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from sympy.assumptions import Predicate |
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from sympy.multipledispatch import Dispatcher |
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class IntegerPredicate(Predicate): |
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""" |
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Integer predicate. |
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Explanation |
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=========== |
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``Q.integer(x)`` is true iff ``x`` belongs to the set of integer |
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numbers. |
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Examples |
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======== |
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>>> from sympy import Q, ask, S |
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>>> ask(Q.integer(5)) |
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True |
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>>> ask(Q.integer(S(1)/2)) |
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False |
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References |
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========== |
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.. [1] https://en.wikipedia.org/wiki/Integer |
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""" |
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name = 'integer' |
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handler = Dispatcher( |
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"IntegerHandler", |
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doc=("Handler for Q.integer.\n\n" |
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"Test that an expression belongs to the field of integer numbers.") |
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) |
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class RationalPredicate(Predicate): |
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""" |
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Rational number predicate. |
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Explanation |
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=========== |
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``Q.rational(x)`` is true iff ``x`` belongs to the set of |
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rational numbers. |
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Examples |
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======== |
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>>> from sympy import ask, Q, pi, S |
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>>> ask(Q.rational(0)) |
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True |
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>>> ask(Q.rational(S(1)/2)) |
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True |
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>>> ask(Q.rational(pi)) |
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False |
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References |
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========== |
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.. [1] https://en.wikipedia.org/wiki/Rational_number |
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""" |
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name = 'rational' |
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handler = Dispatcher( |
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"RationalHandler", |
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doc=("Handler for Q.rational.\n\n" |
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"Test that an expression belongs to the field of rational numbers.") |
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) |
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class IrrationalPredicate(Predicate): |
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""" |
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Irrational number predicate. |
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Explanation |
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=========== |
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``Q.irrational(x)`` is true iff ``x`` is any real number that |
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cannot be expressed as a ratio of integers. |
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Examples |
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======== |
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>>> from sympy import ask, Q, pi, S, I |
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>>> ask(Q.irrational(0)) |
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False |
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>>> ask(Q.irrational(S(1)/2)) |
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False |
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>>> ask(Q.irrational(pi)) |
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True |
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>>> ask(Q.irrational(I)) |
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False |
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References |
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========== |
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.. [1] https://en.wikipedia.org/wiki/Irrational_number |
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""" |
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name = 'irrational' |
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handler = Dispatcher( |
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"IrrationalHandler", |
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doc=("Handler for Q.irrational.\n\n" |
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"Test that an expression is irrational numbers.") |
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) |
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class RealPredicate(Predicate): |
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r""" |
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Real number predicate. |
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Explanation |
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=========== |
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``Q.real(x)`` is true iff ``x`` is a real number, i.e., it is in the |
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interval `(-\infty, \infty)`. Note that, in particular the |
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infinities are not real. Use ``Q.extended_real`` if you want to |
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consider those as well. |
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A few important facts about reals: |
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- Every real number is positive, negative, or zero. Furthermore, |
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because these sets are pairwise disjoint, each real number is |
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exactly one of those three. |
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- Every real number is also complex. |
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- Every real number is finite. |
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- Every real number is either rational or irrational. |
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- Every real number is either algebraic or transcendental. |
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- The facts ``Q.negative``, ``Q.zero``, ``Q.positive``, |
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``Q.nonnegative``, ``Q.nonpositive``, ``Q.nonzero``, |
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``Q.integer``, ``Q.rational``, and ``Q.irrational`` all imply |
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``Q.real``, as do all facts that imply those facts. |
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- The facts ``Q.algebraic``, and ``Q.transcendental`` do not imply |
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``Q.real``; they imply ``Q.complex``. An algebraic or |
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transcendental number may or may not be real. |
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- The "non" facts (i.e., ``Q.nonnegative``, ``Q.nonzero``, |
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``Q.nonpositive`` and ``Q.noninteger``) are not equivalent to |
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not the fact, but rather, not the fact *and* ``Q.real``. |
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For example, ``Q.nonnegative`` means ``~Q.negative & Q.real``. |
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So for example, ``I`` is not nonnegative, nonzero, or |
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nonpositive. |
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Examples |
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======== |
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>>> from sympy import Q, ask, symbols |
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>>> x = symbols('x') |
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>>> ask(Q.real(x), Q.positive(x)) |
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True |
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>>> ask(Q.real(0)) |
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True |
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References |
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========== |
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.. [1] https://en.wikipedia.org/wiki/Real_number |
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""" |
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name = 'real' |
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handler = Dispatcher( |
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"RealHandler", |
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doc=("Handler for Q.real.\n\n" |
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"Test that an expression belongs to the field of real numbers.") |
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) |
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class ExtendedRealPredicate(Predicate): |
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r""" |
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Extended real predicate. |
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Explanation |
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=========== |
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``Q.extended_real(x)`` is true iff ``x`` is a real number or |
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`\{-\infty, \infty\}`. |
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See documentation of ``Q.real`` for more information about related |
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facts. |
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Examples |
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======== |
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>>> from sympy import ask, Q, oo, I |
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>>> ask(Q.extended_real(1)) |
