feat: add Gradio interface for simultaneous equation solving; update equations tab to include new solver

maths/equations/equations_tab.py

@@ -2,10 +2,23 @@ import gradio as gr
 from maths.equations.solve_quadratic import solve_quadratic_interface, quadratic_visualizer_interface
 from maths.equations.solve_cubic import cubic_solver_interface
 from maths.equations.solve_poly import poly_solver_interface
+from maths.equations.solve_simultaneous import simultaneous_solver_interface
 
 
 equations_tab = gr.TabbedInterface(
-    [solve_quadratic_interface, quadratic_visualizer_interface, cubic_solver_interface, poly_solver_interface],
-    ["Quadratic Solver", "Quadratic Visualizer", "Cubic Solver", "Polynomial Solver"],
+    [
+        solve_quadratic_interface,
+        quadratic_visualizer_interface,
+        cubic_solver_interface,
+        poly_solver_interface,
+        simultaneous_solver_interface
+    ],
+    [
+        "Quadratic Solver",
+        "Quadratic Visualizer",
+        "Cubic Solver",
+        "Polynomial Solver",
+        "Simultaneous Equation Solver"
+    ],
     title="Equations"
 )

maths/equations/solve_poly.py

@@ -1,4 +1,5 @@
 import numpy as np
+import gradio as gr
 
 def solve_polynomial(coeffs):
     """

maths/equations/solve_simultaneous.py

@@ -0,0 +1,35 @@
+import gradio as gr
+import numpy as np
+
+def solve_simultaneous_interface(coeffs, constants):
+    """
+    coeffs: Multiline string, each line is comma-separated coefficients for one equation.
+    constants: Comma-separated string of constants (right-hand side values).
+    """
+    try:
+        coeff_lines = [line.strip() for line in coeffs.strip().splitlines() if line.strip()]
+        matrix = [list(map(float, line.split(','))) for line in coeff_lines]
+        A = np.array(matrix)
+        b = np.array([float(x) for x in constants.strip().split(',')])
+        if A.shape[0] != A.shape[1]:
+            return f"Number of equations and unknowns must match (got {A.shape[0]} equations, {A.shape[1]} unknowns)."
+        if b.shape[0] != A.shape[0]:
+            return f"Number of constants must match number of equations."
+        solution = np.linalg.solve(A, b)
+        output = ""
+        for idx, val in enumerate(solution):
+            output += f"Variable {idx+1}: {val}\n"
+        return output
+    except Exception as e:
+        return f"Error: {e}"
+
+simultaneous_solver_interface = gr.Interface(
+    fn=solve_simultaneous_interface,
+    inputs=[
+        gr.Textbox(lines=4, label="Coefficients (one equation per line, comma-separated)", placeholder="e.g.\n1,2\n3,4"),
+        gr.Textbox(label="Constants (comma-separated)", placeholder="e.g. 5, 6")
+    ],
+    outputs="text",
+    title="Simultaneous Linear Equation Solver",
+    description="Solve simultaneous linear equations. Enter coefficients for each equation (one per line), and constants."
+)