        Called after update during each iteration of
+        the event loop. Put OpenGL rendering calls
+        here.
+        """
+        pass
+
+if __name__ == '__main__':
+    ManagedWindow()

llmeval-env/lib/python3.10/site-packages/sympy/plotting/pygletplot/plot.py

@@ -0,0 +1,464 @@
+from threading import RLock
+
+# it is sufficient to import "pyglet" here once
+try:
+    import pyglet.gl as pgl
+except ImportError:
+    raise ImportError("pyglet is required for plotting.\n "
+                      "visit https://pyglet.org/")
+
+from sympy.core.numbers import Integer
+from sympy.external.gmpy import SYMPY_INTS
+from sympy.geometry.entity import GeometryEntity
+from sympy.plotting.pygletplot.plot_axes import PlotAxes
+from sympy.plotting.pygletplot.plot_mode import PlotMode
+from sympy.plotting.pygletplot.plot_object import PlotObject
+from sympy.plotting.pygletplot.plot_window import PlotWindow
+from sympy.plotting.pygletplot.util import parse_option_string
+from sympy.utilities.decorator import doctest_depends_on
+from sympy.utilities.iterables import is_sequence
+
+from time import sleep
+from os import getcwd, listdir
+
+import ctypes
+
+@doctest_depends_on(modules=('pyglet',))
+class PygletPlot:
+    """
+    Plot Examples
+    =============
+
+    See examples/advanced/pyglet_plotting.py for many more examples.
+
+    >>> from sympy.plotting.pygletplot import PygletPlot as Plot
+    >>> from sympy.abc import x, y, z
+
+    >>> Plot(x*y**3-y*x**3)
+    [0]: -x**3*y + x*y**3, 'mode=cartesian'
+
+    >>> p = Plot()
+    >>> p[1] = x*y
+    >>> p[1].color = z, (0.4,0.4,0.9), (0.9,0.4,0.4)
+
+    >>> p = Plot()
+    >>> p[1] =  x**2+y**2
+    >>> p[2] = -x**2-y**2
+
+
+    Variable Intervals
+    ==================
+
+    The basic format is [var, min, max, steps], but the
+    syntax is flexible and arguments left out are taken
+    from the defaults for the current coordinate mode:
+
+    >>> Plot(x**2) # implies [x,-5,5,100]
+    [0]: x**2, 'mode=cartesian'
+    >>> Plot(x**2, [], []) # [x,-1,1,40], [y,-1,1,40]
+    [0]: x**2, 'mode=cartesian'
+    >>> Plot(x**2-y**2, [100], [100]) # [x,-1,1,100], [y,-1,1,100]
+    [0]: x**2 - y**2, 'mode=cartesian'
+    >>> Plot(x**2, [x,-13,13,100])
+    [0]: x**2, 'mode=cartesian'
+    >>> Plot(x**2, [-13,13]) # [x,-13,13,100]
+    [0]: x**2, 'mode=cartesian'
+    >>> Plot(x**2, [x,-13,13]) # [x,-13,13,10]
+    [0]: x**2, 'mode=cartesian'
+    >>> Plot(1*x, [], [x], mode='cylindrical')
+    ... # [unbound_theta,0,2*Pi,40], [x,-1,1,20]
+    [0]: x, 'mode=cartesian'
+
+
+    Coordinate Modes
+    ================
+
+    Plot supports several curvilinear coordinate modes, and
+    they independent for each plotted function. You can specify
+    a coordinate mode explicitly with the 'mode' named argument,
+    but it can be automatically determined for Cartesian or
+    parametric plots, and therefore must only be specified for
+    polar, cylindrical, and spherical modes.
+
+    Specifically, Plot(function arguments) and Plot[n] =
+    (function arguments) will interpret your arguments as a
+    Cartesian plot if you provide one function and a parametric
+    plot if you provide two or three functions. Similarly, the
+    arguments will be interpreted as a curve if one variable is
+    used, and a surface if two are used.
+
+    Supported mode names by number of variables:
+
+    1: parametric, cartesian, polar
+    2: parametric, cartesian, cylindrical = polar, spherical
+
+    >>> Plot(1, mode='spherical')
+
+
+    Calculator-like Interface
+    =========================
+
+    >>> p = Plot(visible=False)
+    >>> f = x**2
+    >>> p[1] = f
+    >>> p[2] = f.diff(x)
+    >>> p[3] = f.diff(x).diff(x)
+    >>> p
+    [1]: x**2, 'mode=cartesian'
+    [2]: 2*x, 'mode=cartesian'
+    [3]: 2, 'mode=cartesian'
+    >>> p.show()
+    >>> p.clear()
+    >>> p
+    <blank plot>
+    >>> p[1] =  x**2+y**2
+    >>> p[1].style = 'solid'
+    >>> p[2] = -x**2-y**2
+    >>> p[2].style = 'wireframe'
+    >>> p[1].color = z, (0.4,0.4,0.9), (0.9,0.4,0.4)
+    >>> p[1].style = 'both'
+    >>> p[2].style = 'both'
+    >>> p.close()
+
+
+    Plot Window Keyboard Controls
+    =============================
+
+    Screen Rotation:
+        X,Y axis      Arrow Keys, A,S,D,W, Numpad 4,6,8,2
+        Z axis        Q,E, Numpad 7,9
+
+    Model Rotation:
+        Z axis        Z,C, Numpad 1,3
+
+    Zoom:             R,F, PgUp,PgDn, Numpad +,-
+
+    Reset Camera:     X, Numpad 5
+
+    Camera Presets:
+        XY            F1
+        XZ            F2
+        YZ            F3
+        Perspective   F4
+
+    Sensitivity Modifier: SHIFT
+
+    Axes Toggle:
+        Visible       F5
+        Colors        F6
+
+    Close Window:     ESCAPE
+
+    =============================
+
+    """
+
+    @doctest_depends_on(modules=('pyglet',))
+    def __init__(self, *fargs, **win_args):
+        """
+        Positional Arguments
+        ====================
+
+        Any given positional arguments are used to
+        initialize a plot function at index 1. In
+        other words...
+
+        >>> from sympy.plotting.pygletplot import PygletPlot as Plot
+        >>> from sympy.abc import x
+        >>> p = Plot(x**2, visible=False)
+
+        ...is equivalent to...
+
+        >>> p = Plot(visible=False)
+        >>> p[1] = x**2
+
+        Note that in earlier versions of the plotting
+        module, you were able to specify multiple
+        functions in the initializer. This functionality
+        has been dropped in favor of better automatic
+        plot plot_mode detection.
+
+
+        Named Arguments
+        ===============
+
+        axes
+            An option string of the form
+            "key1=value1; key2 = value2" which
+            can use the following options:
+
+            style = ordinate
+                none OR frame OR box OR ordinate
+
+            stride = 0.25
+                val OR (val_x, val_y, val_z)
+
+            overlay = True (draw on top of plot)
+                True OR False
+
+            colored = False (False uses Black,
+                             True uses colors
+                             R,G,B = X,Y,Z)
+                True OR False
+
+            label_axes = False (display axis names
+                                at endpoints)
+                True OR False
+
+        visible = True (show immediately
+            True OR False
+
+
+        The following named arguments are passed as
+        arguments to window initialization:
+
+        antialiasing = True
+            True OR False
+
+        ortho = False
+            True OR False
+
+        invert_mouse_zoom = False
+            True OR False
+
+        """
+        # Register the plot modes
+        from . import plot_modes # noqa
+
+        self._win_args = win_args
+        self._window = None
+
+        self._render_lock = RLock()
+
+        self._functions = {}
+        self._pobjects = []
+        self._screenshot = ScreenShot(self)
+
+        axe_options = parse_option_string(win_args.pop('axes', ''))
+        self.axes = PlotAxes(**axe_options)
+        self._pobjects.append(self.axes)
+
+        self[0] = fargs
+        if win_args.get('visible', True):
+            self.show()
+
+    ## Window Interfaces
+
+    def show(self):
+        """
+        Creates and displays a plot window, or activates it
+        (gives it focus) if it has already been created.
+        """
+        if self._window and not self._window.has_exit:
+            self._window.activate()
+        else:
+            self._win_args['visible'] = True
+            self.axes.reset_resources()
+
+            #if hasattr(self, '_doctest_depends_on'):
+            #    self._win_args['runfromdoctester'] = True
+
+            self._window = PlotWindow(self, **self._win_args)
+
+    def close(self):
+        """
+        Closes the plot window.
+        """
+        if self._window:
+            self._window.close()
+
+    def saveimage(self, outfile=None, format='', size=(600, 500)):
+        """
+        Saves a screen capture of the plot window to an
+        image file.
+
+        If outfile is given, it can either be a path
+        or a file object. Otherwise a png image will
+        be saved to the current working directory.
+        If the format is omitted, it is determined from
+        the filename extension.
+        """
+        self._screenshot.save(outfile, format, size)
+
+    ## Function List Interfaces
+
+    def clear(self):
+        """
+        Clears the function list of this plot.
+        """
+        self._render_lock.acquire()
+        self._functions = {}
+        self.adjust_all_bounds()
+        self._render_lock.release()
+
+    def __getitem__(self, i):
+        """
+        Returns the function at position i in the
+        function list.
+        """
+        return self._functions[i]
+
+    def __setitem__(self, i, args):
+        """
+        Parses and adds a PlotMode to the function
+        list.
+        """
+        if not (isinstance(i, (SYMPY_INTS, Integer)) and i >= 0):
+            raise ValueError("Function index must "
+                             "be an integer >= 0.")
+
+        if isinstance(args, PlotObject):
+            f = args
+        else:
+            if (not is_sequence(args)) or isinstance(args, GeometryEntity):
+                args = [args]
+            if len(args) == 0:
+                return  # no arguments given
+            kwargs = {"bounds_callback": self.adjust_all_bounds}
+            f = PlotMode(*args, **kwargs)
+
+        if f:
+            self._render_lock.acquire()
+            self._functions[i] = f
+            self._render_lock.release()
+        else:
+            raise ValueError("Failed to parse '%s'."
+                    % ', '.join(str(a) for a in args))
+
+    def __delitem__(self, i):
+        """
+        Removes the function in the function list at
+        position i.
+        """
+        self._render_lock.acquire()
+        del self._functions[i]
+        self.adjust_all_bounds()
+        self._render_lock.release()
+
+    def firstavailableindex(self):
+        """
+        Returns the first unused index in the function list.
+        """
+        i = 0
+        self._render_lock.acquire()
+        while i in self._functions:
+            i += 1
+        self._render_lock.release()
+        return i
+
+    def append(self, *args):
+        """
+        Parses and adds a PlotMode to the function
+        list at the first available index.
+        """
+        self.__setitem__(self.firstavailableindex(), args)
+
+    def __len__(self):
+        """
+        Returns the number of functions in the function list.
+        """
+        return len(self._functions)
+
+    def __iter__(self):
+        """
+        Allows iteration of the function list.
+        """
+        return self._functions.itervalues()
+
+    def __repr__(self):
+        return str(self)
+
+    def __str__(self):
+        """
+        Returns a string containing a new-line separated
+        list of the functions in the function list.
+        """
+        s = ""
+        if len(self._functions) == 0:
+            s += "<blank plot>"
+        else:
+            self._render_lock.acquire()
+            s += "\n".join(["%s[%i]: %s" % ("", i, str(self._functions[i]))
+                            for i in self._functions])
+            self._render_lock.release()
+        return s
+
+    def adjust_all_bounds(self):
+        self._render_lock.acquire()
+        self.axes.reset_bounding_box()
+        for f in self._functions:
+            self.axes.adjust_bounds(self._functions[f].bounds)
+        self._render_lock.release()
+
+    def wait_for_calculations(self):
+        sleep(0)
+        self._render_lock.acquire()
+        for f in self._functions:
+            a = self._functions[f]._get_calculating_verts
+            b = self._functions[f]._get_calculating_cverts
+            while a() or b():
+                sleep(0)
+        self._render_lock.release()
+
+class ScreenShot:
+    def __init__(self, plot):
+        self._plot = plot
+        self.screenshot_requested = False
+        self.outfile = None
+        self.format = ''
+        self.invisibleMode = False
+        self.flag = 0
+
+    def __bool__(self):
+        return self.screenshot_requested
+
+    def _execute_saving(self):
+        if self.flag < 3:
+            self.flag += 1
+            return
+
+        size_x, size_y = self._plot._window.get_size()
+        size = size_x*size_y*4*ctypes.sizeof(ctypes.c_ubyte)
+        image = ctypes.create_string_buffer(size)
+        pgl.glReadPixels(0, 0, size_x, size_y, pgl.GL_RGBA, pgl.GL_UNSIGNED_BYTE, image)
+        from PIL import Image
+        im = Image.frombuffer('RGBA', (size_x, size_y),
+                              image.raw, 'raw', 'RGBA', 0, 1)
+        im.transpose(Image.FLIP_TOP_BOTTOM).save(self.outfile, self.format)
+
+        self.flag = 0
+        self.screenshot_requested = False
+        if self.invisibleMode:
+            self._plot._window.close()
+
+    def save(self, outfile=None, format='', size=(600, 500)):
+        self.outfile = outfile
+        self.format = format
+        self.size = size
+        self.screenshot_requested = True
+
+        if not self._plot._window or self._plot._window.has_exit:
+            self._plot._win_args['visible'] = False
+
+            self._plot._win_args['width'] = size[0]
+            self._plot._win_args['height'] = size[1]
+
+            self._plot.axes.reset_resources()
+            self._plot._window = PlotWindow(self._plot, **self._plot._win_args)
+            self.invisibleMode = True
+
+        if self.outfile is None:
+            self.outfile = self._create_unique_path()
+            print(self.outfile)
+
+    def _create_unique_path(self):
+        cwd = getcwd()
+        l = listdir(cwd)
+        path = ''
+        i = 0
+        while True:
+            if not 'plot_%s.png' % i in l:
+                path = cwd + '/plot_%s.png' % i
+                break
+            i += 1
+        return path

