Create solver.py

solver.py

@@ -0,0 +1,123 @@
+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, ""