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, simplify, expand, log, exp, sin, cos, tan, asin, acos, atan, Symbol, factorial, laplace_transform

def format_expression(expr):
    """Format expression to make it more readable."""
    # Convert string representation to a more readable format
    str_expr = str(expr)
    replacements = {
        '**': '^',
        '*x': 'x',
        'exp': 'e^',
        'sqrt': '√',
        'factorial': '!'
    }
    for old, new in replacements.items():
        str_expr = str_expr.replace(old, new)
    return str_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',
            '!': 'factorial',
        }
        for old, new in replacements.items():
            equation_str = equation_str.replace(old, new)

        # 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:
        # Preprocess the expression
        processed_expr = preprocess_equation(expr_str)
        x = Symbol('x')

        # Check for special operations
        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
            expr = parse_expr(processed_expr, transformations=(standard_transformations + (implicit_multiplication_application,)))
            result = expr.doit()
            return f"{format_expression(expr)} = {format_expression(result)}"

        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)}")

def solve_equation(equation_str):
    """Solve the given equation and return the solution."""
    try:
        if '=' not in equation_str:
            return process_expression(equation_str)

        # Preprocess equation
        equation_str = preprocess_equation(equation_str)

        # Split equation into left and right parts
        left_side, right_side = [side.strip() for side in equation_str.split('=')]

        # Parse both sides with implicit multiplication
        transformations = standard_transformations + (implicit_multiplication_application,)
        left_expr = parse_expr(left_side, transformations=transformations)
        right_expr = parse_expr(right_side, transformations=transformations)
        equation = left_expr - right_expr

        # Solve the equation
        x = Symbol('x')
        solution = solve(equation, x)

        # Format solution
        if len(solution) == 0:
            return "No solution exists"
        elif len(solution) == 1:
            return f"x = {format_expression(solution[0])}"
        else:
            return "x = " + ", ".join([format_expression(sol) for sol in solution])

    except Exception as e:
        raise Exception(f"Invalid equation format: {str(e)}")

def generate_steps(equation_str):
    """Generate step-by-step solution for the equation or expression."""
    steps = []
    try:
        if '=' not in equation_str:
            steps.append(f"1. Original expression: {equation_str}")
            result = process_expression(equation_str)
            steps.append(f"2. Result: {result}")
            return steps

        # Preprocess equation
        processed_eq = preprocess_equation(equation_str)

        # Split equation into left and right parts
        left_side, right_side = [side.strip() for side in processed_eq.split('=')]

        # Parse expressions with implicit multiplication
        transformations = standard_transformations + (implicit_multiplication_application,)
        left_expr = parse_expr(left_side, transformations=transformations)
        right_expr = parse_expr(right_side, transformations=transformations)

        # Step 1: Show original equation
        steps.append(f"1. Original equation: {format_expression(left_expr)} = {format_expression(right_expr)}")

        # Step 2: Move all terms to left side
        equation = left_expr - right_expr
        steps.append(f"2. Move all terms to left side: {format_expression(equation)} = 0")

        # Step 3: Factor if possible
        factored = sp.factor(equation)
        if factored != equation:
            steps.append(f"3. Factor the equation: {format_expression(factored)} = 0")

        # Step 4: Solve
        x = Symbol('x')
        solution = solve(equation, x)
        steps.append(f"4. Solve for x: x = {', '.join([format_expression(sol) for sol in solution])}")

        # Step 5: Verify solutions
        steps.append("5. Verify solutions:")
        for sol in solution:
            result = equation.subs(x, sol)
            steps.append(f"   When x = {format_expression(sol)}, equation equals {format_expression(result)}")

        return steps

    except Exception as e:
        raise Exception(f"Error generating steps: {str(e)}")