llmeval-env/lib/python3.10/site-packages/sympy/plotting/pygletplot/plot_axes.py

@@ -0,0 +1,251 @@
+import pyglet.gl as pgl
+from pyglet import font
+
+from sympy.core import S
+from sympy.plotting.pygletplot.plot_object import PlotObject
+from sympy.plotting.pygletplot.util import billboard_matrix, dot_product, \
+        get_direction_vectors, strided_range, vec_mag, vec_sub
+from sympy.utilities.iterables import is_sequence
+
+
+class PlotAxes(PlotObject):
+
+    def __init__(self, *args,
+            style='', none=None, frame=None, box=None, ordinate=None,
+            stride=0.25,
+            visible='', overlay='', colored='', label_axes='', label_ticks='',
+            tick_length=0.1,
+            font_face='Arial', font_size=28,
+            **kwargs):
+        # initialize style parameter
+        style = style.lower()
+
+        # allow alias kwargs to override style kwarg
+        if none is not None:
+            style = 'none'
+        if frame is not None:
+            style = 'frame'
+        if box is not None:
+            style = 'box'
+        if ordinate is not None:
+            style = 'ordinate'
+
+        if style in ['', 'ordinate']:
+            self._render_object = PlotAxesOrdinate(self)
+        elif style in ['frame', 'box']:
+            self._render_object = PlotAxesFrame(self)
+        elif style in ['none']:
+            self._render_object = None
+        else:
+            raise ValueError(("Unrecognized axes style %s.") % (style))
+
+        # initialize stride parameter
+        try:
+            stride = eval(stride)
+        except TypeError:
+            pass
+        if is_sequence(stride):
+            if len(stride) != 3:
+                raise ValueError("length should be equal to 3")
+            self._stride = stride
+        else:
+            self._stride = [stride, stride, stride]
+        self._tick_length = float(tick_length)
+
+        # setup bounding box and ticks
+        self._origin = [0, 0, 0]
+        self.reset_bounding_box()
+
+        def flexible_boolean(input, default):
+            if input in [True, False]:
+                return input
+            if input in ('f', 'F', 'false', 'False'):
+                return False
+            if input in ('t', 'T', 'true', 'True'):
+                return True
+            return default
+
+        # initialize remaining parameters
+        self.visible = flexible_boolean(kwargs, True)
+        self._overlay = flexible_boolean(overlay, True)
+        self._colored = flexible_boolean(colored, False)
+        self._label_axes = flexible_boolean(label_axes, False)
+        self._label_ticks = flexible_boolean(label_ticks, True)
+
+        # setup label font
+        self.font_face = font_face
+        self.font_size = font_size
+
+        # this is also used to reinit the
+        # font on window close/reopen
+        self.reset_resources()
+
+    def reset_resources(self):
+        self.label_font = None
+
+    def reset_bounding_box(self):
+        self._bounding_box = [[None, None], [None, None], [None, None]]
+        self._axis_ticks = [[], [], []]
+
+    def draw(self):
+        if self._render_object:
+            pgl.glPushAttrib(pgl.GL_ENABLE_BIT | pgl.GL_POLYGON_BIT | pgl.GL_DEPTH_BUFFER_BIT)
+            if self._overlay:
+                pgl.glDisable(pgl.GL_DEPTH_TEST)
+            self._render_object.draw()
+            pgl.glPopAttrib()
+
+    def adjust_bounds(self, child_bounds):
+        b = self._bounding_box
+        c = child_bounds
+        for i in range(3):
+            if abs(c[i][0]) is S.Infinity or abs(c[i][1]) is S.Infinity:
+                continue
+            b[i][0] = c[i][0] if b[i][0] is None else min([b[i][0], c[i][0]])
+            b[i][1] = c[i][1] if b[i][1] is None else max([b[i][1], c[i][1]])
+            self._bounding_box = b
+            self._recalculate_axis_ticks(i)
+
+    def _recalculate_axis_ticks(self, axis):
+        b = self._bounding_box
+        if b[axis][0] is None or b[axis][1] is None:
+            self._axis_ticks[axis] = []
+        else:
+            self._axis_ticks[axis] = strided_range(b[axis][0], b[axis][1],
+                                                   self._stride[axis])
+
+    def toggle_visible(self):
+        self.visible = not self.visible
+
+    def toggle_colors(self):
+        self._colored = not self._colored
+
+
+class PlotAxesBase(PlotObject):
+
+    def __init__(self, parent_axes):
+        self._p = parent_axes
+
+    def draw(self):
+        color = [([0.2, 0.1, 0.3], [0.2, 0.1, 0.3], [0.2, 0.1, 0.3]),
+                 ([0.9, 0.3, 0.5], [0.5, 1.0, 0.5], [0.3, 0.3, 0.9])][self._p._colored]
+        self.draw_background(color)
+        self.draw_axis(2, color[2])
+        self.draw_axis(1, color[1])
+        self.draw_axis(0, color[0])
+
+    def draw_background(self, color):
+        pass  # optional
+
+    def draw_axis(self, axis, color):
+        raise NotImplementedError()
+
+    def draw_text(self, text, position, color, scale=1.0):
+        if len(color) == 3:
+            color = (color[0], color[1], color[2], 1.0)
+
+        if self._p.label_font is None:
+            self._p.label_font = font.load(self._p.font_face,
+                                           self._p.font_size,
+                                           bold=True, italic=False)
+
+        label = font.Text(self._p.label_font, text,
+                          color=color,
+                          valign=font.Text.BASELINE,
+                          halign=font.Text.CENTER)
+
+        pgl.glPushMatrix()
+        pgl.glTranslatef(*position)
+        billboard_matrix()
+        scale_factor = 0.005 * scale
+        pgl.glScalef(scale_factor, scale_factor, scale_factor)
+        pgl.glColor4f(0, 0, 0, 0)
+        label.draw()
+        pgl.glPopMatrix()
+
+    def draw_line(self, v, color):
+        o = self._p._origin
+        pgl.glBegin(pgl.GL_LINES)
+        pgl.glColor3f(*color)
+        pgl.glVertex3f(v[0][0] + o[0], v[0][1] + o[1], v[0][2] + o[2])
+        pgl.glVertex3f(v[1][0] + o[0], v[1][1] + o[1], v[1][2] + o[2])
+        pgl.glEnd()
+
+
+class PlotAxesOrdinate(PlotAxesBase):
+
+    def __init__(self, parent_axes):
+        super().__init__(parent_axes)
+
+    def draw_axis(self, axis, color):
+        ticks = self._p._axis_ticks[axis]
+        radius = self._p._tick_length / 2.0
+        if len(ticks) < 2:
+            return
+
+        # calculate the vector for this axis
+        axis_lines = [[0, 0, 0], [0, 0, 0]]
+        axis_lines[0][axis], axis_lines[1][axis] = ticks[0], ticks[-1]
+        axis_vector = vec_sub(axis_lines[1], axis_lines[0])
+
+        # calculate angle to the z direction vector
+        pos_z = get_direction_vectors()[2]
+        d = abs(dot_product(axis_vector, pos_z))
+        d = d / vec_mag(axis_vector)
+
+        # don't draw labels if we're looking down the axis
+        labels_visible = abs(d - 1.0) > 0.02
+
+        # draw the ticks and labels
+        for tick in ticks:
+            self.draw_tick_line(axis, color, radius, tick, labels_visible)
+
+        # draw the axis line and labels
+        self.draw_axis_line(axis, color, ticks[0], ticks[-1], labels_visible)
+
+    def draw_axis_line(self, axis, color, a_min, a_max, labels_visible):
+        axis_line = [[0, 0, 0], [0, 0, 0]]
+        axis_line[0][axis], axis_line[1][axis] = a_min, a_max
+        self.draw_line(axis_line, color)
+        if labels_visible:
+            self.draw_axis_line_labels(axis, color, axis_line)
+
+    def draw_axis_line_labels(self, axis, color, axis_line):
+        if not self._p._label_axes:
+            return
+        axis_labels = [axis_line[0][::], axis_line[1][::]]
+        axis_labels[0][axis] -= 0.3
+        axis_labels[1][axis] += 0.3
+        a_str = ['X', 'Y', 'Z'][axis]
+        self.draw_text("-" + a_str, axis_labels[0], color)
+        self.draw_text("+" + a_str, axis_labels[1], color)
+
+    def draw_tick_line(self, axis, color, radius, tick, labels_visible):
+        tick_axis = {0: 1, 1: 0, 2: 1}[axis]
+        tick_line = [[0, 0, 0], [0, 0, 0]]
+        tick_line[0][axis] = tick_line[1][axis] = tick
+        tick_line[0][tick_axis], tick_line[1][tick_axis] = -radius, radius
+        self.draw_line(tick_line, color)
+        if labels_visible:
+            self.draw_tick_line_label(axis, color, radius, tick)
+
+    def draw_tick_line_label(self, axis, color, radius, tick):
+        if not self._p._label_axes:
+            return
+        tick_label_vector = [0, 0, 0]
+        tick_label_vector[axis] = tick
+        tick_label_vector[{0: 1, 1: 0, 2: 1}[axis]] = [-1, 1, 1][
+            axis] * radius * 3.5
+        self.draw_text(str(tick), tick_label_vector, color, scale=0.5)
+
+
+class PlotAxesFrame(PlotAxesBase):
+
+    def __init__(self, parent_axes):
+        super().__init__(parent_axes)
+
+    def draw_background(self, color):
+        pass
+
+    def draw_axis(self, axis, color):
+        raise NotImplementedError()

llmeval-env/lib/python3.10/site-packages/sympy/plotting/pygletplot/plot_camera.py

