solver.py

import sympy as sp
from sympy.parsing.sympy_parser import parse_expr, standard_transformations, implicit_multiplication_application
from sympy.solvers import solve
from sympy import integrate, diff, latex,simplify, expand, log, exp, sin, cos, tan, asin, acos, atan, Symbol, factorial, laplace_transform
import re
def format_expression(expr):
    latex_expr = latex(expr)
    replacements = {
        '**': '^',  # Power notation
        '*x': 'x',  # Remove unnecessary multiplication signs
        '*(': '(',  # Remove multiplication before parentheses
        'exp': 'e^',  # Exponential notation
        'sqrt': '√',  # Square root
        'factorial': '!',  # Factorial symbol
        'gamma': 'Γ',  # Gamma function
        'Gamma': 'Γ',  # Sometimes SymPy capitalizes it
        'fresnels': 'S',  # Fresnel S integral
        'fresnelc': 'C',  # Fresnel C integral
        'hyper': '₁F₂',  # Generalized hypergeometric function
        'log': 'ln',  # Natural logarithm
        'oo': '∞',  # Infinity symbol
        'pi': 'π',  # Pi symbol
        'E': 'ℯ',  # Euler's constant
        'I': '𝒊',  # Imaginary unit
        'Abs': '|',  # Absolute value
        'Integral': '∫',  # Integral symbol
        'Derivative': 'd/dx',  # Differentiation
        'Sum': 'Σ',  # Summation symbol
        'Product': '∏',  # Product symbol
        'sin': 'sin', 'cos': 'cos', 'tan': 'tan',  # Trig functions (unchanged)
        'asin': 'sin⁻¹', 'acos': 'cos⁻¹', 'atan': 'tan⁻¹',  # Inverse trig
        'sinh': 'sinh', 'cosh': 'cosh', 'tanh': 'tanh',  # Hyperbolic trig
        'asinh': 'sinh⁻¹', 'acosh': 'cosh⁻¹', 'atanh': 'tanh⁻¹',  # Inverse hyperbolic trig
        'diff': 'd/dx',  # Derivative notation
        'integrate': '∫',  # Integral notation
        'Limit': 'lim',  # Limit notation
        'floor': '⌊',  # Floor function
        'ceiling': '⌈',  # Ceiling function
        'mod': 'mod',  # Modulus (unchanged)
        'Re': 'ℜ',  # Real part
        'Im': 'ℑ'  # Imaginary part
    }
    for old, new in replacements.items():
        latex_expr = latex_expr.replace(old, new)

    return f"$$ {latex_expr} $$"

def preprocess_equation(equation_str):
    """Convert user-friendly equation format to SymPy format."""
    try:
        # Replace common mathematical notations
        replacements = {
            '^': '**',
            'sin⁻¹': 'asin',
            'cos⁻¹': 'acos',
            'tan⁻¹': 'atan',
            'e^': 'exp',
            'ln': 'log',  # Convert ln to log (SymPy default)
            '√': 'sqrt',  # Convert square root symbol to sqrt()
            '!': '.factorial()',  # Convert factorial to function call
        }
        for old, new in replacements.items():
            equation_str = equation_str.replace(old, new)
            
        equation_str = re.sub(r'(\d+)!', r'factorial(\1)', equation_str)

        # Handle exponential expressions
        if 'exp' in equation_str:
            parts = equation_str.split('exp')
            for i in range(1, len(parts)):
                if parts[i] and parts[i][0] != '(':
                    parts[i] = '(' + parts[i]
                    if '=' in parts[i]:
                        exp_part, rest = parts[i].split('=', 1)
                        parts[i] = exp_part + ')=' + rest
                    else:
                        parts[i] = parts[i] + ')'
            equation_str = 'exp'.join(parts)

        # Add multiplication symbol where needed
        processed = ''
        i = 0
        while i < len(equation_str):
            if i + 1 < len(equation_str):
                if equation_str[i].isdigit() and equation_str[i+1] == 'x':
                    processed += equation_str[i] + '*'
                    i += 1
                    continue
            processed += equation_str[i]
            i += 1

        return processed
    except Exception as e:
        raise Exception(f"Error in equation format: {str(e)}")

def process_expression(expr_str):
    """Process mathematical expressions without equations."""
    try:
        processed_expr = preprocess_equation(expr_str)
        x = Symbol('x')
        

        if expr_str.startswith('∫'):  # Integration
            expr_to_integrate = processed_expr[1:].strip()
            expr = parse_expr(expr_to_integrate, transformations=(standard_transformations + (implicit_multiplication_application,)))
            result = integrate(expr, x)
            return f"∫{format_expression(expr)} = {format_expression(result)}"

        elif expr_str.startswith('d/dx'):  # Differentiation
            expr_to_diff = processed_expr[4:].strip()
            if expr_to_diff.startswith('(') and expr_to_diff.endswith(')'):
                expr_to_diff = expr_to_diff[1:-1]
            expr = parse_expr(expr_to_diff, transformations=(standard_transformations + (implicit_multiplication_application,)))
            result = diff(expr, x)
            return f"d/dx({format_expression(expr)}) = {format_expression(result)}"

