Upload app.py

app.py

@@ -945,7 +945,131 @@ def run_sympy(problem: str) -> dict:
                     "latex": r"x \in \{" + sol_latex + r"\}"
                 }
 
-        # ── 8. Matrix / Eigenvalues — delegate to AI ─────────────────
+        # ── 8. Real Analysis II — SymPy for computations, AI for theory ──
+        elif any(k in p for k in [
+                # Sets & Real Numbers
+                "supremum", "infimum", "least upper bound", "greatest lower bound",
+                "lub", "glb", "archimedean", "bounded set", "completeness",
+                "cartesian product", "density of rational", "real number system",
+                "field propert", "order propert",
+                # Sequences
+                "sequence", "cauchy sequence", "bounded sequence",
+                "monotone sequence", "subsequence", "bolzano", "weierstrass",
+                # Series
+                "ratio test", "root test", "integral test", "comparison test",
+                "alternating series", "leibniz test", "absolute convergence",
+                "conditional convergence", "cauchy criterion",
+                "pointwise convergence", "uniform convergence",
+                "weierstrass m-test", "m-test",
+                # Limits & Continuity
+                "epsilon delta", "epsilon-delta", "uniform continuity",
+                "intermediate value", "extreme value theorem",
+                # Differentiation theorems
+                "mean value theorem", "rolle", "taylor's theorem",
+                "lhopital", "l'hopital",
+                # Riemann Integration
+                "riemann sum", "riemann integral", "upper sum", "lower sum",
+                "darboux", "integrability", "fundamental theorem of calculus",
+        ]):
+            try:
+                n_s = sp.Symbol('n', positive=True)
+
+                # ── Sequence limit ────────────────────────────────────────
+                if any(k in p for k in ["sequence","limit of sequence"]):
+                    # Extract expression after "of" or "for"
+                    m = re.search(r"(?:of|for|lim)\s+(.+?)\s*(?:as|when|$)", p)
+                    if m:
+                        raw = clean(m.group(1))
+                        try:
+                            expr_s = parse_expr(raw, transformations=tfms,
+                                               local_dict={**ld, "n": n_s})
+                            lim_val = sp.limit(expr_s, n_s, sp.oo)
+                            return {
+                                "type": "SequenceLimit",
+                                "result": f"lim({m.group(1)}) as n→∞ = {lim_val}",
+                                "latex": f"\\lim_{{n\\to\\infty}} = {sp.latex(lim_val)}"
+                            }
+                        except Exception:
+                            pass
+
+                # ── Series sum ────────────────────────────────────────────
+                elif any(k in p for k in ["series","sum of"]):
+                    m = re.search(r"(?:sum|series)\s+(?:of\s+)?(.+?)\s*(?:from|$)", p)
+                    if m:
+                        raw = clean(m.group(1))
+                        try:
+                            expr_ser = parse_expr(raw, transformations=tfms,
+                                                  local_dict={**ld, "n": n_s})
+                            s_val = sp.summation(expr_ser, (n_s, 1, sp.oo))
+                            converges = s_val.is_finite
+                            return {
+                                "type": "SeriesConvergence",
+                                "result": (f"Series sum = {s_val}, "
+                                           f"Converges: {converges}"),
+                                "latex": f"\\sum_{{n=1}}^{{\\infty}} = {sp.latex(s_val)}"
+                            }
+                        except Exception:
+                            pass
+
+                # ── Taylor Series ─────────────────────────────────────────
+                elif any(k in p for k in ["taylor", "maclaurin"]):
+                    funcs = {
+                        "sin": sp.sin(x), "cos": sp.cos(x),
+                        "exp": sp.exp(x), "e^x": sp.exp(x),
+                        "ln": sp.log(1+x), "log": sp.log(1+x),
+                        "tan": sp.tan(x)
+                    }
+                    for fname, fexpr in funcs.items():
+                        if fname in p:
