Gröbner basis project
Codebase for research into Gröbner basis computation
test_cab_es6.cpp

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

\[ u + v + y + 32002 ,\\ t + 2 u + z + -3 ,\\ t + 2 v + y + 32002 ,\\ 32002 t + 32002 u + 32002 v + x + 32002 y + 32002 z ,\\ t u x^2 + 26650 y z^3 ,\\ 28222 t y + v z \]

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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", "u", "v", "x", "y", "z" } ;
Polynomial_Ring R(6, FF, X );
Monomial one { 0, 0, 0, 0, 0, 0 };
// set up our polynomials
// first poly
Monomial u1 { 0, 1, 0, 0, 0, 0 };
Monomial v1 { 0, 0, 1, 0, 0, 0 };
Monomial y1 { 0, 0, 0, 0, 1, 0 };
Monomial M1 [] { u1, v1, y1, one };
Prime_Field_Element C1 [] { a, a, a, -a };
Constant_Polynomial f1(4, R, M1, C1);
// second poly
Monomial t1 { 1, 0, 0, 0, 0, 0 };
Monomial z1 { 0, 0, 0, 0, 0, 1 };
Monomial M2 [] { t1, u1, z1, one };
Prime_Field_Element C2 [] { a, a*2, a, a*(-3) };
Constant_Polynomial f2(4, R, M2, C2);
f2.sort_by_order();
// third poly
Monomial M3 [] { t1, v1, y1, one };
Prime_Field_Element C3 [] { a, a*2, a, -a };
Constant_Polynomial f3(4, R, M3, C3);
// fourth poly
Monomial x1 { 0, 0, 0, 1, 0, 0 };
Monomial M4 [] { t1, u1, v1, x1, y1, z1 };
Prime_Field_Element C4 [] { -a, -a, -a, a, -a, -a };
Constant_Polynomial f4(6, R, M4, C4);
// fifth poly
Monomial tux2 { 1, 1, 0, 2, 0, 0 };
Monomial yz3 { 0, 0, 0, 0, 1, 3 };
Monomial M5 [] { tux2, yz3 };
Prime_Field_Element C5 [] { a, -a*1569*((a*31250).inverse()) };
Constant_Polynomial f5(2, R, M5, C5);
f5.sort_by_order();
// sixth poly
Monomial ty { 1, 0, 0, 0, 1, 0 };
Monomial vz { 0, 0, 1, 0, 0, 1 };
Monomial M6 [] { ty, vz };
Prime_Field_Element C6 [] { -a*587*((a*15625).inverse()), a };
Constant_Polynomial f6(2, R, M6, C6);
f6.sort_by_order();
// message
cout << "Computing a Groebner basis for\n\t" << f1
<< ",\n\t" << f2
<< ",\n\t" << f3
<< ",\n\t" << f4
<< ",\n\t" << f5
<< ",\n\t" << f6
<< endl;
// compute basis
list<Abstract_Polynomial *> F;
F.push_back(&f1); F.push_back(&f2); F.push_back(&f3);
F.push_back(&f4); F.push_back(&f5); F.push_back(&f6);
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());
delete g;
}
cout << "bye\n";
}