Create linear.py

linear.py

@@ -0,0 +1,136 @@
+#linear.py
+
+import gradio as gr
+import sympy as sp
+import numpy as np
+import matplotlib.pyplot as plt
+import random
+
+x, y = sp.symbols('x y')
+
+def generate_linear_template():
+    return "$$ a_1x + b_1y = c_1 \\ a_2x + b_2y = c_2 $$"
+
+def load_linear_example():
+    examples = [
+        ("1 -4 -2", "5 1 9"),
+        ("2 1 8", "1 -1 2"),
+        ("3 2 12", "1 1 5"),
+        ("4 -1 3", "2 3 6"),
+        ("1 2 10", "3 -1 5")
+    ]
+    return random.choice(examples)
+
+def solve_linear_system_from_coeffs(eq1_str, eq2_str):
+    try:
+        coeffs1 = list(map(float, eq1_str.strip().split()))
+        coeffs2 = list(map(float, eq2_str.strip().split()))
+
+        if len(coeffs1) != 3 or len(coeffs2) != 3:
+            return "⚠️ Please enter exactly 3 coefficients for each equation.", None, None, None
+
+        a1, b1, c1 = coeffs1
+        a2, b2, c2 = coeffs2
+
+        eq1 = sp.Eq(a1 * x + b1 * y, c1)
+        eq2 = sp.Eq(a2 * x + b2 * y, c2)
+
+        sol = sp.solve([eq1, eq2], (x, y), dict=True)
+        if not sol:
+            return "❌ No unique solution.", None, None, None
+
+        solution = sol[0]
+        eq_latex = f"$$ {sp.latex(eq1)} \\ {sp.latex(eq2)} $$"
+
+        steps = rf"""
+### 📌 Step-by-step Solution
+1. **Original Equations:**
+   $$ {sp.latex(eq1)} $$
+   $$ {sp.latex(eq2)} $$
+2. **Standard Form:** Already provided.
+3. **Solve using SymPy `solve`:** Internally applies substitution/elimination.
+4. **Solve for `x` and `y`:**
+   $$ x = {sp.latex(solution[x])}, \quad y = {sp.latex(solution[y])} $$
+5. **Verification:** Substitute back into both equations."""
+
+        x_vals = np.linspace(-10, 10, 400)
+        f1 = sp.solve(eq1, y)
+        f2 = sp.solve(eq2, y)
+
+        fig, ax = plt.subplots()
+        if f1:
+            f1_func = sp.lambdify(x, f1[0], modules='numpy')
+            ax.plot(x_vals, f1_func(x_vals), label=sp.latex(eq1))
+        if f2:
+            f2_func = sp.lambdify(x, f2[0], modules='numpy')
+            ax.plot(x_vals, f2_func(x_vals), label=sp.latex(eq2))
+
+        ax.plot(solution[x], solution[y], 'ro', label=f"Solution ({solution[x]}, {solution[y]})")
+        ax.axhline(0, color='black', linewidth=0.5)
+        ax.axvline(0, color='black', linewidth=0.5)
+        ax.legend()
+        ax.set_title("📊 Graph of the Equations")
+        ax.grid(True)
+
+        return eq_latex, steps, fig, ""
+    except Exception as e:
+        return f"❌ Error: {e}", None, None, None
+
+def linear_tab():
+    with gr.Tab("📊 Linear System Solver"):
+        gr.Markdown("## 📈 Solve 2x2 Linear System")
+        linear_template = gr.Markdown(value=generate_linear_template())
+
+        with gr.Row():
+            linear_eq1_input = gr.Textbox(label="Equation 1 Coefficients (a1 b1 c1)", placeholder="e.g. 2 1 8")
+            linear_eq2_input = gr.Textbox(label="Equation 2 Coefficients (a2 b2 c2)", placeholder="e.g. 1 -1 2")
+
+        linear_example_btn = gr.Button("🔁 Load Example")
+        preview_button = gr.Button("🔍 Preview Equations")
+
+        linear_equation_display = gr.Markdown()
+        with gr.Row():
+            confirm_btn = gr.Button("✅ Display Solution", visible=False)
+            cancel_btn = gr.Button("✏️ Make Changes in Equation", visible=False)
+
+        linear_steps_md = gr.Markdown()
+        linear_plot = gr.Plot()
+        linear_error = gr.Textbox(visible=False)
+
+        def update_example():
+            eq1, eq2 = load_linear_example()
+            return eq1, eq2
+
+        linear_example_btn.click(fn=update_example, inputs=[], outputs=[linear_eq1_input, linear_eq2_input])
+
+        def preview_equations(eq1_str, eq2_str):
+            try:
+                coeffs1 = list(map(float, eq1_str.strip().split()))
+                coeffs2 = list(map(float, eq2_str.strip().split()))
+                if len(coeffs1) != 3 or len(coeffs2) != 3:
+                    return "⚠️ Please enter exactly 3 coefficients for each equation.", gr.update(visible=False), gr.update(visible=False)
+                a1, b1, c1 = coeffs1
+                a2, b2, c2 = coeffs2
+                eq1 = sp.Eq(a1 * x + b1 * y, c1)
+                eq2 = sp.Eq(a2 * x + b2 * y, c2)
+                eq_latex = f"### ✅ Confirm Equations\n\n$$ {sp.latex(eq1)} \\\\ {sp.latex(eq2)} $$"
+                return eq_latex, gr.update(visible=True), gr.update(visible=True)
+            except Exception as e:
+                return f"❌ Error parsing equations: {e}", gr.update(visible=False), gr.update(visible=False)
+
+        preview_button.click(
+            fn=preview_equations,
+            inputs=[linear_eq1_input, linear_eq2_input],
+            outputs=[linear_equation_display, confirm_btn, cancel_btn]
+        )
+
+        cancel_btn.click(
+            fn=lambda: (gr.update(visible=False), gr.update(visible=False), "", None, None),
+            outputs=[confirm_btn, cancel_btn, linear_equation_display, linear_steps_md, linear_plot]
+        )
+
+        confirm_btn.click(
+            fn=solve_linear_system_from_coeffs,
+            inputs=[linear_eq1_input, linear_eq2_input],
+            outputs=[linear_equation_display, linear_steps_md, linear_plot, linear_error]
+        )