Update app.py

app.py

@@ -82,14 +82,13 @@ def solve_polynomial(image, llm_url):
             expr = expr.subs(sp.pi, sp.Float(3.1416)).subs(sp.E, sp.Float(2.7183))
             if not isinstance(expr, sp.Equality):
                 raise ValueError("Expression is not an equation.")
-            lhs_minus_rhs = expr.lhs - expr.rhs
-            if not lhs_minus_rhs.is_polynomial():
-                raise ValueError("Expression is not a polynomial.")
-            junk_symbols = {"pm", "cdot", "mathrm", "boldmath", "bar", "L"}
-            symbols = {str(s) for s in expr.free_symbols}
-            if symbols & junk_symbols:
-                raise ValueError("Expression contains junk symbols.")
-        except Exception:
+            lhs = expr.lhs - expr.rhs
+            if not lhs.is_polynomial():
+                raise ValueError("Not a polynomial")
+            junk = {"pm", "cdot", "mathrm", "boldmath", "bar", "L"}
+            if {str(s) for s in expr.free_symbols} & junk:
+                raise ValueError("Junk in symbols")
+        except:
             fixed_latex = request_llm_fallback(cleaned_latex, llm_url)
             cleaned_latex = clean_latex(fixed_latex)
             try:
@@ -97,51 +96,76 @@ def solve_polynomial(image, llm_url):
                 expr = expr.subs(sp.pi, sp.Float(3.1416)).subs(sp.E, sp.Float(2.7183))
                 if not isinstance(expr, sp.Equality):
                     raise ValueError("Expression is not an equation.")
-                lhs_minus_rhs = expr.lhs - expr.rhs
-                if not lhs_minus_rhs.is_polynomial():
-                    raise ValueError("Expression is not a polynomial.")
-                symbols = {str(s) for s in expr.free_symbols}
-                if symbols & junk_symbols:
-                    raise ValueError("Expression contains junk symbols.")
-            except Exception:
-                expr = None
-        if expr is None:
-            return f"❌ Could not parse expression even after fallback:\n\n```latex\n{cleaned_latex}\n```", cleaned_latex, ""
-        output = (
-            f"## 📄 Extracted LaTeX\n\n```latex\n{latex_result}\n```\n"
-            f"\n---\n## 🧹 Cleaned LaTeX Used\n\n```latex\n{cleaned_latex}\n```\n"
-            f"\n---\n## 🧠 Parsed Expression\n\n$$ {sp.latex(expr)} $$\n\n---\n"
-        )
-        if isinstance(expr, sp.Equality):
-            lhs = expr.lhs - expr.rhs
-            output += f"## ✏️ Step 1: Standard Form\n$$ {sp.latex(lhs)} = 0 $$\n---\n"
-            output += f"## 🧩 Step 2: Factor\n$$ {sp.latex(sp.factor(lhs))} = 0 $$\n---\n"
-            x_sym = None
-            for sym in lhs.free_symbols:
-                if str(sym) == "x":
-                    x_sym = sym
-                    break
-            if x_sym is None:
-                raise ValueError("❌ Could not find variable 'x' in the equation.")
-            roots = sp.solve(sp.Eq(lhs, 0), x_sym, dict=True)
-            output += "## ✅ Step 3: Solve Roots\n"
-            if roots:
-                output += "$$\n\\begin{aligned}\n"
-                for i, sol in enumerate(roots, 1):
-                    for var, val in sol.items():
-                        evaluated = val.evalf(6)
-                        output += f"\\text{{Root {i}}}:\\quad {var} &\\approx {sp.latex(evaluated)} \\\\\n"
-                output += "\\end{aligned}\n$$\n"
-        else:
-            simplified = sp.simplify(expr)
-            output += f"## ➕ Simplified Expression\n$$ {sp.latex(simplified)} $$"
-        return output, cleaned_latex, ""
+                lhs = expr.lhs - expr.rhs
+                if not lhs.is_polynomial():
+                    raise ValueError("Not a polynomial")
+            except:
+                return f"❌ Could not parse expression after fallback:\n\n```latex\n{cleaned_latex}\n```", cleaned_latex, ""
+
+        output = f"## 📄 Extracted LaTeX\n```latex\n{latex_result}\n```\n"
+        output += f"---\n## 🧹 Cleaned LaTeX\n```latex\n{cleaned_latex}\n```\n"
+        output += f"---\n## 🧠 Parsed Expression\n$$ {sp.latex(expr)} $$\n"
+
+        lhs = expr.lhs - expr.rhs
+        factor = sp.factor(lhs)
+        output += f"---\n## ✏️ Standard Form\n$$ {sp.latex(lhs)} = 0 $$\n"
+        output += f"---\n## 🧩 Factorized\n$$ {sp.latex(factor)} = 0 $$\n"
+
+        x = next(iter(lhs.free_symbols))
+        roots = sp.solve(lhs, x)
+        output += "## ✅ Roots\n"
+        output += "$$\n\\begin{aligned}\n"
+        root_strs = []
+        for i, r in enumerate(roots, 1):
+            root_val = sp.N(r, 6)
+            output += f"\\text{{Root {i}}}:\\quad x &\\approx {sp.latex(root_val)} \\\\\n"
+            root_strs.append(str(root_val))
+        output += "\\end{aligned}\n$$\n"
+
+        # 🔍 Build structured LLM prompt
+        prompt = ""
+        try:
+            coeffs = sp.Poly(lhs, x).all_coeffs()
+            if len(coeffs) == 3:
+                a, b, c = [float(k) for k in coeffs]
+                prod = a * c
+                found = False
+                for m in range(-100, 101):
+                    if m == 0 or prod % m != 0:
+                        continue
+                    n = prod / m
+                    if m + n == b:
+                        found = True
+                        prompt = (
+                            f"Equation: {lhs} = 0\n"
+                            f"Factor: {factor} = 0\n"
+                            f"Roots: {root_strs}\n\n"
+                            f"Middle-term factorization is applicable: "
+                            f"a = {a}, b = {b}, c = {c}, a*c = {prod}. "
+                            f"{m} and {n} satisfy m*n = ac and m+n = b.\n"
+                            f"Explain this step-by-step in human style."
+                        )
+                        break
+                if not found:
+                    raise Exception("No middle term")
+            else:
+                raise Exception("Not quadratic")
+        except:
+            prompt = (
+                f"Equation: {lhs} = 0\n"
+                f"Factor: {factor} = 0\n"
+                f"Roots: {root_strs}\n\n"
+                f"Middle-term factorization is not suitable. "
+                f"Explain using quadratic formula (Sreedhar Acharya) with step-by-step clarity."
+            )
+
+        return output, cleaned_latex, prompt
     except Exception as e:
-        return f"❌ **Error**: {str(e)}", "", ""
+        return f"❌ Error: {str(e)}", "", ""
 