@@ -0,0 +1,128 @@
+import pyglet.gl as pgl
+from sympy.plotting.pygletplot.plot_rotation import get_spherical_rotatation
+from sympy.plotting.pygletplot.util import get_model_matrix, model_to_screen, \
+                                            screen_to_model, vec_subs
+
+
+class PlotCamera:
+
+    min_dist = 0.05
+    max_dist = 500.0
+
+    min_ortho_dist = 100.0
+    max_ortho_dist = 10000.0
+
+    _default_dist = 6.0
+    _default_ortho_dist = 600.0
+
+    rot_presets = {
+        'xy': (0, 0, 0),
+        'xz': (-90, 0, 0),
+        'yz': (0, 90, 0),
+        'perspective': (-45, 0, -45)
+    }
+
+    def __init__(self, window, ortho=False):
+        self.window = window
+        self.axes = self.window.plot.axes
+        self.ortho = ortho
+        self.reset()
+
+    def init_rot_matrix(self):
+        pgl.glPushMatrix()
+        pgl.glLoadIdentity()
+        self._rot = get_model_matrix()
+        pgl.glPopMatrix()
+
+    def set_rot_preset(self, preset_name):
+        self.init_rot_matrix()
+        try:
+            r = self.rot_presets[preset_name]
+        except AttributeError:
+            raise ValueError(
+                "%s is not a valid rotation preset." % preset_name)
+        try:
+            self.euler_rotate(r[0], 1, 0, 0)
+            self.euler_rotate(r[1], 0, 1, 0)
+            self.euler_rotate(r[2], 0, 0, 1)
+        except AttributeError:
+            pass
+
+    def reset(self):
+        self._dist = 0.0
+        self._x, self._y = 0.0, 0.0
+        self._rot = None
+        if self.ortho:
+            self._dist = self._default_ortho_dist
+        else:
+            self._dist = self._default_dist
+        self.init_rot_matrix()
+
+    def mult_rot_matrix(self, rot):
+        pgl.glPushMatrix()
+        pgl.glLoadMatrixf(rot)
+        pgl.glMultMatrixf(self._rot)
+        self._rot = get_model_matrix()
+        pgl.glPopMatrix()
+
+    def setup_projection(self):
+        pgl.glMatrixMode(pgl.GL_PROJECTION)
+        pgl.glLoadIdentity()
+        if self.ortho:
+            # yep, this is pseudo ortho (don't tell anyone)
+            pgl.gluPerspective(
+                0.3, float(self.window.width)/float(self.window.height),
+                self.min_ortho_dist - 0.01, self.max_ortho_dist + 0.01)
+        else:
+            pgl.gluPerspective(
+                30.0, float(self.window.width)/float(self.window.height),
+                self.min_dist - 0.01, self.max_dist + 0.01)
+        pgl.glMatrixMode(pgl.GL_MODELVIEW)
+
+    def _get_scale(self):
+        return 1.0, 1.0, 1.0
+
+    def apply_transformation(self):
+        pgl.glLoadIdentity()
+        pgl.glTranslatef(self._x, self._y, -self._dist)
+        if self._rot is not None:
+            pgl.glMultMatrixf(self._rot)
+        pgl.glScalef(*self._get_scale())
+
+    def spherical_rotate(self, p1, p2, sensitivity=1.0):
+        mat = get_spherical_rotatation(p1, p2, self.window.width,
+                                       self.window.height, sensitivity)
+        if mat is not None:
+            self.mult_rot_matrix(mat)
+
+    def euler_rotate(self, angle, x, y, z):
+        pgl.glPushMatrix()
+        pgl.glLoadMatrixf(self._rot)
+        pgl.glRotatef(angle, x, y, z)
+        self._rot = get_model_matrix()
+        pgl.glPopMatrix()
+
+    def zoom_relative(self, clicks, sensitivity):
+
+        if self.ortho:
+            dist_d = clicks * sensitivity * 50.0
+            min_dist = self.min_ortho_dist
+            max_dist = self.max_ortho_dist
+        else:
+            dist_d = clicks * sensitivity
+            min_dist = self.min_dist
+            max_dist = self.max_dist
+
+        new_dist = (self._dist - dist_d)
+        if (clicks < 0 and new_dist < max_dist) or new_dist > min_dist:
+            self._dist = new_dist
+
+    def mouse_translate(self, x, y, dx, dy):
+        pgl.glPushMatrix()
+        pgl.glLoadIdentity()
+        pgl.glTranslatef(0, 0, -self._dist)
+        z = model_to_screen(0, 0, 0)[2]
+        d = vec_subs(screen_to_model(x, y, z), screen_to_model(x - dx, y - dy, z))
+        pgl.glPopMatrix()
+        self._x += d[0]
+        self._y += d[1]

llmeval-env/lib/python3.10/site-packages/sympy/plotting/pygletplot/plot_controller.py

@@ -0,0 +1,218 @@
+from pyglet.window import key
+from pyglet.window.mouse import LEFT, RIGHT, MIDDLE
+from sympy.plotting.pygletplot.util import get_direction_vectors, get_basis_vectors
+
+
+class PlotController:
+
+    normal_mouse_sensitivity = 4.0
+    modified_mouse_sensitivity = 1.0
+
+    normal_key_sensitivity = 160.0
+    modified_key_sensitivity = 40.0
+
+    keymap = {
+        key.LEFT: 'left',
+        key.A: 'left',
+        key.NUM_4: 'left',
+
+        key.RIGHT: 'right',
+        key.D: 'right',
+        key.NUM_6: 'right',
+
+        key.UP: 'up',
+        key.W: 'up',
+        key.NUM_8: 'up',
+
+        key.DOWN: 'down',
+        key.S: 'down',
+        key.NUM_2: 'down',
+
+        key.Z: 'rotate_z_neg',
+        key.NUM_1: 'rotate_z_neg',
+
+        key.C: 'rotate_z_pos',
+        key.NUM_3: 'rotate_z_pos',
+
+        key.Q: 'spin_left',
+        key.NUM_7: 'spin_left',
+        key.E: 'spin_right',
+        key.NUM_9: 'spin_right',
+
+        key.X: 'reset_camera',
+        key.NUM_5: 'reset_camera',
+
+        key.NUM_ADD: 'zoom_in',
+        key.PAGEUP: 'zoom_in',
+        key.R: 'zoom_in',
+
+        key.NUM_SUBTRACT: 'zoom_out',
+        key.PAGEDOWN: 'zoom_out',
+        key.F: 'zoom_out',
+
+        key.RSHIFT: 'modify_sensitivity',
+        key.LSHIFT: 'modify_sensitivity',
+
+        key.F1: 'rot_preset_xy',
+        key.F2: 'rot_preset_xz',
+        key.F3: 'rot_preset_yz',
+        key.F4: 'rot_preset_perspective',
+
+        key.F5: 'toggle_axes',
+        key.F6: 'toggle_axe_colors',
+
+        key.F8: 'save_image'
+    }
+
+    def __init__(self, window, *, invert_mouse_zoom=False, **kwargs):
+        self.invert_mouse_zoom = invert_mouse_zoom
+        self.window = window
+        self.camera = window.camera
+        self.action = {
+            # Rotation around the view Y (up) vector
+            'left': False,
+            'right': False,
+            # Rotation around the view X vector
+            'up': False,
+            'down': False,
+            # Rotation around the view Z vector
+            'spin_left': False,
+            'spin_right': False,
+            # Rotation around the model Z vector
+            'rotate_z_neg': False,
+            'rotate_z_pos': False,
+            # Reset to the default rotation
+            'reset_camera': False,
+            # Performs camera z-translation
+            'zoom_in': False,
+            'zoom_out': False,
+            # Use alternative sensitivity (speed)
+            'modify_sensitivity': False,
+            # Rotation presets
+            'rot_preset_xy': False,
+            'rot_preset_xz': False,
+            'rot_preset_yz': False,
+            'rot_preset_perspective': False,
+            # axes
+            'toggle_axes': False,
+            'toggle_axe_colors': False,
+            # screenshot
+            'save_image': False
+        }
+
+    def update(self, dt):
+        z = 0
+        if self.action['zoom_out']:
+            z -= 1
+        if self.action['zoom_in']:
+            z += 1
+        if z != 0:
+            self.camera.zoom_relative(z/10.0, self.get_key_sensitivity()/10.0)
+
+        dx, dy, dz = 0, 0, 0
+        if self.action['left']:
+            dx -= 1
+        if self.action['right']:
+            dx += 1
+        if self.action['up']:
+            dy -= 1
+        if self.action['down']:
+            dy += 1
+        if self.action['spin_left']:
+            dz += 1
+        if self.action['spin_right']:
+            dz -= 1
+
+        if not self.is_2D():
+            if dx != 0:
+                self.camera.euler_rotate(dx*dt*self.get_key_sensitivity(),
+                                         *(get_direction_vectors()[1]))
+            if dy != 0:
+                self.camera.euler_rotate(dy*dt*self.get_key_sensitivity(),
+                                         *(get_direction_vectors()[0]))
+            if dz != 0:
+                self.camera.euler_rotate(dz*dt*self.get_key_sensitivity(),
+                                         *(get_direction_vectors()[2]))
+        else:
+            self.camera.mouse_translate(0, 0, dx*dt*self.get_key_sensitivity(),
+                                        -dy*dt*self.get_key_sensitivity())
+
+        rz = 0
+        if self.action['rotate_z_neg'] and not self.is_2D():
+            rz -= 1
+        if self.action['rotate_z_pos'] and not self.is_2D():
+            rz += 1
+
+        if rz != 0:
+            self.camera.euler_rotate(rz*dt*self.get_key_sensitivity(),
+                                     *(get_basis_vectors()[2]))
+
+        if self.action['reset_camera']:
+            self.camera.reset()
+
+        if self.action['rot_preset_xy']:
+            self.camera.set_rot_preset('xy')
+        if self.action['rot_preset_xz']:
+            self.camera.set_rot_preset('xz')
+        if self.action['rot_preset_yz']:
+            self.camera.set_rot_preset('yz')
+        if self.action['rot_preset_perspective']:
+            self.camera.set_rot_preset('perspective')
+
+        if self.action['toggle_axes']:
+            self.action['toggle_axes'] = False
+            self.camera.axes.toggle_visible()
+
+        if self.action['toggle_axe_colors']:
+            self.action['toggle_axe_colors'] = False
+            self.camera.axes.toggle_colors()
+
+        if self.action['save_image']:
+            self.action['save_image'] = False
+            self.window.plot.saveimage()
+
+        return True
+
+    def get_mouse_sensitivity(self):
+        if self.action['modify_sensitivity']:
+            return self.modified_mouse_sensitivity
+        else:
+            return self.normal_mouse_sensitivity
+
+    def get_key_sensitivity(self):
+        if self.action['modify_sensitivity']:
+            return self.modified_key_sensitivity
+        else:
+            return self.normal_key_sensitivity
+
+    def on_key_press(self, symbol, modifiers):
+        if symbol in self.keymap:
+            self.action[self.keymap[symbol]] = True
+
+    def on_key_release(self, symbol, modifiers):
+        if symbol in self.keymap:
+            self.action[self.keymap[symbol]] = False
+
+    def on_mouse_drag(self, x, y, dx, dy, buttons, modifiers):
+        if buttons & LEFT:
+            if self.is_2D():
+                self.camera.mouse_translate(x, y, dx, dy)
+            else:
+                self.camera.spherical_rotate((x - dx, y - dy), (x, y),
+                                             self.get_mouse_sensitivity())
+        if buttons & MIDDLE:
+            self.camera.zoom_relative([1, -1][self.invert_mouse_zoom]*dy,
+                                      self.get_mouse_sensitivity()/20.0)
+        if buttons & RIGHT:
+            self.camera.mouse_translate(x, y, dx, dy)
+
+    def on_mouse_scroll(self, x, y, dx, dy):
+        self.camera.zoom_relative([1, -1][self.invert_mouse_zoom]*dy,
+                                  self.get_mouse_sensitivity())
+
+    def is_2D(self):
+        functions = self.window.plot._functions
+        for i in functions:
+            if len(functions[i].i_vars) > 1 or len(functions[i].d_vars) > 2:
+                return False
+        return True

