app.py

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

# Generate abstract polynomial form for given degree
def generate_polynomial_template(degree):
    terms = [f"_x^{degree - i}" for i in range(degree)] + ["_"]
    return " + ".join(terms) + " = 0"

# Solve and plot polynomial
def solve_polynomial(degree, coeff_string):
    try:
        coeffs = list(map(float, coeff_string.strip().split()))
        if len(coeffs) != degree + 1:
            return "⚠️ Please enter exactly {} coefficients.".format(degree + 1), None, None

        poly = sum([coeffs[i] * sp.symbols('x')**(degree - i) for i in range(degree + 1)])
        simplified = sp.simplify(poly)
        factored = sp.factor(simplified)
        roots = sp.solve(sp.Eq(simplified, 0), sp.symbols('x'))

        # Prepare root output in regular format
        roots_output = "$$"
        for i, r in enumerate(roots, 1):
            roots_output += f"r_{{{i}}} = {sp.latex(sp.nsimplify(r, rational=True))} \\ "
        roots_output += "$$"

        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"
        steps_output += f"### 🤩 Factored\n\n$$ {sp.latex(factored)} = 0 $$\n\n"
        steps_output += f"### 🥮 Roots (Real and Complex)\n\n{roots_output}"

        # Plotting
        x_vals = np.linspace(-10, 10, 400)
        y_vals = np.polyval(coeffs, x_vals)

        fig, ax = plt.subplots()
        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.grid(True)
        ax.set_title("📈 Graph of the Polynomial")
        ax.set_xlabel("x")
        ax.set_ylabel("f(x)")
        ax.legend()

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

# Gradio UI
def update_template(degree):
    return generate_polynomial_template(degree)

with gr.Blocks() as demo:
    gr.Markdown("## 🔢 Polynomial Solver (Symbolic + Graph)")

    with gr.Row():
        degree_slider = gr.Slider(1, 8, value=3, step=1, label="Degree of Polynomial")
        template_display = gr.Textbox(label="Polynomial Template (Fill in Coefficients)", interactive=False)

    coeff_input = gr.Textbox(label="Enter Coefficients (space-separated)", placeholder="e.g. 1 -6 11 -6")

    steps_md = gr.Markdown()
    plot_output = gr.Plot()
    error_box = gr.Textbox(visible=False)

    with gr.Row():
        solve_button = gr.Button("Plot Polynomial")

    degree_slider.change(fn=update_template, inputs=degree_slider, outputs=template_display)
    solve_button.click(fn=solve_polynomial, inputs=[degree_slider, coeff_input], outputs=[steps_md, plot_output, error_box])

    demo.load(fn=update_template, inputs=degree_slider, outputs=template_display)

    demo.launch()