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True |
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>>> ask(Q.extended_real(I)) |
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False |
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>>> ask(Q.extended_real(oo)) |
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True |
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""" |
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name = 'extended_real' |
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handler = Dispatcher( |
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"ExtendedRealHandler", |
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doc=("Handler for Q.extended_real.\n\n" |
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"Test that an expression belongs to the field of extended real\n" |
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"numbers, that is real numbers union {Infinity, -Infinity}.") |
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) |
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class HermitianPredicate(Predicate): |
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""" |
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Hermitian predicate. |
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Explanation |
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=========== |
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``ask(Q.hermitian(x))`` is true iff ``x`` belongs to the set of |
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Hermitian operators. |
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References |
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========== |
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.. [1] https://mathworld.wolfram.com/HermitianOperator.html |
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""" |
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name = 'hermitian' |
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handler = Dispatcher( |
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"HermitianHandler", |
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doc=("Handler for Q.hermitian.\n\n" |
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"Test that an expression belongs to the field of Hermitian operators.") |
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) |
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class ComplexPredicate(Predicate): |
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""" |
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Complex number predicate. |
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Explanation |
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=========== |
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``Q.complex(x)`` is true iff ``x`` belongs to the set of complex |
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numbers. Note that every complex number is finite. |
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Examples |
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======== |
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>>> from sympy import Q, Symbol, ask, I, oo |
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>>> x = Symbol('x') |
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>>> ask(Q.complex(0)) |
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True |
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>>> ask(Q.complex(2 + 3*I)) |
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True |
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>>> ask(Q.complex(oo)) |
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False |
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References |
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========== |
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.. [1] https://en.wikipedia.org/wiki/Complex_number |
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""" |
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name = 'complex' |
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handler = Dispatcher( |
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"ComplexHandler", |
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doc=("Handler for Q.complex.\n\n" |
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"Test that an expression belongs to the field of complex numbers.") |
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) |
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class ImaginaryPredicate(Predicate): |
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""" |
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Imaginary number predicate. |
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Explanation |
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=========== |
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``Q.imaginary(x)`` is true iff ``x`` can be written as a real |
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number multiplied by the imaginary unit ``I``. Please note that ``0`` |
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is not considered to be an imaginary number. |
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Examples |
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======== |
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>>> from sympy import Q, ask, I |
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>>> ask(Q.imaginary(3*I)) |
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True |
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>>> ask(Q.imaginary(2 + 3*I)) |
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False |
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>>> ask(Q.imaginary(0)) |
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False |
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References |
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========== |
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.. [1] https://en.wikipedia.org/wiki/Imaginary_number |
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""" |
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name = 'imaginary' |
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handler = Dispatcher( |
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"ImaginaryHandler", |
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doc=("Handler for Q.imaginary.\n\n" |
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"Test that an expression belongs to the field of imaginary numbers,\n" |
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"that is, numbers in the form x*I, where x is real.") |
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) |
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class AntihermitianPredicate(Predicate): |
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""" |
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Antihermitian predicate. |
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Explanation |
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=========== |
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``Q.antihermitian(x)`` is true iff ``x`` belongs to the field of |
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antihermitian operators, i.e., operators in the form ``x*I``, where |
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``x`` is Hermitian. |
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References |
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========== |
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.. [1] https://mathworld.wolfram.com/HermitianOperator.html |
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""" |
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name = 'antihermitian' |
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handler = Dispatcher( |
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"AntiHermitianHandler", |
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doc=("Handler for Q.antihermitian.\n\n" |
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"Test that an expression belongs to the field of anti-Hermitian\n" |
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"operators, that is, operators in the form x*I, where x is Hermitian.") |
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) |
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class AlgebraicPredicate(Predicate): |
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r""" |
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Algebraic number predicate. |
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Explanation |
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=========== |
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``Q.algebraic(x)`` is true iff ``x`` belongs to the set of |
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algebraic numbers. ``x`` is algebraic if there is some polynomial |
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in ``p(x)\in \mathbb\{Q\}[x]`` such that ``p(x) = 0``. |
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Examples |
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======== |
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>>> from sympy import ask, Q, sqrt, I, pi |
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>>> ask(Q.algebraic(sqrt(2))) |
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True |
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>>> ask(Q.algebraic(I)) |
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True |
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>>> ask(Q.algebraic(pi)) |
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False |
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References |
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========== |
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.. [1] https://en.wikipedia.org/wiki/Algebraic_number |
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""" |
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name = 'algebraic' |
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AlgebraicHandler = Dispatcher( |
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"AlgebraicHandler", |
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doc="""Handler for Q.algebraic key.""" |
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) |
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class TranscendentalPredicate(Predicate): |
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""" |
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Transcedental number predicate. |
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Explanation |
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=========== |
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``Q.transcendental(x)`` is true iff ``x`` belongs to the set of |
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transcendental numbers. A transcendental number is a real |
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or complex number that is not algebraic. |
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""" |
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name = 'transcendental' |
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handler = Dispatcher( |
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"Transcendental", |
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doc="""Handler for Q.transcendental key.""" |
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) |
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