llmeval-env/lib/python3.10/site-packages/sympy/plotting/pygletplot/plot_curve.py

@@ -0,0 +1,82 @@
+import pyglet.gl as pgl
+from sympy.core import S
+from sympy.plotting.pygletplot.plot_mode_base import PlotModeBase
+
+
+class PlotCurve(PlotModeBase):
+
+    style_override = 'wireframe'
+
+    def _on_calculate_verts(self):
+        self.t_interval = self.intervals[0]
+        self.t_set = list(self.t_interval.frange())
+        self.bounds = [[S.Infinity, S.NegativeInfinity, 0],
+                       [S.Infinity, S.NegativeInfinity, 0],
+                       [S.Infinity, S.NegativeInfinity, 0]]
+        evaluate = self._get_evaluator()
+
+        self._calculating_verts_pos = 0.0
+        self._calculating_verts_len = float(self.t_interval.v_len)
+
+        self.verts = []
+        b = self.bounds
+        for t in self.t_set:
+            try:
+                _e = evaluate(t)    # calculate vertex
+            except (NameError, ZeroDivisionError):
+                _e = None
+            if _e is not None:      # update bounding box
+                for axis in range(3):
+                    b[axis][0] = min([b[axis][0], _e[axis]])
+                    b[axis][1] = max([b[axis][1], _e[axis]])
+            self.verts.append(_e)
+            self._calculating_verts_pos += 1.0
+
+        for axis in range(3):
+            b[axis][2] = b[axis][1] - b[axis][0]
+            if b[axis][2] == 0.0:
+                b[axis][2] = 1.0
+
+        self.push_wireframe(self.draw_verts(False))
+
+    def _on_calculate_cverts(self):
+        if not self.verts or not self.color:
+            return
+
+        def set_work_len(n):
+            self._calculating_cverts_len = float(n)
+
+        def inc_work_pos():
+            self._calculating_cverts_pos += 1.0
+        set_work_len(1)
+        self._calculating_cverts_pos = 0
+        self.cverts = self.color.apply_to_curve(self.verts,
+                                                self.t_set,
+                                                set_len=set_work_len,
+                                                inc_pos=inc_work_pos)
+        self.push_wireframe(self.draw_verts(True))
+
+    def calculate_one_cvert(self, t):
+        vert = self.verts[t]
+        return self.color(vert[0], vert[1], vert[2],
+                          self.t_set[t], None)
+
+    def draw_verts(self, use_cverts):
+        def f():
+            pgl.glBegin(pgl.GL_LINE_STRIP)
+            for t in range(len(self.t_set)):
+                p = self.verts[t]
+                if p is None:
+                    pgl.glEnd()
+                    pgl.glBegin(pgl.GL_LINE_STRIP)
+                    continue
+                if use_cverts:
+                    c = self.cverts[t]
+                    if c is None:
+                        c = (0, 0, 0)
+                    pgl.glColor3f(*c)
+                else:
+                    pgl.glColor3f(*self.default_wireframe_color)
+                pgl.glVertex3f(*p)
+            pgl.glEnd()
+        return f

llmeval-env/lib/python3.10/site-packages/sympy/plotting/pygletplot/plot_interval.py

@@ -0,0 +1,181 @@
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.core.sympify import sympify
+from sympy.core.numbers import Integer
+
+
+class PlotInterval:
+    """
+    """
+    _v, _v_min, _v_max, _v_steps = None, None, None, None
+
+    def require_all_args(f):
+        def check(self, *args, **kwargs):
+            for g in [self._v, self._v_min, self._v_max, self._v_steps]:
+                if g is None:
+                    raise ValueError("PlotInterval is incomplete.")
+            return f(self, *args, **kwargs)
+        return check
+
+    def __init__(self, *args):
+        if len(args) == 1:
+            if isinstance(args[0], PlotInterval):
+                self.fill_from(args[0])
+                return
+            elif isinstance(args[0], str):
+                try:
+                    args = eval(args[0])
+                except TypeError:
+                    s_eval_error = "Could not interpret string %s."
+                    raise ValueError(s_eval_error % (args[0]))
+            elif isinstance(args[0], (tuple, list)):
+                args = args[0]
+            else:
+                raise ValueError("Not an interval.")
+        if not isinstance(args, (tuple, list)) or len(args) > 4:
+            f_error = "PlotInterval must be a tuple or list of length 4 or less."
+            raise ValueError(f_error)
+
+        args = list(args)
+        if len(args) > 0 and (args[0] is None or isinstance(args[0], Symbol)):
+            self.v = args.pop(0)
+        if len(args) in [2, 3]:
+            self.v_min = args.pop(0)
+            self.v_max = args.pop(0)
+            if len(args) == 1:
+                self.v_steps = args.pop(0)
+        elif len(args) == 1:
+            self.v_steps = args.pop(0)
+
+    def get_v(self):
+        return self._v
+
+    def set_v(self, v):
+        if v is None:
+            self._v = None
+            return
+        if not isinstance(v, Symbol):
+            raise ValueError("v must be a SymPy Symbol.")
+        self._v = v
+
+    def get_v_min(self):
+        return self._v_min
+
+    def set_v_min(self, v_min):
+        if v_min is None:
+            self._v_min = None
+            return
+        try:
+            self._v_min = sympify(v_min)
+            float(self._v_min.evalf())
+        except TypeError:
+            raise ValueError("v_min could not be interpreted as a number.")
+
+    def get_v_max(self):
+        return self._v_max
+
+    def set_v_max(self, v_max):
+        if v_max is None:
+            self._v_max = None
+            return
+        try:
+            self._v_max = sympify(v_max)
+            float(self._v_max.evalf())
+        except TypeError:
+            raise ValueError("v_max could not be interpreted as a number.")
+
+    def get_v_steps(self):
+        return self._v_steps
+
+    def set_v_steps(self, v_steps):
+        if v_steps is None:
+            self._v_steps = None
+            return
+        if isinstance(v_steps, int):
+            v_steps = Integer(v_steps)
+        elif not isinstance(v_steps, Integer):
+            raise ValueError("v_steps must be an int or SymPy Integer.")
+        if v_steps <= S.Zero:
+            raise ValueError("v_steps must be positive.")
+        self._v_steps = v_steps
+
+    @require_all_args
+    def get_v_len(self):
+        return self.v_steps + 1
+
+    v = property(get_v, set_v)
+    v_min = property(get_v_min, set_v_min)
+    v_max = property(get_v_max, set_v_max)
+    v_steps = property(get_v_steps, set_v_steps)
+    v_len = property(get_v_len)
+
+    def fill_from(self, b):
+        if b.v is not None:
+            self.v = b.v
+        if b.v_min is not None:
+            self.v_min = b.v_min
+        if b.v_max is not None:
+            self.v_max = b.v_max
+        if b.v_steps is not None:
+            self.v_steps = b.v_steps
+
+    @staticmethod
+    def try_parse(*args):
+        """
+        Returns a PlotInterval if args can be interpreted
+        as such, otherwise None.
+        """
+        if len(args) == 1 and isinstance(args[0], PlotInterval):
+            return args[0]
+        try:
+            return PlotInterval(*args)
+        except ValueError:
+            return None
+
+    def _str_base(self):
+        return ",".join([str(self.v), str(self.v_min),
+                         str(self.v_max), str(self.v_steps)])
+
+    def __repr__(self):
+        """
+        A string representing the interval in class constructor form.
+        """
+        return "PlotInterval(%s)" % (self._str_base())
+
+    def __str__(self):
+        """
+        A string representing the interval in list form.
+        """
+        return "[%s]" % (self._str_base())
+
+    @require_all_args
+    def assert_complete(self):
+        pass
+
+    @require_all_args
+    def vrange(self):
+        """
+        Yields v_steps+1 SymPy numbers ranging from
+        v_min to v_max.
+        """
+        d = (self.v_max - self.v_min) / self.v_steps
+        for i in range(self.v_steps + 1):
+            a = self.v_min + (d * Integer(i))
+            yield a
+
+    @require_all_args
+    def vrange2(self):
+        """
+        Yields v_steps pairs of SymPy numbers ranging from
+        (v_min, v_min + step) to (v_max - step, v_max).
+        """
+        d = (self.v_max - self.v_min) / self.v_steps
+        a = self.v_min + (d * S.Zero)
+        for i in range(self.v_steps):
+            b = self.v_min + (d * Integer(i + 1))
+            yield a, b
+            a = b
+
+    def frange(self):
+        for i in self.vrange():
+            yield float(i.evalf())