        elif 'factorial' in processed_expr:  # Factorial case
            expr = parse_expr(processed_expr, transformations=(standard_transformations + (implicit_multiplication_application,)))
            result = expr.doit()  # Compute the factorial correctly
            return f"{format_expression(expr)} = {result}"


        elif '/' in expr_str:  # Handle fractions and return decimal
            expr = parse_expr(processed_expr, transformations=(standard_transformations + (implicit_multiplication_application,)))
            simplified = simplify(expr)
            decimal_value = float(simplified)
            return f"Simplified: {format_expression(simplified)}\nDecimal: {decimal_value}"

        else:  # Regular expression simplification
            expr = parse_expr(processed_expr, transformations=(standard_transformations + (implicit_multiplication_application,)))
            simplified = simplify(expr)
            expanded = expand(simplified)
            return f"Simplified: {format_expression(simplified)}\nExpanded: {format_expression(expanded)}"

    except Exception as e:
        raise Exception(f"Error processing expression: {str(e)}")


    except Exception as e:
        raise Exception(f"Error processing expression: {str(e)}")

def to_latex(expr):
    """Converts a SymPy expression into LaTeX format."""
    return f"$$ {sp.latex(expr)} $$"

def solve_equation(equation_str):
    """Solves an equation and returns a detailed LaTeX-formatted step-by-step solution."""
    try:
        if '=' not in equation_str:
            return process_expression(equation_str)

        left_side, right_side = [side.strip() for side in equation_str.split('=')]
        
        transformations = standard_transformations + (implicit_multiplication_application,)
        left_expr = sp.parse_expr(left_side, transformations=transformations)
        right_expr = sp.parse_expr(right_side, transformations=transformations)
        equation = left_expr - right_expr

        x = Symbol('x')
        solutions = solve(equation, x)

        steps = []
        steps.append(f"**Step 1:** Original equation: \n{to_latex(left_expr)} = {to_latex(right_expr)}")
        steps.append(f"**Step 2:** Move all terms to one side: \n{to_latex(equation)} = 0")

        factored = sp.factor(equation)
        if factored != equation:
            steps.append(f"**Step 3:** Factorizing the equation: \n{to_latex(factored)} = 0")

        steps.append(f"**Step 4:** Solving for x:")
        for sol in solutions:
            steps.append(f"   x = {to_latex(sol)}")

        steps.append("**Step 5:** Verification:")
        for sol in solutions:
            verification = equation.subs(x, sol)
            steps.append(f"   When x = {to_latex(sol)}, the equation evaluates to {to_latex(verification)}")

        return "\n".join(steps)

    except Exception as e:
        return f"Error: {str(e)}"

def integrate_expression(expression_str):
    """Computes the integral of a given expression and provides detailed LaTeX-formatted steps."""
    try:
        x = Symbol('x')
        expr = sp.parse_expr(expression_str, transformations=standard_transformations + (implicit_multiplication_application,))

        steps = []
        steps.append(f"**Step 1:** Original integral: \n$$ \\int {sp.latex(expr)} \\,dx $$")

        if '^' in expression_str:
            steps.append("**Step 2:** Checking if substitution is needed.")

        result = integrate(expr, x)
        steps.append(f"**Step 3:** Applying integration formula(s):")
        steps.append(f"$$ \\int f(x) \\,dx = F(x) + C $$")
        steps.append(f"**Step 4:** Solution: \n$$ {sp.latex(result)} + C $$")

        return "\n".join(steps)

    except Exception as e:
        return f"Error: {str(e)}"

def laplace_transform_expression(expression_str):
    """Computes the Laplace transform of a given expression with LaTeX-formatted steps."""
    try:
        t, s = sp.symbols('t s')
        expr = sp.parse_expr(expression_str, transformations=standard_transformations + (implicit_multiplication_application,))

        steps = []
        steps.append(f"**Step 1:** Original function: \n$$ \\mathcal{L}\\{{ {sp.latex(expr)} \\}}(t) $$")

        L_transform = laplace_transform(expr, t, s, noconds=True)

        steps.append(f"**Step 2:** Applying Laplace Transform:")
        steps.append("$$ \\mathcal{L}\\{ f(t) \\} = \\int_{0}^{\\infty} e^{-st} f(t) \\,dt $$")
        steps.append(f"**Step 3:** Solution: \n$$ {sp.latex(L_transform)} $$")

        return "\n".join(steps)

    except Exception as e:
        return f"Error: {str(e)}"

def process_input(equation):
    """Determine whether the input is an equation, an integral, or a Laplace transform."""
    try:
        if "laplace" in equation.lower():
            solution = laplace_transform_expression(equation)
        elif "integrate" in equation.lower():
            solution = integrate_expression(equation)
        else:
            solution = solve_equation(equation)
        
        return solution

    except Exception as e:
        return f"Error processing input: {str(e)}"