feat: enhance Gradio interfaces for cubic, polynomial, quadratic, and simultaneous equation solvers with detailed descriptions and examples

maths/equations/solve_cubic.py

@@ -42,5 +42,16 @@ cubic_solver_interface = gr.Interface(
     ],
     outputs="text",
     title="Cubic Equation Solver",
-    description="Solve ax³ + bx² + cx + d = 0"
+    description="""
+Solve cubic equations of the form ax³ + bx² + cx + d = 0. Enter the coefficients for your cubic equation.
+
+Example: For x³ - 6x² + 11x - 6 = 0, enter a=1, b=-6, c=11, d=-6.
+
+Returns all real and complex roots.
+""",
+    examples=[
+        [1, -6, 11, -6],
+        [2, 0, -4, 2],
+        [1, 0, 0, -8]
+    ]
 )

maths/equations/solve_poly.py

@@ -37,5 +37,16 @@ poly_solver_interface = gr.Interface(
     inputs=gr.Textbox(label="Coefficients (comma-separated, highest degree first)", placeholder="e.g. 1, 0, -2, -8"),
     outputs="text",
     title="Polynomial Equation Solver",
-    description="Find roots of any polynomial. Enter coefficients separated by commas (highest degree first)."
+    description="""
+Find roots of any polynomial equation. Enter the coefficients separated by commas, starting with the highest degree.
+
+Example: For x⁴ - 2x² - 8 = 0, enter: 1, 0, -2, 0, -8
+
+Supports real and complex roots for polynomials of any degree.
+""",
+    examples=[
+        ["1, 0, -2, 0, -8"],
+        ["2, -3, 0, 1"],
+        ["1, -6, 11, -6"]
+    ]
 )

maths/equations/solve_quadratic.py

@@ -104,7 +104,21 @@ solve_quadratic_interface = gr.Interface(
     ],
     outputs="text",
     title="Quadratic Equation Solver",
-    description="Solve ax² + bx + c = 0 and find vertex"
+    description="""
+Solve ax² + bx + c = 0 and find the vertex. Enter the coefficients for your quadratic equation and select the output format.
+
+Example: For x² - 3x + 2 = 0, enter a=1, b=-3, c=2.
+
+Output format:
+- 'string': plain text
+- 'dict': formatted output
+- 'surd': exact roots (if possible)
+""",
+    examples=[
+        [1, -3, 2, "dict"],
+        [2, 4, -6, "string"],
+        [1, 2, 1, "surd"]
+    ]
 )
 
 def plot_quadratic(a, b, c):
@@ -178,5 +192,14 @@ quadratic_visualizer_interface = gr.Interface(
     ],
     outputs=gr.Plot(),
     title="Quadratic Function Visualizer",
-    description="Visualize the graph of a quadratic function f(x) = ax² + bx + c with its vertex and roots"
+    description="""
+Visualize the graph of a quadratic function f(x) = ax² + bx + c, including its vertex and real roots (if any).
+
+Example: For f(x) = x² - 4x + 3, enter a=1, b=-4, c=3.
+""",
+    examples=[
+        [1, -4, 3],
+        [2, 0, -8],
+        [1, 2, 1]
+    ]
 )

maths/equations/solve_simultaneous.py

@@ -31,5 +31,12 @@ simultaneous_solver_interface = gr.Interface(
     ],
     outputs="text",
     title="Simultaneous Linear Equation Solver",
-    description="Solve simultaneous linear equations. Enter coefficients for each equation (one per line), and constants."
+    description="""
+Solve systems of simultaneous linear equations. Enter the coefficients for each equation (one per line, comma-separated) and the constants (right-hand side values).\n\nExample: For the system\n\n  x + 2y = 5\n  3x + 4y = 6\n\nEnter coefficients:\n1,2\n3,4\n\nEnter constants:\n5,6
+""",
+    examples=[
+        ["1,2\n3,4", "5,6"],
+        ["2,1\n1,3", "8,13"],
+        ["1,1,1\n2,3,4\n1,2,3", "6,20,14"]
+    ]
 )