llmeval-env/lib/python3.10/site-packages/sympy/plotting/pygletplot/plot_mode.py

@@ -0,0 +1,400 @@
+from .plot_interval import PlotInterval
+from .plot_object import PlotObject
+from .util import parse_option_string
+from sympy.core.symbol import Symbol
+from sympy.core.sympify import sympify
+from sympy.geometry.entity import GeometryEntity
+from sympy.utilities.iterables import is_sequence
+
+
+class PlotMode(PlotObject):
+    """
+    Grandparent class for plotting
+    modes. Serves as interface for
+    registration, lookup, and init
+    of modes.
+
+    To create a new plot mode,
+    inherit from PlotModeBase
+    or one of its children, such
+    as PlotSurface or PlotCurve.
+    """
+
+    ## Class-level attributes
+    ## used to register and lookup
+    ## plot modes. See PlotModeBase
+    ## for descriptions and usage.
+
+    i_vars, d_vars = '', ''
+    intervals = []
+    aliases = []
+    is_default = False
+
+    ## Draw is the only method here which
+    ## is meant to be overridden in child
+    ## classes, and PlotModeBase provides
+    ## a base implementation.
+    def draw(self):
+        raise NotImplementedError()
+
+    ## Everything else in this file has to
+    ## do with registration and retrieval
+    ## of plot modes. This is where I've
+    ## hidden much of the ugliness of automatic
+    ## plot mode divination...
+
+    ## Plot mode registry data structures
+    _mode_alias_list = []
+    _mode_map = {
+        1: {1: {}, 2: {}},
+        2: {1: {}, 2: {}},
+        3: {1: {}, 2: {}},
+    }  # [d][i][alias_str]: class
+    _mode_default_map = {
+        1: {},
+        2: {},
+        3: {},
+    }  # [d][i]: class
+    _i_var_max, _d_var_max = 2, 3
+
+    def __new__(cls, *args, **kwargs):
+        """
+        This is the function which interprets
+        arguments given to Plot.__init__ and
+        Plot.__setattr__. Returns an initialized
+        instance of the appropriate child class.
+        """
+
+        newargs, newkwargs = PlotMode._extract_options(args, kwargs)
+        mode_arg = newkwargs.get('mode', '')
+
+        # Interpret the arguments
+        d_vars, intervals = PlotMode._interpret_args(newargs)
+        i_vars = PlotMode._find_i_vars(d_vars, intervals)
+        i, d = max([len(i_vars), len(intervals)]), len(d_vars)
+
+        # Find the appropriate mode
+        subcls = PlotMode._get_mode(mode_arg, i, d)
+
+        # Create the object
+        o = object.__new__(subcls)
+
+        # Do some setup for the mode instance
+        o.d_vars = d_vars
+        o._fill_i_vars(i_vars)
+        o._fill_intervals(intervals)
+        o.options = newkwargs
+
+        return o
+
+    @staticmethod
+    def _get_mode(mode_arg, i_var_count, d_var_count):
+        """
+        Tries to return an appropriate mode class.
+        Intended to be called only by __new__.
+
+        mode_arg
+            Can be a string or a class. If it is a
+            PlotMode subclass, it is simply returned.
+            If it is a string, it can an alias for
+            a mode or an empty string. In the latter
+            case, we try to find a default mode for
+            the i_var_count and d_var_count.
+
+        i_var_count
+            The number of independent variables
+            needed to evaluate the d_vars.
+
+        d_var_count
+            The number of dependent variables;
+            usually the number of functions to
+            be evaluated in plotting.
+
+        For example, a Cartesian function y = f(x) has
+        one i_var (x) and one d_var (y). A parametric
+        form x,y,z = f(u,v), f(u,v), f(u,v) has two
+        two i_vars (u,v) and three d_vars (x,y,z).
+        """
+        # if the mode_arg is simply a PlotMode class,
+        # check that the mode supports the numbers
+        # of independent and dependent vars, then
+        # return it
+        try:
+            m = None
+            if issubclass(mode_arg, PlotMode):
+                m = mode_arg
+        except TypeError:
+            pass
+        if m:
+            if not m._was_initialized:
+                raise ValueError(("To use unregistered plot mode %s "
+                                  "you must first call %s._init_mode().")
+                                 % (m.__name__, m.__name__))
+            if d_var_count != m.d_var_count:
+                raise ValueError(("%s can only plot functions "
+                                  "with %i dependent variables.")
+                                 % (m.__name__,
+                                     m.d_var_count))
+            if i_var_count > m.i_var_count:
+                raise ValueError(("%s cannot plot functions "
+                                  "with more than %i independent "
+                                  "variables.")
+                                 % (m.__name__,
+                                     m.i_var_count))
+            return m
+        # If it is a string, there are two possibilities.
+        if isinstance(mode_arg, str):
+            i, d = i_var_count, d_var_count
+            if i > PlotMode._i_var_max:
+                raise ValueError(var_count_error(True, True))
+            if d > PlotMode._d_var_max:
+                raise ValueError(var_count_error(False, True))
+            # If the string is '', try to find a suitable
+            # default mode
+            if not mode_arg:
+                return PlotMode._get_default_mode(i, d)
+            # Otherwise, interpret the string as a mode
+            # alias (e.g. 'cartesian', 'parametric', etc)
+            else:
+                return PlotMode._get_aliased_mode(mode_arg, i, d)
+        else:
+            raise ValueError("PlotMode argument must be "
+                             "a class or a string")
+
+    @staticmethod
+    def _get_default_mode(i, d, i_vars=-1):
+        if i_vars == -1:
+            i_vars = i
+        try:
+            return PlotMode._mode_default_map[d][i]
+        except KeyError:
+            # Keep looking for modes in higher i var counts
+            # which support the given d var count until we
+            # reach the max i_var count.
+            if i < PlotMode._i_var_max:
+                return PlotMode._get_default_mode(i + 1, d, i_vars)
+            else:
+                raise ValueError(("Couldn't find a default mode "
+                                  "for %i independent and %i "
+                                  "dependent variables.") % (i_vars, d))
+
+    @staticmethod
+    def _get_aliased_mode(alias, i, d, i_vars=-1):
+        if i_vars == -1:
+            i_vars = i
+        if alias not in PlotMode._mode_alias_list:
+            raise ValueError(("Couldn't find a mode called"
+                              " %s. Known modes: %s.")
+                             % (alias, ", ".join(PlotMode._mode_alias_list)))
+        try:
+            return PlotMode._mode_map[d][i][alias]
+        except TypeError:
+            # Keep looking for modes in higher i var counts
+            # which support the given d var count and alias
+            # until we reach the max i_var count.
+            if i < PlotMode._i_var_max:
+                return PlotMode._get_aliased_mode(alias, i + 1, d, i_vars)
+            else:
+                raise ValueError(("Couldn't find a %s mode "
+                                  "for %i independent and %i "
+                                  "dependent variables.")
+                                 % (alias, i_vars, d))
+
+    @classmethod
+    def _register(cls):
+        """
+        Called once for each user-usable plot mode.
+        For Cartesian2D, it is invoked after the
+        class definition: Cartesian2D._register()
+        """
+        name = cls.__name__
+        cls._init_mode()
+
+        try:
+            i, d = cls.i_var_count, cls.d_var_count
+            # Add the mode to _mode_map under all
+            # given aliases
+            for a in cls.aliases:
+                if a not in PlotMode._mode_alias_list:
+                    # Also track valid aliases, so
+                    # we can quickly know when given
+                    # an invalid one in _get_mode.
+                    PlotMode._mode_alias_list.append(a)
+                PlotMode._mode_map[d][i][a] = cls
+            if cls.is_default:
+                # If this mode was marked as the
+                # default for this d,i combination,
+                # also set that.
+                PlotMode._mode_default_map[d][i] = cls
+
+        except Exception as e:
+            raise RuntimeError(("Failed to register "
+                              "plot mode %s. Reason: %s")
+                               % (name, (str(e))))
+
+    @classmethod
+    def _init_mode(cls):
+        """
+        Initializes the plot mode based on
+        the 'mode-specific parameters' above.
+        Only intended to be called by
+        PlotMode._register(). To use a mode without
+        registering it, you can directly call
+        ModeSubclass._init_mode().
+        """
+        def symbols_list(symbol_str):
+            return [Symbol(s) for s in symbol_str]
+
+        # Convert the vars strs into
+        # lists of symbols.
+        cls.i_vars = symbols_list(cls.i_vars)
+        cls.d_vars = symbols_list(cls.d_vars)
+
+        # Var count is used often, calculate
+        # it once here
+        cls.i_var_count = len(cls.i_vars)
+        cls.d_var_count = len(cls.d_vars)
+
+        if cls.i_var_count > PlotMode._i_var_max:
+            raise ValueError(var_count_error(True, False))
+        if cls.d_var_count > PlotMode._d_var_max:
+            raise ValueError(var_count_error(False, False))
+
+        # Try to use first alias as primary_alias
+        if len(cls.aliases) > 0:
+            cls.primary_alias = cls.aliases[0]
+        else:
+            cls.primary_alias = cls.__name__
+
+        di = cls.intervals
+        if len(di) != cls.i_var_count:
+            raise ValueError("Plot mode must provide a "
+                             "default interval for each i_var.")
+        for i in range(cls.i_var_count):
+            # default intervals must be given [min,max,steps]
+            # (no var, but they must be in the same order as i_vars)
+            if len(di[i]) != 3:
+                raise ValueError("length should be equal to 3")
+
+            # Initialize an incomplete interval,
+            # to later be filled with a var when
+            # the mode is instantiated.
+            di[i] = PlotInterval(None, *di[i])
+
+        # To prevent people from using modes
+        # without these required fields set up.
+        cls._was_initialized = True
+
+    _was_initialized = False
+
+    ## Initializer Helper Methods
+
+    @staticmethod
+    def _find_i_vars(functions, intervals):
+        i_vars = []
+
+        # First, collect i_vars in the
+        # order they are given in any
+        # intervals.
+        for i in intervals:
+            if i.v is None:
+                continue
+            elif i.v in i_vars:
+                raise ValueError(("Multiple intervals given "
+                                  "for %s.") % (str(i.v)))
+            i_vars.append(i.v)
+
+        # Then, find any remaining
+        # i_vars in given functions
+        # (aka d_vars)
+        for f in functions:
+            for a in f.free_symbols:
+                if a not in i_vars:
+                    i_vars.append(a)
+
+        return i_vars
+
+    def _fill_i_vars(self, i_vars):
+        # copy default i_vars
+        self.i_vars = [Symbol(str(i)) for i in self.i_vars]
+        # replace with given i_vars
+        for i in range(len(i_vars)):
+            self.i_vars[i] = i_vars[i]
+
+    def _fill_intervals(self, intervals):
+        # copy default intervals
+        self.intervals = [PlotInterval(i) for i in self.intervals]
+        # track i_vars used so far
+        v_used = []
+        # fill copy of default
+        # intervals with given info
+        for i in range(len(intervals)):
+            self.intervals[i].fill_from(intervals[i])
+            if self.intervals[i].v is not None:
+                v_used.append(self.intervals[i].v)
+        # Find any orphan intervals and
+        # assign them i_vars
+        for i in range(len(self.intervals)):
+            if self.intervals[i].v is None:
+                u = [v for v in self.i_vars if v not in v_used]
+                if len(u) == 0:
+                    raise ValueError("length should not be equal to 0")
+                self.intervals[i].v = u[0]
+                v_used.append(u[0])
+
+    @staticmethod
+    def _interpret_args(args):
+        interval_wrong_order = "PlotInterval %s was given before any function(s)."
+        interpret_error = "Could not interpret %s as a function or interval."
+
+        functions, intervals = [], []
+        if isinstance(args[0], GeometryEntity):
+            for coords in list(args[0].arbitrary_point()):
+                functions.append(coords)
+            intervals.append(PlotInterval.try_parse(args[0].plot_interval()))
+        else:
+            for a in args:
+                i = PlotInterval.try_parse(a)
+                if i is not None:
+                    if len(functions) == 0:
+                        raise ValueError(interval_wrong_order % (str(i)))
+                    else:
+                        intervals.append(i)
+                else:
+                    if is_sequence(a, include=str):
+                        raise ValueError(interpret_error % (str(a)))
+                    try:
+                        f = sympify(a)
+                        functions.append(f)
+                    except TypeError:
+                        raise ValueError(interpret_error % str(a))
+
+        return functions, intervals
+
+    @staticmethod
+    def _extract_options(args, kwargs):
+        newkwargs, newargs = {}, []
+        for a in args:
+            if isinstance(a, str):
+                newkwargs = dict(newkwargs, **parse_option_string(a))
+            else:
+                newargs.append(a)
+        newkwargs = dict(newkwargs, **kwargs)
+        return newargs, newkwargs
+
+
+def var_count_error(is_independent, is_plotting):
+    """
+    Used to format an error message which differs
+    slightly in 4 places.
+    """
+    if is_plotting:
+        v = "Plotting"
+    else:
+        v = "Registering plot modes"
+    if is_independent:
+        n, s = PlotMode._i_var_max, "independent"
+    else:
+        n, s = PlotMode._d_var_max, "dependent"
+    return ("%s with more than %i %s variables "
+            "is not supported.") % (v, n, s)