 def wrapped_solver(img, url):
-    result, cleaned, _ = solve_polynomial(img, url)
-    return result, cleaned
+    result, cleaned, prompt = solve_polynomial(img, url)
+    return result, cleaned, prompt
 
 def solve_from_coeffs(degree, coeff_str):
     try:
@@ -189,12 +213,13 @@ with gr.Blocks() as demo:
         llm_url = gr.Textbox(label="🔗 Enter LLM Microservice URL (from Colab)", placeholder="https://xxxx.ngrok-free.app")
         image_input = gr.Image(type="pil", label="📷 Upload Image of Polynomial")
         hidden_latex = gr.Textbox(visible=False)
+        explanation_prompt = gr.Textbox(visible=False)
         output_box = gr.Markdown(label="📋 Step-by-step Solution")
         submit_btn = gr.Button("🔍 Solve")
-        submit_btn.click(fn=wrapped_solver, inputs=[image_input, llm_url], outputs=[output_box, hidden_latex])
+        submit_btn.click(fn=wrapped_solver, inputs=[image_input, llm_url], outputs=[output_box, hidden_latex, explanation_prompt])
         explain_box = gr.Markdown(label="🗣️ Human-style Explanation")
         explain_btn = gr.Button("🧠 Explain Human-Solution")
-        explain_btn.click(fn=request_llm_explanation, inputs=[hidden_latex, llm_url], outputs=explain_box)
+        explain_btn.click(fn=request_llm_explanation, inputs=[explanation_prompt, llm_url], outputs=explain_box)
 
     with gr.Tab("🧮 Solve by Coefficients"):
         degree_input = gr.Number(label="Enter Degree of Polynomial (e.g. 3)")