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,sqrt, 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 'sqrt' in processed_expr.lower():  
            try:
                transformations = standard_transformations + (implicit_multiplication_application,)
        
        # Remove "sqrt" and parse the expression inside
                expr = sp.parse_expr(processed_expr.replace("sqrt", ""), transformations=transformations)  
        
                sqrt_result = sp.sqrt(expr)  
        
        # If it's sqrt(x^2), simplify it to |x|
                simplified_result = sp.simplify(sqrt_result)
        
                steps = []
                steps.append(f"**Step 1:** Original expression: \n{to_latex(expr)}")
        
        # Case 1: Perfect Squares → Show exact value (e.g., sqrt(9) = ±3)
                if sqrt_result.is_Integer:
                    steps.append(f"**Step 2:** √{to_latex(expr)} is a perfect square")
                    steps.append(f"**Step 3:** Solution: \n±{to_latex(sqrt_result)}")
                    solution = "\n".join(steps)

        # Case 2: Non-Perfect Squares → Show decimal value (e.g., sqrt(2) ≈ 1.41)
                elif sqrt_result.is_real and not sqrt_result.is_rational:
                    decimal_value = float(sqrt_result.evalf())
                    steps.append(f"**Step 2:** √{to_latex(expr)} is not a perfect square")
                    steps.append(f"**Step 3:** Approximate value: \n{decimal_value}")
                    solution = "\n".join(steps)

        # Case 3: Expressions like √x² → |x|
                elif simplified_result != sqrt_result:
                    steps.append(f"**Step 2:** Simplification using identity: \n{to_latex(simplified_result)}")
                    solution = "\n".join(steps)

        # Case 4: General Expression → Return as-is
                else:
                    steps.append(f"**Step 2:** Taking square root: \n{to_latex(sqrt_result)}")
                    steps.append(f"**Step 3:** Considering both positive and negative roots: \n±{to_latex(sqrt_result)}")
                    solution = "\n".join(steps)

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