llmeval-env/lib/python3.10/site-packages/sympy/plotting/pygletplot/plot_mode_base.py

@@ -0,0 +1,378 @@
+import pyglet.gl as pgl
+from sympy.core import S
+from sympy.plotting.pygletplot.color_scheme import ColorScheme
+from sympy.plotting.pygletplot.plot_mode import PlotMode
+from sympy.utilities.iterables import is_sequence
+from time import sleep
+from threading import Thread, Event, RLock
+import warnings
+
+
+class PlotModeBase(PlotMode):
+    """
+    Intended parent class for plotting
+    modes. Provides base functionality
+    in conjunction with its parent,
+    PlotMode.
+    """
+
+    ##
+    ## Class-Level Attributes
+    ##
+
+    """
+    The following attributes are meant
+    to be set at the class level, and serve
+    as parameters to the plot mode registry
+    (in PlotMode). See plot_modes.py for
+    concrete examples.
+    """
+
+    """
+    i_vars
+        'x' for Cartesian2D
+        'xy' for Cartesian3D
+        etc.
+
+    d_vars
+        'y' for Cartesian2D
+        'r' for Polar
+        etc.
+    """
+    i_vars, d_vars = '', ''
+
+    """
+    intervals
+        Default intervals for each i_var, and in the
+        same order. Specified [min, max, steps].
+        No variable can be given (it is bound later).
+    """
+    intervals = []
+
+    """
+    aliases
+        A list of strings which can be used to
+        access this mode.
+        'cartesian' for Cartesian2D and Cartesian3D
+        'polar' for Polar
+        'cylindrical', 'polar' for Cylindrical
+
+        Note that _init_mode chooses the first alias
+        in the list as the mode's primary_alias, which
+        will be displayed to the end user in certain
+        contexts.
+    """
+    aliases = []
+
+    """
+    is_default
+        Whether to set this mode as the default
+        for arguments passed to PlotMode() containing
+        the same number of d_vars as this mode and
+        at most the same number of i_vars.
+    """
+    is_default = False
+
+    """
+    All of the above attributes are defined in PlotMode.
+    The following ones are specific to PlotModeBase.
+    """
+
+    """
+    A list of the render styles. Do not modify.
+    """
+    styles = {'wireframe': 1, 'solid': 2, 'both': 3}
+
+    """
+    style_override
+        Always use this style if not blank.
+    """
+    style_override = ''
+
+    """
+    default_wireframe_color
+    default_solid_color
+        Can be used when color is None or being calculated.
+        Used by PlotCurve and PlotSurface, but not anywhere
+        in PlotModeBase.
+    """
+
+    default_wireframe_color = (0.85, 0.85, 0.85)
+    default_solid_color = (0.6, 0.6, 0.9)
+    default_rot_preset = 'xy'
+
+    ##
+    ## Instance-Level Attributes
+    ##
+
+    ## 'Abstract' member functions
+    def _get_evaluator(self):
+        if self.use_lambda_eval:
+            try:
+                e = self._get_lambda_evaluator()
+                return e
+            except Exception:
+                warnings.warn("\nWarning: creating lambda evaluator failed. "
+                       "Falling back on SymPy subs evaluator.")
+        return self._get_sympy_evaluator()
+
+    def _get_sympy_evaluator(self):
+        raise NotImplementedError()
+
+    def _get_lambda_evaluator(self):
+        raise NotImplementedError()
+
+    def _on_calculate_verts(self):
+        raise NotImplementedError()
+
+    def _on_calculate_cverts(self):
+        raise NotImplementedError()
+
+    ## Base member functions
+    def __init__(self, *args, bounds_callback=None, **kwargs):
+        self.verts = []
+        self.cverts = []
+        self.bounds = [[S.Infinity, S.NegativeInfinity, 0],
+                       [S.Infinity, S.NegativeInfinity, 0],
+                       [S.Infinity, S.NegativeInfinity, 0]]
+        self.cbounds = [[S.Infinity, S.NegativeInfinity, 0],
+                        [S.Infinity, S.NegativeInfinity, 0],
+                        [S.Infinity, S.NegativeInfinity, 0]]
+
+        self._draw_lock = RLock()
+
+        self._calculating_verts = Event()
+        self._calculating_cverts = Event()
+        self._calculating_verts_pos = 0.0
+        self._calculating_verts_len = 0.0
+        self._calculating_cverts_pos = 0.0
+        self._calculating_cverts_len = 0.0
+
+        self._max_render_stack_size = 3
+        self._draw_wireframe = [-1]
+        self._draw_solid = [-1]
+
+        self._style = None
+        self._color = None
+
+        self.predraw = []
+        self.postdraw = []
+
+        self.use_lambda_eval = self.options.pop('use_sympy_eval', None) is None
+        self.style = self.options.pop('style', '')
+        self.color = self.options.pop('color', 'rainbow')
+        self.bounds_callback = bounds_callback
+
+        self._on_calculate()
+
+    def synchronized(f):
+        def w(self, *args, **kwargs):
+            self._draw_lock.acquire()
+            try:
+                r = f(self, *args, **kwargs)
+                return r
+            finally:
+                self._draw_lock.release()
+        return w
+
+    @synchronized
+    def push_wireframe(self, function):
+        """
+        Push a function which performs gl commands
+        used to build a display list. (The list is
+        built outside of the function)
+        """
+        assert callable(function)
+        self._draw_wireframe.append(function)
+        if len(self._draw_wireframe) > self._max_render_stack_size:
+            del self._draw_wireframe[1]  # leave marker element
+
+    @synchronized
+    def push_solid(self, function):
+        """
+        Push a function which performs gl commands
+        used to build a display list. (The list is
+        built outside of the function)
+        """
+        assert callable(function)
+        self._draw_solid.append(function)
+        if len(self._draw_solid) > self._max_render_stack_size:
+            del self._draw_solid[1]  # leave marker element
+
+    def _create_display_list(self, function):
+        dl = pgl.glGenLists(1)
+        pgl.glNewList(dl, pgl.GL_COMPILE)
+        function()
+        pgl.glEndList()
+        return dl
+
+    def _render_stack_top(self, render_stack):
+        top = render_stack[-1]
+        if top == -1:
+            return -1  # nothing to display
+        elif callable(top):
+            dl = self._create_display_list(top)
+            render_stack[-1] = (dl, top)
+            return dl  # display newly added list
+        elif len(top) == 2:
+            if pgl.GL_TRUE == pgl.glIsList(top[0]):
+                return top[0]  # display stored list
+            dl = self._create_display_list(top[1])
+            render_stack[-1] = (dl, top[1])
+            return dl  # display regenerated list
+
+    def _draw_solid_display_list(self, dl):
+        pgl.glPushAttrib(pgl.GL_ENABLE_BIT | pgl.GL_POLYGON_BIT)
+        pgl.glPolygonMode(pgl.GL_FRONT_AND_BACK, pgl.GL_FILL)
+        pgl.glCallList(dl)
+        pgl.glPopAttrib()
+
+    def _draw_wireframe_display_list(self, dl):
+        pgl.glPushAttrib(pgl.GL_ENABLE_BIT | pgl.GL_POLYGON_BIT)
+        pgl.glPolygonMode(pgl.GL_FRONT_AND_BACK, pgl.GL_LINE)
+        pgl.glEnable(pgl.GL_POLYGON_OFFSET_LINE)
+        pgl.glPolygonOffset(-0.005, -50.0)
+        pgl.glCallList(dl)
+        pgl.glPopAttrib()
+
+    @synchronized
+    def draw(self):
+        for f in self.predraw:
+            if callable(f):
+                f()
+        if self.style_override:
+            style = self.styles[self.style_override]
+        else:
+            style = self.styles[self._style]
+        # Draw solid component if style includes solid
+        if style & 2:
+            dl = self._render_stack_top(self._draw_solid)
+            if dl > 0 and pgl.GL_TRUE == pgl.glIsList(dl):
+                self._draw_solid_display_list(dl)
+        # Draw wireframe component if style includes wireframe
+        if style & 1:
+            dl = self._render_stack_top(self._draw_wireframe)
+            if dl > 0 and pgl.GL_TRUE == pgl.glIsList(dl):
+                self._draw_wireframe_display_list(dl)
+        for f in self.postdraw:
+            if callable(f):
+                f()
+
+    def _on_change_color(self, color):
+        Thread(target=self._calculate_cverts).start()
+
+    def _on_calculate(self):
+        Thread(target=self._calculate_all).start()
+
+    def _calculate_all(self):
+        self._calculate_verts()
+        self._calculate_cverts()
+
+    def _calculate_verts(self):
+        if self._calculating_verts.is_set():
+            return
+        self._calculating_verts.set()
+        try:
+            self._on_calculate_verts()
+        finally:
+            self._calculating_verts.clear()
+        if callable(self.bounds_callback):
+            self.bounds_callback()
+
+    def _calculate_cverts(self):
+        if self._calculating_verts.is_set():
+            return
+        while self._calculating_cverts.is_set():
+            sleep(0)  # wait for previous calculation
+        self._calculating_cverts.set()
+        try:
+            self._on_calculate_cverts()
+        finally:
+            self._calculating_cverts.clear()
+
+    def _get_calculating_verts(self):
+        return self._calculating_verts.is_set()
+
+    def _get_calculating_verts_pos(self):
+        return self._calculating_verts_pos
+
+    def _get_calculating_verts_len(self):
+        return self._calculating_verts_len
+
+    def _get_calculating_cverts(self):
+        return self._calculating_cverts.is_set()
+
+    def _get_calculating_cverts_pos(self):
+        return self._calculating_cverts_pos
+
+    def _get_calculating_cverts_len(self):
+        return self._calculating_cverts_len
+
+    ## Property handlers
+    def _get_style(self):
+        return self._style
+
+    @synchronized
+    def _set_style(self, v):
+        if v is None:
+            return
+        if v == '':
+            step_max = 0
+            for i in self.intervals:
+                if i.v_steps is None:
+                    continue
+                step_max = max([step_max, int(i.v_steps)])
+            v = ['both', 'solid'][step_max > 40]
+        if v not in self.styles:
+            raise ValueError("v should be there in self.styles")
+        if v == self._style:
+            return
+        self._style = v
+
+    def _get_color(self):
+        return self._color
+
+    @synchronized
+    def _set_color(self, v):
+        try:
+            if v is not None:
+                if is_sequence(v):
+                    v = ColorScheme(*v)
+                else:
+                    v = ColorScheme(v)
+            if repr(v) == repr(self._color):
+                return
+            self._on_change_color(v)
+            self._color = v
+        except Exception as e:
+            raise RuntimeError("Color change failed. "
+                                "Reason: %s" % (str(e)))
+
+    style = property(_get_style, _set_style)
+    color = property(_get_color, _set_color)
+
+    calculating_verts = property(_get_calculating_verts)
+    calculating_verts_pos = property(_get_calculating_verts_pos)
+    calculating_verts_len = property(_get_calculating_verts_len)
+
+    calculating_cverts = property(_get_calculating_cverts)
+    calculating_cverts_pos = property(_get_calculating_cverts_pos)
+    calculating_cverts_len = property(_get_calculating_cverts_len)
+
+    ## String representations
+
+    def __str__(self):
+        f = ", ".join(str(d) for d in self.d_vars)
+        o = "'mode=%s'" % (self.primary_alias)
+        return ", ".join([f, o])
+
+    def __repr__(self):
+        f = ", ".join(str(d) for d in self.d_vars)
+        i = ", ".join(str(i) for i in self.intervals)
+        d = [('mode', self.primary_alias),
+             ('color', str(self.color)),
+             ('style', str(self.style))]
+
+        o = "'%s'" % ("; ".join("%s=%s" % (k, v)
+                                for k, v in d if v != 'None'))
+        return ", ".join([f, i, o])

