Create polynomial.py

polynomial.py

@@ -0,0 +1,158 @@
+import gradio as gr
+import sympy as sp
+import numpy as np
+import matplotlib.pyplot as plt
+
+# Define symbolic variable for polynomial operations
+x = sp.symbols('x')
+
+# Function to generate a LaTeX template for a polynomial based on its degree
+def generate_polynomial_template(degree):
+    terms = [f"a_{{{i}}}x^{degree - i}" for i in range(degree)]
+    terms.append(f"a_{{{degree}}}")
+    return "$$" + " + ".join(terms) + " = 0$$"
+
+# Function to load example coefficients for a given polynomial degree
+def load_poly_example(degree):
+    examples = {
+        1: "3 9",
+        2: "1 -3 2",
+        3: "1 -6 11 -6",
+        4: "1 0 -5 0 4",
+        5: "1 -9 3 8 1 8",
+        6: "1 -9 3 8 1 8 3",
+        7: "1 -9 3 8 1 8 6 2",
+        8: "1 -9 3 8 1 8 2 3 7"
+    }
+    return examples.get(degree, "")
+
+# Function to solve the polynomial equation and generate a graph
+def solve_polynomial(degree, coeff_string, real_only):
+    try:
+        coeffs = list(map(float, 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)
+        factored = sp.factor(simplified)
+        roots = sp.solve(sp.Eq(simplified, 0), x)
+
+        if real_only:
+            roots = [r for r in roots if sp.im(r) == 0]
+
+        roots_output = "$$\n" + "\\ ".join(
+            [f"r_{{{i}}} = {sp.latex(sp.nsimplify(r, rational=True))}" for i, r in enumerate(roots, 1)]
+        ) + "\n$$"
+
+        steps_output = f"""
+### Polynomial Expression
+$$ {sp.latex(poly)} = 0 $$
+### Simplified
+$$ {sp.latex(simplified)} = 0 $$
+### Factored
+$$ {sp.latex(factored)} = 0 $$
+### Roots {'(Only Real)' if real_only else '(All Roots)'}
+{roots_output}
+        """
+
+        x_vals = np.linspace(-10, 10, 400)
+        y_vals = np.polyval(coeffs, x_vals)
+
+        fig, ax = plt.subplots(figsize=(6, 4))
+        ax.plot(x_vals, y_vals, label="Polynomial", color="blue")
+        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, ""
+
+# Function to create the Polynomial Solver tab with Gradio components
+def polynomial_tab():
+    with gr.Tab("Polynomial Solver"):
+        # Row for displaying the equation template and real roots checkbox
+        with gr.Row():
+            template_display = gr.Markdown(value=generate_polynomial_template(2))
+            real_checkbox = gr.Checkbox(label="Show Only Real Roots", value=False)
+
+        # Row for selecting the polynomial degree and entering coefficients
+        with gr.Row():
+            degree_slider = gr.Slider(1, 8, value=2, step=1, label="Select Degree of Polynomial Equation")
+            coeff_input = gr.Textbox(label="Enter Coefficients (space-separated)", placeholder="e.g. 1 -3 2")
+
+        # Row for example and preview buttons
+        with gr.Row():
+            example_btn = gr.Button("Load Example")
+            preview_poly_button = gr.Button("Preview Equation")
+
+        # Row for displaying the confirmed equation
+        with gr.Row():
+            poly_equation_display = gr.Markdown()
+
+        # Row for confirm and cancel buttons
+        with gr.Row():
+            confirm_poly_btn = gr.Button("Display Solution", visible=False)
+            cancel_poly_btn = gr.Button("Make Changes in Equation", visible=False)
+
+        # Markdown component to display step-by-step solution
+        steps_md = gr.Markdown()
+
+        # Plot component to display the polynomial graph
+        plot_output = gr.Plot()
+
+        # Textbox to display errors (initially hidden)
+        error_box = gr.Textbox(visible=False)
+
+        # Function to preview the polynomial equation based on user input
+        def preview_polynomial(degree, coeff_string, real_only):
+            try:
+                coeffs = list(map(float, coeff_string.strip().split()))
+                if len(coeffs) != degree + 1:
+                    return f"⚠️ Please enter exactly {degree + 1} coefficients.", gr.update(visible=False), gr.update(visible=False), "", None
+                poly = sum([coeffs[i] * x**(degree - i) for i in range(degree + 1)])
+                eq_latex = f"### ✅ Confirm Polynomial\n\n$$ {sp.latex(poly)} = 0 $$"
+                return eq_latex, gr.update(visible=True), gr.update(visible=True), "", None
+            except Exception as e:
+                return f"❌ Error parsing coefficients: {e}", gr.update(visible=False), gr.update(visible=False), "", None
+
+        # Event handler for preview button click
+        preview_poly_button.click(
+            fn=preview_polynomial,
+            inputs=[degree_slider, coeff_input, real_checkbox],
+            outputs=[poly_equation_display, confirm_poly_btn, cancel_poly_btn, steps_md, plot_output]
+        )
+
+        # Function to handle cancellation of the preview
+        def cancel_poly():
+            return gr.update(visible=False), gr.update(visible=False), "", "", None
+
+        # Event handler for cancel button click
+        cancel_poly_btn.click(
+            fn=cancel_poly,
+            inputs=[],
+            outputs=[confirm_poly_btn, cancel_poly_btn, poly_equation_display, steps_md, plot_output]
+        )
+
+        # Event handler for confirm button click to solve and display results
+        confirm_poly_btn.click(
+            fn=solve_polynomial,
+            inputs=[degree_slider, coeff_input, real_checkbox],
+            outputs=[steps_md, plot_output, error_box]
+        )
+
+        # Event handler to update the template when the degree slider changes
+        degree_slider.change(fn=generate_polynomial_template, inputs=degree_slider, outputs=template_display)
+
+        # Event handler to load an example when the example button is clicked
+        example_btn.click(fn=load_poly_example, inputs=degree_slider, outputs=coeff_input)
+
+        # Initialize the template display with the default degree (2) on load
+        template_display.value = generate_polynomial_template(2)
+
+    return template_display, real_checkbox, degree_slider, coeff_input, example_btn, preview_poly_button, poly_equation_display, confirm_poly_btn, cancel_poly_btn, steps_md, plot_output, error_box