Update app.py

app.py

@@ -85,9 +85,6 @@ def solve_polynomial(image, llm_url):
             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)
@@ -140,10 +137,10 @@ def solve_polynomial(image, llm_url):
                             f"Equation: {lhs} = 0\n"
                             f"Factor: {factor} = 0\n"
                             f"Roots: {root_strs}\n\n"
-                            f"Middle-term factorization is applicable: "
+                            f"Middle-term factorization used: "
                             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."
+                            f"Explain clearly, step-by-step.\n<|end|>"
                         )
                         break
                 if not found:
@@ -155,8 +152,9 @@ def solve_polynomial(image, llm_url):
                 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."
+                f"Middle-term factorization was not suitable.\n"
+                f"Used Sreedhar Acharya quadratic formula instead.\n"
+                f"Explain this step-by-step.\n<|end|>"
             )
 
         return output, cleaned_latex, prompt
@@ -199,9 +197,7 @@ def solve_from_coeffs(degree, coeff_str):
             f"Equation: {equation_str}\n"
             f"Factor: {factored_str} = 0\n"
             f"Roots: {roots_str}\n\n"
-            "Explain the solution step-by-step in human language. Use middle-term factorization if possible, "
-            "otherwise use the quadratic formula (Sreedhar Acharya method). "
-            "These roots are correct (up to approximation), so base your reasoning on them."
+            f"Explain the above solution in simple steps.\n<|end|>"
         )
 
         return result, llm_prompt