llmeval-env/lib/python3.10/site-packages/sympy/plotting/pygletplot/plot_modes.py

@@ -0,0 +1,209 @@
+from sympy.utilities.lambdify import lambdify
+from sympy.core.numbers import pi
+from sympy.functions import sin, cos
+from sympy.plotting.pygletplot.plot_curve import PlotCurve
+from sympy.plotting.pygletplot.plot_surface import PlotSurface
+
+from math import sin as p_sin
+from math import cos as p_cos
+
+
+def float_vec3(f):
+    def inner(*args):
+        v = f(*args)
+        return float(v[0]), float(v[1]), float(v[2])
+    return inner
+
+
+class Cartesian2D(PlotCurve):
+    i_vars, d_vars = 'x', 'y'
+    intervals = [[-5, 5, 100]]
+    aliases = ['cartesian']
+    is_default = True
+
+    def _get_sympy_evaluator(self):
+        fy = self.d_vars[0]
+        x = self.t_interval.v
+
+        @float_vec3
+        def e(_x):
+            return (_x, fy.subs(x, _x), 0.0)
+        return e
+
+    def _get_lambda_evaluator(self):
+        fy = self.d_vars[0]
+        x = self.t_interval.v
+        return lambdify([x], [x, fy, 0.0])
+
+
+class Cartesian3D(PlotSurface):
+    i_vars, d_vars = 'xy', 'z'
+    intervals = [[-1, 1, 40], [-1, 1, 40]]
+    aliases = ['cartesian', 'monge']
+    is_default = True
+
+    def _get_sympy_evaluator(self):
+        fz = self.d_vars[0]
+        x = self.u_interval.v
+        y = self.v_interval.v
+
+        @float_vec3
+        def e(_x, _y):
+            return (_x, _y, fz.subs(x, _x).subs(y, _y))
+        return e
+
+    def _get_lambda_evaluator(self):
+        fz = self.d_vars[0]
+        x = self.u_interval.v
+        y = self.v_interval.v
+        return lambdify([x, y], [x, y, fz])
+
+
+class ParametricCurve2D(PlotCurve):
+    i_vars, d_vars = 't', 'xy'
+    intervals = [[0, 2*pi, 100]]
+    aliases = ['parametric']
+    is_default = True
+
+    def _get_sympy_evaluator(self):
+        fx, fy = self.d_vars
+        t = self.t_interval.v
+
+        @float_vec3
+        def e(_t):
+            return (fx.subs(t, _t), fy.subs(t, _t), 0.0)
+        return e
+
+    def _get_lambda_evaluator(self):
+        fx, fy = self.d_vars
+        t = self.t_interval.v
+        return lambdify([t], [fx, fy, 0.0])
+
+
+class ParametricCurve3D(PlotCurve):
+    i_vars, d_vars = 't', 'xyz'
+    intervals = [[0, 2*pi, 100]]
+    aliases = ['parametric']
+    is_default = True
+
+    def _get_sympy_evaluator(self):
+        fx, fy, fz = self.d_vars
+        t = self.t_interval.v
+
+        @float_vec3
+        def e(_t):
+            return (fx.subs(t, _t), fy.subs(t, _t), fz.subs(t, _t))
+        return e
+
+    def _get_lambda_evaluator(self):
+        fx, fy, fz = self.d_vars
+        t = self.t_interval.v
+        return lambdify([t], [fx, fy, fz])
+
+
+class ParametricSurface(PlotSurface):
+    i_vars, d_vars = 'uv', 'xyz'
+    intervals = [[-1, 1, 40], [-1, 1, 40]]
+    aliases = ['parametric']
+    is_default = True
+
+    def _get_sympy_evaluator(self):
+        fx, fy, fz = self.d_vars
+        u = self.u_interval.v
+        v = self.v_interval.v
+
+        @float_vec3
+        def e(_u, _v):
+            return (fx.subs(u, _u).subs(v, _v),
+                    fy.subs(u, _u).subs(v, _v),
+                    fz.subs(u, _u).subs(v, _v))
+        return e
+
+    def _get_lambda_evaluator(self):
+        fx, fy, fz = self.d_vars
+        u = self.u_interval.v
+        v = self.v_interval.v
+        return lambdify([u, v], [fx, fy, fz])
+
+
+class Polar(PlotCurve):
+    i_vars, d_vars = 't', 'r'
+    intervals = [[0, 2*pi, 100]]
+    aliases = ['polar']
+    is_default = False
+
+    def _get_sympy_evaluator(self):
+        fr = self.d_vars[0]
+        t = self.t_interval.v
+
+        def e(_t):
+            _r = float(fr.subs(t, _t))
+            return (_r*p_cos(_t), _r*p_sin(_t), 0.0)
+        return e
+
+    def _get_lambda_evaluator(self):
+        fr = self.d_vars[0]
+        t = self.t_interval.v
+        fx, fy = fr*cos(t), fr*sin(t)
+        return lambdify([t], [fx, fy, 0.0])
+
+
+class Cylindrical(PlotSurface):
+    i_vars, d_vars = 'th', 'r'
+    intervals = [[0, 2*pi, 40], [-1, 1, 20]]
+    aliases = ['cylindrical', 'polar']
+    is_default = False
+
+    def _get_sympy_evaluator(self):
+        fr = self.d_vars[0]
+        t = self.u_interval.v
+        h = self.v_interval.v
+
+        def e(_t, _h):
+            _r = float(fr.subs(t, _t).subs(h, _h))
+            return (_r*p_cos(_t), _r*p_sin(_t), _h)
+        return e
+
+    def _get_lambda_evaluator(self):
+        fr = self.d_vars[0]
+        t = self.u_interval.v
+        h = self.v_interval.v
+        fx, fy = fr*cos(t), fr*sin(t)
+        return lambdify([t, h], [fx, fy, h])
+
+
+class Spherical(PlotSurface):
+    i_vars, d_vars = 'tp', 'r'
+    intervals = [[0, 2*pi, 40], [0, pi, 20]]
+    aliases = ['spherical']
+    is_default = False
+
+    def _get_sympy_evaluator(self):
+        fr = self.d_vars[0]
+        t = self.u_interval.v
+        p = self.v_interval.v
+
+        def e(_t, _p):
+            _r = float(fr.subs(t, _t).subs(p, _p))
+            return (_r*p_cos(_t)*p_sin(_p),
+                    _r*p_sin(_t)*p_sin(_p),
+                    _r*p_cos(_p))
+        return e
+
+    def _get_lambda_evaluator(self):
+        fr = self.d_vars[0]
+        t = self.u_interval.v
+        p = self.v_interval.v
+        fx = fr * cos(t) * sin(p)
+        fy = fr * sin(t) * sin(p)
+        fz = fr * cos(p)
+        return lambdify([t, p], [fx, fy, fz])
+
+Cartesian2D._register()
+Cartesian3D._register()
+ParametricCurve2D._register()
+ParametricCurve3D._register()
+ParametricSurface._register()
+Polar._register()
+Cylindrical._register()
+Spherical._register()

llmeval-env/lib/python3.10/site-packages/sympy/plotting/pygletplot/plot_object.py

@@ -0,0 +1,17 @@
+class PlotObject:
+    """
+    Base class for objects which can be displayed in
+    a Plot.
+    """
+    visible = True
+
+    def _draw(self):
+        if self.visible:
+            self.draw()
+
+    def draw(self):
+        """
+        OpenGL rendering code for the plot object.
+        Override in base class.
+        """
+        pass

llmeval-env/lib/python3.10/site-packages/sympy/plotting/pygletplot/plot_rotation.py

