Update image.py

image.py

@@ -128,25 +128,28 @@ def extract_polynomial_coefficients(latex_str):
             "variable": "x"
         }
 
-def solve_polynomial(degree, coeff_string, real_only, variable="x"):
+def solve_polynomial(degree, coeff_string, real_only, variable_name="x"):
     try:
+        variable = sp.Symbol(variable_name)
         coeffs = list(map(float, coeff_string.strip().split()))
         if len(coeffs) != degree + 1:
             return f"⚠️ Please enter exactly {degree + 1} coefficients.", None, None
 
-        var = get_variable_symbol(variable)
-        poly = sum([coeffs[i] * var**(degree - i) for i in range(degree + 1)])
+        # Build the polynomial expression
+        poly = sum([coeffs[i] * variable**(degree - i) for i in range(degree + 1)])
         simplified = sp.simplify(poly)
         factored = sp.factor(simplified)
-        roots = sp.solve(sp.Eq(simplified, 0), var)
+        roots = sp.solve(sp.Eq(simplified, 0), variable)
 
         if real_only:
             roots = [r for r in roots if sp.im(r) == 0]
 
+        # Format roots in LaTeX
         roots_output = "$$\n" + "\\ ".join(
             [f"r_{{{i}}} = {sp.latex(sp.nsimplify(r, rational=True))}" for i, r in enumerate(roots, 1)]
         ) + "\n$$"
 
+        # Format steps in LaTeX
         steps_output = f"""
 ### Polynomial Expression
 $$ {sp.latex(poly)} = 0 $$
@@ -158,6 +161,7 @@ $$ {sp.latex(factored)} = 0 $$
 {roots_output}
         """
 
+        # Generate plot using numeric x-axis
         x_vals = np.linspace(-10, 10, 400)
         y_vals = np.polyval(coeffs, x_vals)
 
@@ -167,8 +171,8 @@ $$ {sp.latex(factored)} = 0 $$
         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.set_xlabel(str(variable))
+        ax.set_ylabel("f(" + str(variable) + ")")
         ax.legend()
 
         return steps_output, fig, ""