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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, ""
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