// GetCoeffs vector<GiNaC::ex> GetCoeffs(GiNaC::ex Ex, GiNaC::symbol Sym) { assert(Ex.is_polynomial(Sym)); vector<GiNaC::ex> Coeffs; unsigned Degree = Ex.degree(Sym); for (unsigned Idx = 0; Idx <= Degree; ++Idx) Coeffs.push_back(Ex.coeff(Sym, Idx)); return Coeffs; }
// Solve vector<double> Solve(GiNaC::ex Ex, GiNaC::symbol Sym) { vector<double> Roots; unsigned Degree = Ex.degree(Sym); auto Coeffs = GetCoeffs(Ex, Sym); // Bhaskara. if (Degree == 2) { GiNaC::ex A = Coeffs[2]; GiNaC::ex B = Coeffs[1]; GiNaC::ex C = Coeffs[0]; GiNaC::ex Delta = B*B - 4 * A * C; // Guaranteed real roots. if (GiNaC::is_a<GiNaC::numeric>(Delta) && !GiNaC::ex_to<GiNaC::numeric>(Delta).is_negative()) { GiNaC::ex Delta = GiNaC::sqrt(B*B - 4 * A * C).evalf(); GiNaC::ex One = ((-B) + Delta)/(2*A); GiNaC::ex Two = ((-B) - Delta)/(2*A); if (GiNaC::is_a<GiNaC::numeric>(One)) Roots.push_back(GiNaC::ex_to<GiNaC::numeric>(One.evalf()).to_double()); if (GiNaC::is_a<GiNaC::numeric>(Two)) Roots.push_back(GiNaC::ex_to<GiNaC::numeric>(Two.evalf()).to_double()); } } // Cardano. else if (Degree == 3) { GiNaC::ex A = Coeffs[3]; GiNaC::ex B = Coeffs[2]; GiNaC::ex C = Coeffs[1]; GiNaC::ex D = Coeffs[1]; GiNaC::ex Delta0 = B*B - 3 * A * C; GiNaC::ex Delta1 = 2 * B*B*B - 9 * A * B * C + 27 * A * A * D; GiNaC::ex CD = Delta1 + GiNaC::sqrt(Delta1 * Delta1 - 4 * GiNaC::pow(Delta0, 3)); CD = CD/2; CD = GiNaC::pow(CD, GiNaC::numeric(1)/3); GiNaC::symbol U("u"); GiNaC::ex Var = GiNaC::numeric(-1)/(3 * A) * (B + U * CD + Delta0/(U * CD)); GiNaC::ex One = Var.subs(U == 1); GiNaC::ex Two = Var.subs(U == ((-1 + GiNaC::sqrt(GiNaC::numeric(-3)))/2)); GiNaC::ex Three = Var.subs(U == ((-1 - GiNaC::sqrt(GiNaC::numeric(-3)))/2)); if (GiNaC::is_a<GiNaC::numeric>(One)) Roots.push_back(GiNaC::ex_to<GiNaC::numeric>(One.evalf()).to_double()); if (GiNaC::is_a<GiNaC::numeric>(Two)) Roots.push_back(GiNaC::ex_to<GiNaC::numeric>(Two.evalf()).to_double()); if (GiNaC::is_a<GiNaC::numeric>(Three)) Roots.push_back(GiNaC::ex_to<GiNaC::numeric>(Three.evalf()).to_double()); } return Roots; }
bool TestExpr::runOnModule(Module&) { Expr A("a"); Expr B("b"); assert(A + B == B + A); assert(A * B == B * A); assert(A - B != B - A); assert(A / B != B / A); //map<GiNaC::symbol, int> GetMaxExps(GiNaC::ex Ex); GiNaC::symbol GA("a"); GiNaC::symbol GB("b"); GiNaC::ex EZ = 5 * GA * GA * GA + 4 * GB + 1; assert(EZ.is_polynomial(GA)); assert(EZ.degree(GA) == 3); assert(EZ.coeff(GA, 3) == GiNaC::numeric(5)); assert(EZ.coeff(GA, 2) == GiNaC::numeric(0)); assert(EZ.coeff(GA, 1) == GiNaC::numeric(0)); assert(EZ.coeff(GA, 0) == 4 * GB + 1); assert(EZ.is_polynomial(GB)); assert(EZ.degree(GB) == 1); assert(EZ.coeff(GB, 1) == GiNaC::numeric(4)); assert(EZ.coeff(GB, 0) == 5 * GA * GA * GA + 1); auto SEZ = GetSymbols(EZ); assert(SEZ.size() == 2); assert(SEZ.count(GA) && SEZ.count(GB)); auto CEZGA = GetCoeffs(EZ, GA); assert(CEZGA.size() == 4); assert(CEZGA[3] == GiNaC::numeric(5)); assert(CEZGA[2] == GiNaC::numeric(0)); assert(CEZGA[1] == GiNaC::numeric(0)); assert(CEZGA[0] == 4 * GB + 1); auto CEZGB = GetCoeffs(EZ, GB); assert(CEZGB.size() == 2); assert(CEZGB[1] == GiNaC::numeric(4)); assert(CEZGB[0] == 5 * GA * GA * GA + 1); auto EF = GA * GA - 1; auto EFSolve = Solve(EF, GA); assert(EFSolve.size() == 2); assert(Round(EFSolve[0]) == -1 || Round(EFSolve[1]) == -1); assert(Round(EFSolve[0]) == 1 || Round(EFSolve[1]) == 1); auto EFNegs = NegativeOrdinate(EFSolve, GA, EF); assert(EFNegs.empty()); EF = GA * GA - 2 * GA + 1; EFSolve = Solve(EF, GA); assert(EFSolve.size() == 2); assert(Round(EFSolve[0]) == 1 && Round(EFSolve[1]) == 1); EFNegs = NegativeOrdinate(EFSolve, GA, EF); assert(EFNegs.empty()); EF = (-1) * GA * GA + GA - 1; EFSolve = Solve(EF, GA); assert(EFSolve.size() == 0); EFNegs = NegativeOrdinate(EFSolve, GA, EF); assert(EFNegs.size() == 1); assert(EFNegs[0].first.is_equal(GiNaC::inf(-1))); assert(EFNegs[0].second.is_equal(GiNaC::inf(1))); return false; }