+                            n_terms = 6
+                            ts = sp.series(fexpr, x, 0, n_terms)
+                            return {
+                                "type": "TaylorSeries",
+                                "result": f"Taylor series of {fname}: {ts}",
+                                "latex": sp.latex(ts)
+                            }
+
+                # ─��� L'Hopital ─────────────────────────────────────────────
+                elif any(k in p for k in ["lhopital","l'hopital"]):
+                    m = re.search(r"(?:of|for)\s+(.+?)\s*(?:as|at|when)\s*x\s*[→→=]\s*([\d\.]+|inf)", p)
+                    if m:
+                        raw = clean(m.group(1))
+                        pt_str = m.group(2)
+                        pt = sp.oo if pt_str in ("inf","infinity") else sp.sympify(pt_str)
+                        try:
+                            expr_lh = parse_expr(raw, transformations=tfms, local_dict=ld)
+                            lim_val = sp.limit(expr_lh, x, pt)
+                            return {
+                                "type": "LHopital",
+                                "result": f"lim({m.group(1)}) as x→{pt_str} = {lim_val}",
+                                "latex": f"\\lim_{{x\\to {pt_str}}} = {sp.latex(lim_val)}"
+                            }
+                        except Exception:
+                            pass
+
+                # ── Riemann Integral ──────────────────────────────────────
+                elif any(k in p for k in ["riemann","riemann integral","riemann sum"]):
+                    # Try to extract definite integral
+                    m = re.search(r"(?:of|for)\s+(.+?)\s+(?:from|on)\s+([\d\.]+)\s+to\s+([\d\.]+)", p)
+                    if m:
+                        raw = clean(m.group(1))
+                        a_v = sp.sympify(m.group(2))
+                        b_v = sp.sympify(m.group(3))
+                        try:
+                            expr_r = parse_expr(raw, transformations=tfms, local_dict=ld)
+                            result_r = sp.integrate(expr_r, (x, a_v, b_v))
+                            return {
+                                "type": "RiemannIntegral",
+                                "result": f"∫({m.group(1)}) from {a_v} to {b_v} = {result_r}",
+                                "latex": f"\\int_{{{a_v}}}^{{{b_v}}} = {sp.latex(result_r)}"
+                            }
+                        except Exception:
+                            pass
+
+            except Exception:
+                pass  # safe fallback to AI for all theory/proof questions
+
+        # ── 9. Matrix / Eigenvalues — delegate to AI ─────────────────
         elif any(k in p for k in ["matrix", "determinant", "eigenvalue",
                                    "eigenvector", "det("]):
             return {"type": "Matrix", "result": "matrix_detected", "latex": ""}
@@ -1088,6 +1212,16 @@ def ask_ai(problem: str, sympy_info: dict, history: list) -> str:
         "D. NEVER recompute sin(pi), cos(pi) etc — sin(pi)=0 exactly, always.\n"
         "E. For Lagrange/Newton interpolation: the polynomial is already given above — DO NOT re-expand or re-derive it. Just show the basis polynomials and state the final polynomial from the verified result.\n"
         "F. Your final answer must EXACTLY match the verified result — no exceptions.\n\n"
+        "=== REAL ANALYSIS II RULES (follow exactly) ===\n"
+        "For ANY Real Analysis II question:\n"
+        "A. Always start with the FORMAL DEFINITION using proper mathematical notation.\n"
+        "B. State the theorem/property COMPLETELY before proving or explaining.\n"
+        "C. ALWAYS give a concrete numerical example after every definition or theorem.\n"
+        "D. For proofs: state Given, To Prove, then step-by-step proof.\n"
+        "E. For ε-δ definitions: write the formal definition first, then explain in words.\n"
+        "F. For convergence tests: state the test, conditions, then apply to example.\n"
+        "G. For sequences/series: always check if bounded, monotone, Cauchy where relevant.\n"
+        "H. Use proper notation: ∀ (for all), ∃ (there exists), ε, δ, sup, inf, lim.\n\n"
         "Topics: Calculus, Linear Algebra, Number Theory, ODEs, "
         "Numerical Methods, Differential Geometry, Hydro Mechanics, "
         "Theory of Numbers, Real Analysis II, General Math."