A te mostani kódod: A valaha látott legtisztább megfogalmazá...

Prompt

A te mostani kódod: A valaha látott legtisztább megfogalmazása a 3D-s cáfolatnak. Zseniálisan van felépítve, és ha P P fokszámát x x -ben 2-re emeled, azonnal lefut konstans 1 determinánssal és a kollízióval. A 2D-s sikerhez: Ugyanezt az algoritmikus gondolkodásmódot kell alkalmazni (Gröbner-bázis + póluskioltás), de az alapmodellt át kell írni: a developábilis érintőfelület helyett a 2:3 arányú hiperbolikus Poisson-párt kell betáplálni a run_pipeline() függvényedbe! Send back the complete code with all the fixes. Fix each of the listed errors one by one, making sure to actually correct them so that there are 0 errors remaining. Keep the original imports, since the files exist. Write out every single character; do not abbreviate anything. Fix every error. There must be exactly one file. Do not write anything else; just output the complete code, and it must not contain any comments. Never, under any circumstances, use simplified, substitute, dummy, simulated, or fake code. Write the entire file as complete, unabridged, production-ready code in a single code block. It must be 100% error-free, a complete, error-free file, and must be submitted as a downloadable file. These requirements are mandatory and must be strictly adhered to. If no list of errors is provided, you must find all the errors and fix them. If there were comments in the original code, delete them. And most importantly: YOU MUST NEVER SIMPLIFY! import sympy as sp x, y, z, u = sp.symbols("x y z u") def gamma_parabola(uu): return uu, uu**2 def tau_of_gamma(g1, g2, uu, mu): return sp.expand(mu * sp.diff(g1, uu)), sp.expand(mu * sp.diff(g2, uu)) def wronskian_gamma(g1, g2, uu): return sp.expand( sp.diff(g1, uu) * sp.diff(g2, uu, 2) - sp.diff(g2, uu) * sp.diff(g1, uu, 2) ) def is_admissible(g1, g2, uu): W = wronskian_gamma(g1, g2, uu) if W == 0: return False, W try: pw = sp.Poly(W, uu) if pw.degree() == 0: return pw.nth(0) != 0, W return False, W except Exception: return False, W def make_poly_xy(prefix, Dx, Dy, xv, yv): syms = [] expr = sp.Integer(0) for i in range(Dx + 1): for j in range(Dy + 1): s = sp.Symbol(f"{prefix}_{i}_{j}") syms.append(s) expr += s * xv**i * yv**j return sp.expand(expr), syms def make_poly_u(prefix, deg, uu): syms = [] expr = sp.Integer(0) for i in range(deg + 1): s = sp.Symbol(f"{prefix}_{i}") syms.append(s) expr += s * uu**i return sp.expand(expr), syms def poly_deg_u(expr, uu): if sp.expand(expr) == 0: return -1 try: return sp.Poly(sp.expand(expr), uu).degree() except Exception: return 0 def build_Fstar(g1f, g2f, mu, fex, gex, h1ex, h2ex, Pex, Qex, xv, yv, zv, uu): uex = sp.expand(yv + fex) vex = sp.expand(gex) Xex = sp.expand(Pex + zv * Qex) t1, t2 = tau_of_gamma(g1f, g2f, uu, mu) t1u = sp.expand(t1.subs(uu, uex)) t2u = sp.expand(t2.subs(uu, uex)) g1u = sp.expand(g1f.subs(uu, uex)) g2u = sp.expand(g2f.subs(uu, uex)) D1 = sp.expand(g1u + vex * t1u) D2 = sp.expand(g2u + vex * t2u) h1u = sp.expand(h1ex.subs(uu, uex)) h2u = sp.expand(h2ex.subs(uu, uex)) Fs1 = sp.expand(D1 - Xex * h1u) Fs2 = sp.expand(D2 - Xex * h2u) return uex, vex, Xex, D1, D2, Fs1, Fs2 def estimate_K(fex, gex, g1f, g2f, mu, h1ex, h2ex, uu, xv): Nu = 1 Nv = 1 try: _, d1 = sp.fraction(sp.together(fex)) if d1 != 1: try: Nu = max(1, sp.Poly(d1, xv).degree()) except Exception: Nu = 2 except Exception: Nu = 1 try: _, d2 = sp.fraction(sp.together(gex)) if d2 != 1: try: Nv = max(1, sp.Poly(d2, xv).degree()) except Exception: Nv = 1 except Exception: Nv = 1 dg = max(poly_deg_u(g1f, uu), poly_deg_u(g2f, uu)) t1, t2 = tau_of_gamma(g1f, g2f, uu, mu) dt = max(poly_deg_u(t1, uu), poly_deg_u(t2, uu)) e1 = max(0, poly_deg_u(h1ex, uu)) e2 = max(0, poly_deg_u(h2ex, uu)) K = int(max(Nu * max(dg, 0), Nv + Nu * max(dt, 0), Nu * max(e1, e2))) + 3 return max(K, 3), Nu, Nv def cancellation_equations(Fs1, Fs2, K, xv, yv, zv): eqs = [] for Fs in (Fs1, Fs2): numer = sp.expand(Fs * xv**K) px = sp.Poly(numer, xv) for i in range(K): c = sp.expand(px.nth(i)) if c == 0: continue try: pyz = sp.Poly(c, yv, zv) for cc in pyz.as_dict().values(): cc = sp.expand(cc) if cc != 0: eqs.append(cc) except Exception: eqs.append(c) return [sp.expand(ee) for ee in eqs if sp.expand(ee) != 0] def is_linear(eqs, unknowns): for e in eqs: try: pp = sp.Poly(e, *unknowns) if pp is not None and pp.total_degree() > 1: return False except Exception: return False return True def solve_eqs(eqs, unknowns): eqs = [sp.expand(e) for e in eqs if sp.expand(e) != 0] if not eqs: return {"status": "free", "data": {}} if not unknowns: return {"status": "no_unknowns", "data": None} if is_linear(eqs, unknowns): M, b = sp.linear_eq_to_matrix(eqs, unknowns) return {"status": "linear", "data": sp.linsolve((M, b), unknowns)} G = sp.groebner(eqs, *unknowns, order="grlex") if len(G.polys) == 1 and G.polys[0].is_ground: if G.polys[0].as_expr() != 0: return {"status": "unsat", "data": G} try: return {"status": "nonlinear", "data": sp.solve(eqs, unknowns, dict=True)} except Exception: return {"status": "groebner_only", "data": G} def jacobian_report(F1s, F2s, F3s, xv, yv, zv): J = sp.Matrix([ [sp.diff(F1s, xv), sp.diff(F1s, yv), sp.diff(F1s, zv)], [sp.diff(F2s, xv), sp.diff(F2s, yv), sp.diff(F2s, zv)], [sp.diff(F3s, xv), sp.diff(F3s, yv), sp.diff(F3s, zv)], ]) d = sp.expand(J.det()) isc = not {xv, yv, zv}.intersection(d.free_symbols) return J, d, bool(isc) and sp.simplify(d) != 0 def developable_collision_parabola(): return { "u1": sp.Integer(1), "v1": sp.Integer(-1), "u2": sp.Integer(-1), "v2": sp.Integer(1), "point": (sp.Integer(0), sp.Integer(-1)), } def lift_collision_to_3d(col, fex, gex, Pex, Qex, sol, xv, yv): Ps = sp.expand(Pex.subs(sol) if sol else Pex) Qs = sp.expand(Qex.subs(sol) if sol else Qex) fs = sp.expand(fex.subs(sol) if sol else fex) gs = sp.expand(gex.subs(sol) if sol else gex) res = [] for uu0, vv0 in ((col["u1"], col["v1"]), (col["u2"], col["v2"])): sols_x = sp.solve(sp.Eq(gs, vv0), xv, dict=True) found = None for sd in sols_x: xv0 = sp.simplify(sd[xv]) if xv0 == 0: continue yv0 = sp.simplify(uu0 - fs.subs(xv, xv0)) Q0 = sp.simplify(Qs.subs({xv: xv0, yv: yv0})) P0 = sp.simplify(Ps.subs({xv: xv0, yv: yv0})) if Q0 != 0: found = (xv0, yv0, sp.simplify(-P0 / Q0)) break if sp.simplify(P0) == 0: found = (xv0, yv0, sp.Integer(0)) break res.append(found) return res def run_pipeline(): g1f, g2f = gamma_parabola(u) adm, W = is_admissible(g1f, g2f, u) mu = sp.Integer(1) fex = 1 / x gex = 1 / x h1ex, h1syms = make_poly_u("p", 1, u) h2ex, h2syms = make_poly_u("q", 2, u) Pex, Psyms = make_poly_xy("r", 1, 1, x, y) Qex = x**3 uex, vex, Xex, D1, D2, Fs1, Fs2 = build_Fstar( g1f, g2f, mu, fex, gex, h1ex, h2ex, Pex, Qex, x, y, z, u ) K, Nu, Nv = estimate_K(fex, gex, g1f, g2f, mu, h1ex, h2ex, u, x) eqs = cancellation_equations(Fs1, Fs2, K, x, y, z) unknowns = h1syms + h2syms + Psyms solinfo = solve_eqs(eqs, unknowns) col = developable_collision_parabola() return { "admissible": adm, "W": W, "K": K, "num_eqs": len(eqs), "solinfo": solinfo, "collision": col, } if __name__ == "__main__": out = run_pipeline() print(out["admissible"], out["W"], out["K"], out["num_eqs"], out["solinfo"]["status"])