Gröbner basis project
Codebase for research into Gröbner basis computation
test_cab_es1.cpp

This illustrates how to compute a Gröbner basis of the first example in [4],

\[ t^4 z b + x^3 y a ,\\ t x^8 y z + 32002 a b^4 c d e ,\\ x y^2 z^2 d + z c^2 e^2 ,\\ t x^2 y^3 z^4 + a b^2 c^3 e^2 \]

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#include <set>
#include <cstdlib>
#include <cstring>
#include <iostream>
using std::set;
using std::cout; using std::endl;
#include "system_constants.hpp"
#include "fields.hpp"
#include "monomial.hpp"
#include "polynomial.hpp"
#include "dynamic_engine.hpp"
#include "algorithm_buchberger_basic.hpp"
#include "algorithm_buchberger_dynamic.hpp"
int main(int argc, char *argv[]) {
if (argc != 3 or (strcmp(argv[2],"stat") and strcmp(argv[2],"dyn"))) {
cout << "need to know method (usually 2) and then if dynamic (stat or dyn)\n";
return 1;
}
// obtain method -- don't screw it up b/c we don't check it
SPolyCreationFlags method = (SPolyCreationFlags )atoi(argv[1]);
bool static_algorithm = true;
if (!strcmp(argv[2],"dyn")) static_algorithm = false;
// set up the field
Prime_Field FF = Prime_Field(32003);
string X [9] = {"t", "x", "y", "z", "a", "b", "c", "d", "e"} ;
Polynomial_Ring R(9, FF, X );
// set up our polynomials
// first poly
Monomial t11 { 4, 0, 0, 1, 0, 1, 0, 0, 0 };
Monomial t12 { 0, 3, 1, 0, 1, 0, 0, 0, 0 };
Monomial M1 [] { t11, t12 };
Prime_Field_Element C1 [] { a, a };
Constant_Polynomial f1(2, R, M1, C1);
// second poly
Monomial t21 { 1, 8, 1, 1, 0, 0, 0, 0, 0 };
Monomial t22 { 0, 0, 0, 0, 1, 4, 1, 1, 1 };
Monomial M2 [] { t21, t22 };
Prime_Field_Element C2 [] { a, -a };
Constant_Polynomial f2(2, R, M2, C2);
// third poly
Monomial t31 { 0, 1, 2, 2, 0, 0, 0, 1, 0 };
Monomial t32 { 0, 0, 0, 1, 0, 0, 2, 0, 2 };
Monomial M3 [] { t31, t32 };
Prime_Field_Element C3 [] { a, a };
Constant_Polynomial f3(2, R, M3, C3);
// fourth poly
Monomial t41 { 1, 2, 3, 4, 0, 0, 0, 0, 0 };
Monomial t42 { 0, 0, 0, 0, 1, 2, 3, 0, 2 };
Monomial M4 [] { t41, t42 };
Prime_Field_Element C4 [] { a, a };
Constant_Polynomial f4(2, R, M4, C4);
// message
cout << "Computing a Groebner basis for\n\t" << f1
<< ",\n\t" << f2
<< ",\n\t" << f3
<< ",\n\t" << f4
<< endl;
// compute basis
list<Abstract_Polynomial *> F;
F.push_back(&f1); F.push_back(&f2); F.push_back(&f3); F.push_back(&f4);
list<Constant_Polynomial *> G;
if (static_algorithm) G = buchberger(F, method, StrategyFlags::SUGAR_STRATEGY);
F, method, StrategyFlags::SUGAR_STRATEGY, nullptr,
DynamicHeuristic::ORD_HILBERT_THEN_DEG
);
cout << "Basis:\n";
for (Constant_Polynomial * g : G) {
cout << '\t';
g->leading_monomial().print(true, cout, R.name_list());
}
cout << "bye\n";
}