@@ -0,0 +1,68 @@
+try:
+    from ctypes import c_float
+except ImportError:
+    pass
+
+import pyglet.gl as pgl
+from math import sqrt as _sqrt, acos as _acos
+
+
+def cross(a, b):
+    return (a[1] * b[2] - a[2] * b[1],
+            a[2] * b[0] - a[0] * b[2],
+            a[0] * b[1] - a[1] * b[0])
+
+
+def dot(a, b):
+    return a[0] * b[0] + a[1] * b[1] + a[2] * b[2]
+
+
+def mag(a):
+    return _sqrt(a[0]**2 + a[1]**2 + a[2]**2)
+
+
+def norm(a):
+    m = mag(a)
+    return (a[0] / m, a[1] / m, a[2] / m)
+
+
+def get_sphere_mapping(x, y, width, height):
+    x = min([max([x, 0]), width])
+    y = min([max([y, 0]), height])
+
+    sr = _sqrt((width/2)**2 + (height/2)**2)
+    sx = ((x - width / 2) / sr)
+    sy = ((y - height / 2) / sr)
+
+    sz = 1.0 - sx**2 - sy**2
+
+    if sz > 0.0:
+        sz = _sqrt(sz)
+        return (sx, sy, sz)
+    else:
+        sz = 0
+        return norm((sx, sy, sz))
+
+rad2deg = 180.0 / 3.141592
+
+
+def get_spherical_rotatation(p1, p2, width, height, theta_multiplier):
+    v1 = get_sphere_mapping(p1[0], p1[1], width, height)
+    v2 = get_sphere_mapping(p2[0], p2[1], width, height)
+
+    d = min(max([dot(v1, v2), -1]), 1)
+
+    if abs(d - 1.0) < 0.000001:
+        return None
+
+    raxis = norm( cross(v1, v2) )
+    rtheta = theta_multiplier * rad2deg * _acos(d)
+
+    pgl.glPushMatrix()
+    pgl.glLoadIdentity()
+    pgl.glRotatef(rtheta, *raxis)
+    mat = (c_float*16)()
+    pgl.glGetFloatv(pgl.GL_MODELVIEW_MATRIX, mat)
+    pgl.glPopMatrix()
+
+    return mat

llmeval-env/lib/python3.10/site-packages/sympy/plotting/pygletplot/plot_surface.py

@@ -0,0 +1,102 @@
+import pyglet.gl as pgl
+
+from sympy.core import S
+from sympy.plotting.pygletplot.plot_mode_base import PlotModeBase
+
+
+class PlotSurface(PlotModeBase):
+
+    default_rot_preset = 'perspective'
+
+    def _on_calculate_verts(self):
+        self.u_interval = self.intervals[0]
+        self.u_set = list(self.u_interval.frange())
+        self.v_interval = self.intervals[1]
+        self.v_set = list(self.v_interval.frange())
+        self.bounds = [[S.Infinity, S.NegativeInfinity, 0],
+                       [S.Infinity, S.NegativeInfinity, 0],
+                       [S.Infinity, S.NegativeInfinity, 0]]
+        evaluate = self._get_evaluator()
+
+        self._calculating_verts_pos = 0.0
+        self._calculating_verts_len = float(
+            self.u_interval.v_len*self.v_interval.v_len)
+
+        verts = []
+        b = self.bounds
+        for u in self.u_set:
+            column = []
+            for v in self.v_set:
+                try:
+                    _e = evaluate(u, v)  # calculate vertex
+                except ZeroDivisionError:
+                    _e = None
+                if _e is not None:  # update bounding box
+                    for axis in range(3):
+                        b[axis][0] = min([b[axis][0], _e[axis]])
+                        b[axis][1] = max([b[axis][1], _e[axis]])
+                column.append(_e)
+                self._calculating_verts_pos += 1.0
+
+            verts.append(column)
+        for axis in range(3):
+            b[axis][2] = b[axis][1] - b[axis][0]
+            if b[axis][2] == 0.0:
+                b[axis][2] = 1.0
+
+        self.verts = verts
+        self.push_wireframe(self.draw_verts(False, False))
+        self.push_solid(self.draw_verts(False, True))
+
+    def _on_calculate_cverts(self):
+        if not self.verts or not self.color:
+            return
+
+        def set_work_len(n):
+            self._calculating_cverts_len = float(n)
+
+        def inc_work_pos():
+            self._calculating_cverts_pos += 1.0
+        set_work_len(1)
+        self._calculating_cverts_pos = 0
+        self.cverts = self.color.apply_to_surface(self.verts,
+                                                  self.u_set,
+                                                  self.v_set,
+                                                  set_len=set_work_len,
+                                                  inc_pos=inc_work_pos)
+        self.push_solid(self.draw_verts(True, True))
+
+    def calculate_one_cvert(self, u, v):
+        vert = self.verts[u][v]
+        return self.color(vert[0], vert[1], vert[2],
+                          self.u_set[u], self.v_set[v])
+
+    def draw_verts(self, use_cverts, use_solid_color):
+        def f():
+            for u in range(1, len(self.u_set)):
+                pgl.glBegin(pgl.GL_QUAD_STRIP)
+                for v in range(len(self.v_set)):
+                    pa = self.verts[u - 1][v]
+                    pb = self.verts[u][v]
+                    if pa is None or pb is None:
+                        pgl.glEnd()
+                        pgl.glBegin(pgl.GL_QUAD_STRIP)
+                        continue
+                    if use_cverts:
+                        ca = self.cverts[u - 1][v]
+                        cb = self.cverts[u][v]
+                        if ca is None:
+                            ca = (0, 0, 0)
+                        if cb is None:
+                            cb = (0, 0, 0)
+                    else:
+                        if use_solid_color:
+                            ca = cb = self.default_solid_color
+                        else:
+                            ca = cb = self.default_wireframe_color
+                    pgl.glColor3f(*ca)
+                    pgl.glVertex3f(*pa)
+                    pgl.glColor3f(*cb)
+                    pgl.glVertex3f(*pb)
+                pgl.glEnd()
+        return f

llmeval-env/lib/python3.10/site-packages/sympy/plotting/pygletplot/plot_window.py

@@ -0,0 +1,144 @@
+from time import perf_counter
+
+
+import pyglet.gl as pgl
+
+from sympy.plotting.pygletplot.managed_window import ManagedWindow
+from sympy.plotting.pygletplot.plot_camera import PlotCamera
+from sympy.plotting.pygletplot.plot_controller import PlotController
+
+
+class PlotWindow(ManagedWindow):
+
+    def __init__(self, plot, antialiasing=True, ortho=False,
+                 invert_mouse_zoom=False, linewidth=1.5, caption="SymPy Plot",
+                 **kwargs):
+        """
+        Named Arguments
+        ===============
+
+        antialiasing = True
+            True OR False
+        ortho = False
+            True OR False
+        invert_mouse_zoom = False
+            True OR False
+        """
+        self.plot = plot
+
+        self.camera = None
+        self._calculating = False
+
+        self.antialiasing = antialiasing
+        self.ortho = ortho
+        self.invert_mouse_zoom = invert_mouse_zoom
+        self.linewidth = linewidth
+        self.title = caption
+        self.last_caption_update = 0
+        self.caption_update_interval = 0.2
+        self.drawing_first_object = True
+
+        super().__init__(**kwargs)
+
+    def setup(self):
+        self.camera = PlotCamera(self, ortho=self.ortho)
+        self.controller = PlotController(self,
+                invert_mouse_zoom=self.invert_mouse_zoom)
+        self.push_handlers(self.controller)
+
+        pgl.glClearColor(1.0, 1.0, 1.0, 0.0)
+        pgl.glClearDepth(1.0)
+
+        pgl.glDepthFunc(pgl.GL_LESS)
+        pgl.glEnable(pgl.GL_DEPTH_TEST)
+
+        pgl.glEnable(pgl.GL_LINE_SMOOTH)
+        pgl.glShadeModel(pgl.GL_SMOOTH)
+        pgl.glLineWidth(self.linewidth)
+
+        pgl.glEnable(pgl.GL_BLEND)
+        pgl.glBlendFunc(pgl.GL_SRC_ALPHA, pgl.GL_ONE_MINUS_SRC_ALPHA)
+
+        if self.antialiasing:
+            pgl.glHint(pgl.GL_LINE_SMOOTH_HINT, pgl.GL_NICEST)
+            pgl.glHint(pgl.GL_POLYGON_SMOOTH_HINT, pgl.GL_NICEST)
+
+        self.camera.setup_projection()
+
+    def on_resize(self, w, h):
+        super().on_resize(w, h)
+        if self.camera is not None:
+            self.camera.setup_projection()
+
+    def update(self, dt):
+        self.controller.update(dt)
+
+    def draw(self):
+        self.plot._render_lock.acquire()
+        self.camera.apply_transformation()
+
+        calc_verts_pos, calc_verts_len = 0, 0
+        calc_cverts_pos, calc_cverts_len = 0, 0
+
+        should_update_caption = (perf_counter() - self.last_caption_update >
+                                 self.caption_update_interval)
+
+        if len(self.plot._functions.values()) == 0:
+            self.drawing_first_object = True
+
+        iterfunctions = iter(self.plot._functions.values())
+
+        for r in iterfunctions:
+            if self.drawing_first_object:
+                self.camera.set_rot_preset(r.default_rot_preset)
+                self.drawing_first_object = False
+
+            pgl.glPushMatrix()
+            r._draw()
+            pgl.glPopMatrix()
+
+            # might as well do this while we are
+            # iterating and have the lock rather
+            # than locking and iterating twice
+            # per frame:
+
+            if should_update_caption:
+                try:
+                    if r.calculating_verts:
+                        calc_verts_pos += r.calculating_verts_pos
+                        calc_verts_len += r.calculating_verts_len
+                    if r.calculating_cverts:
+                        calc_cverts_pos += r.calculating_cverts_pos
+                        calc_cverts_len += r.calculating_cverts_len
+                except ValueError:
+                    pass
+
+        for r in self.plot._pobjects:
+            pgl.glPushMatrix()
+            r._draw()
+            pgl.glPopMatrix()
+
+        if should_update_caption:
+            self.update_caption(calc_verts_pos, calc_verts_len,
+                                calc_cverts_pos, calc_cverts_len)
+            self.last_caption_update = perf_counter()
+
+        if self.plot._screenshot:
+            self.plot._screenshot._execute_saving()
+
+        self.plot._render_lock.release()
+
+    def update_caption(self, calc_verts_pos, calc_verts_len,
+            calc_cverts_pos, calc_cverts_len):
+        caption = self.title
+        if calc_verts_len or calc_cverts_len:
+            caption += " (calculating"
+            if calc_verts_len > 0:
+                p = (calc_verts_pos / calc_verts_len) * 100
+                caption += " vertices %i%%" % (p)
+            if calc_cverts_len > 0:
+                p = (calc_cverts_pos / calc_cverts_len) * 100
+                caption += " colors %i%%" % (p)
+            caption += ")"
+        if self.caption != caption:
+            self.set_caption(caption)