solver.py

import sympy as sp
import numpy as np
import matplotlib.pyplot as plt

x, y = sp.symbols('x y')


def generate_polynomial_template(degree):
    terms = [f"a{i}*x^{degree - i}" for i in range(degree)] + [f"a{degree}"]
    return " + ".join(terms) + " = 0"


def solve_polynomial(degree, coeff_string):
    try:
        coeffs = [sp.sympify(s) for s in coeff_string.strip().split()]
        if len(coeffs) != degree + 1:
            return f"⚠️ Please enter exactly {degree + 1} coefficients.", None, None, ""

        poly = sum([coeffs[i] * x**(degree - i) for i in range(degree + 1)])
        simplified = sp.simplify(poly)

        # Step-by-step factorization
        factored_steps = []
        current_expr = simplified
        while True:
            factored = sp.factor(current_expr)
            if factored == current_expr:
                break
            factored_steps.append(factored)
            current_expr = factored

        roots = sp.solve(sp.Eq(simplified, 0), x)
        root_display = []
        for i, r in enumerate(roots):
            r_simplified = sp.nsimplify(r, rational=True)
            root_display.append(f"r_{{{i+1}}} = {sp.latex(r_simplified)}")

        steps_output = f"### 🧐 Polynomial Expression\n\n$$ {sp.latex(poly)} = 0 $$\n\n"
        steps_output += f"### ✏️ Simplified\n\n$$ {sp.latex(simplified)} = 0 $$\n\n"

        if factored_steps:
            steps_output += "### 🪜 Step-by-Step Factorization\n\n"
            for i, step in enumerate(factored_steps, 1):
                steps_output += f"**Step {i}:** $$ {sp.latex(step)} = 0 $$\n\n"
        else:
            steps_output += "### 🤷 No further factorization possible\n\n"

        steps_output += "### 🥮 Roots\n\n$$ " + " \\quad ".join(root_display) + " $$"

        # Plotting
        f_lambdified = sp.lambdify(x, simplified, modules=["numpy"])
        x_vals = np.linspace(-10, 10, 400)
        y_vals = f_lambdified(x_vals)

        fig, ax = plt.subplots(figsize=(6, 4))
        ax.plot(x_vals, y_vals, label="Polynomial")
        ax.axhline(0, color='black', linewidth=0.5)
        ax.axvline(0, color='black', linewidth=0.5)
        ax.set_title("📈 Graph of the Polynomial")
        ax.set_xlabel("x")
        ax.set_ylabel("f(x)")
        ax.grid(True)

        real_roots = [sp.N(r.evalf()) for r in roots if sp.im(r) == 0]
        for r in real_roots:
            ax.plot([float(r)], [0], 'ro', label="Real Root")

        ax.legend()

        return steps_output, fig, "", steps_output

    except Exception as e:
        return f"❌ Error: {e}", None, "", ""


def solve_linear_system(eq1_str, eq2_str):
    try:
        eq1 = sp.sympify(eq1_str)
        eq2 = sp.sympify(eq2_str)

        sol = sp.solve((eq1, eq2), (x, y), dict=True)

        steps = "### 🔍 Solving System\n\n"
        steps += f"**Equation 1:** $$ {sp.latex(eq1)} $$\n\n"
        steps += f"**Equation 2:** $$ {sp.latex(eq2)} $$\n\n"

        if sol:
            sol = sol[0]
            steps += f"**Solution:** $$ x = {sp.latex(sol[x])}, \\quad y = {sp.latex(sol[y])} $$\n\n"
        else:
            steps += "**❌ No unique solution or inconsistent system**\n"

        # Plotting
        x_vals = np.linspace(-10, 10, 400)
        f1 = sp.solve(eq1, y)
        f2 = sp.solve(eq2, y)

        fig, ax = plt.subplots(figsize=(6, 4))
        if f1 and f2:
            y1_vals = sp.lambdify(x, f1[0], modules=["numpy"])(x_vals)
            y2_vals = sp.lambdify(x, f2[0], modules=["numpy"])(x_vals)
            ax.plot(x_vals, y1_vals, label="Equation 1")
            ax.plot(x_vals, y2_vals, label="Equation 2")

            if sol:
                px = float(sp.N(sol[x]))
                py = float(sp.N(sol[y]))
                ax.plot(px, py, 'ro')
                ax.annotate(f"({px:.2f}, {py:.2f})", (px, py), textcoords="offset points", xytext=(10, 5),
                            ha='center', color='red')

        ax.axhline(0, color='black', linewidth=0.5)
        ax.axvline(0, color='black', linewidth=0.5)
        ax.set_title("📉 Graph of the Linear System")
        ax.set_xlabel("x")
        ax.set_ylabel("y")
        ax.grid(True)
        ax.legend()

        return steps, fig, steps

    except Exception as e:
        return f"❌ Error: {e}", None, ""