Gröbner basis project
Codebase for research into Gröbner basis computation
test_cab_es1.cpp
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17 
18 #include <set>
19 #include <cstdlib>
20 #include <cstring>
21 #include <iostream>
22 
23 using std::set;
24 using std::cout; using std::endl;
25 
26 #include "system_constants.hpp"
27 
28 #include "fields.hpp"
29 #include "monomial.hpp"
30 #include "polynomial.hpp"
31 
32 #include "dynamic_engine.hpp"
33 
34 #include "algorithm_buchberger_basic.hpp"
35 #include "algorithm_buchberger_dynamic.hpp"
36 
37 int main(int argc, char *argv[]) {
38  if (argc != 3 or (strcmp(argv[2],"stat") and strcmp(argv[2],"dyn"))) {
39  cout << "need to know method (usually 2) and then if dynamic (stat or dyn)\n";
40  return 1;
41  }
42  // obtain method -- don't screw it up b/c we don't check it
43  SPolyCreationFlags method = (SPolyCreationFlags )atoi(argv[1]);
44  bool static_algorithm = true;
45  if (!strcmp(argv[2],"dyn")) static_algorithm = false;
46  // set up the field
47  Prime_Field FF = Prime_Field(32003);
48  string X [9] = {"t", "x", "y", "z", "a", "b", "c", "d", "e"} ;
49  Polynomial_Ring R(9, FF, X );
50  Prime_Field_Element a = FF.unity();
51  // set up our polynomials
52  // first poly
53  Monomial t11 { 4, 0, 0, 1, 0, 1, 0, 0, 0 };
54  Monomial t12 { 0, 3, 1, 0, 1, 0, 0, 0, 0 };
55  Monomial M1 [] { t11, t12 };
56  Prime_Field_Element C1 [] { a, a };
57  Constant_Polynomial f1(2, R, M1, C1);
58  f1.sort_by_order();
59  // second poly
60  Monomial t21 { 1, 8, 1, 1, 0, 0, 0, 0, 0 };
61  Monomial t22 { 0, 0, 0, 0, 1, 4, 1, 1, 1 };
62  Monomial M2 [] { t21, t22 };
63  Prime_Field_Element C2 [] { a, -a };
64  Constant_Polynomial f2(2, R, M2, C2);
65  f2.sort_by_order();
66  // third poly
67  Monomial t31 { 0, 1, 2, 2, 0, 0, 0, 1, 0 };
68  Monomial t32 { 0, 0, 0, 1, 0, 0, 2, 0, 2 };
69  Monomial M3 [] { t31, t32 };
70  Prime_Field_Element C3 [] { a, a };
71  Constant_Polynomial f3(2, R, M3, C3);
72  f3.sort_by_order();
73  // fourth poly
74  Monomial t41 { 1, 2, 3, 4, 0, 0, 0, 0, 0 };
75  Monomial t42 { 0, 0, 0, 0, 1, 2, 3, 0, 2 };
76  Monomial M4 [] { t41, t42 };
77  Prime_Field_Element C4 [] { a, a };
78  Constant_Polynomial f4(2, R, M4, C4);
79  f4.sort_by_order();
80  // message
81  cout << "Computing a Groebner basis for\n\t" << f1
82  << ",\n\t" << f2
83  << ",\n\t" << f3
84  << ",\n\t" << f4
85  << endl;
86  // compute basis
87  list<Abstract_Polynomial *> F;
88  F.push_back(&f1); F.push_back(&f2); F.push_back(&f3); F.push_back(&f4);
89  list<Constant_Polynomial *> G;
90  if (static_algorithm) G = buchberger(F, method, StrategyFlags::SUGAR_STRATEGY);
91  else G = buchberger_dynamic(
92  F, method, StrategyFlags::SUGAR_STRATEGY, nullptr,
93  DynamicHeuristic::ORD_HILBERT_THEN_DEG
94  );
95  cout << "Basis:\n";
96  for (Constant_Polynomial * g : G) {
97  cout << '\t';
98  g->leading_monomial().print(true, cout, R.name_list());
99  }
100  cout << "bye\n";
101 }
A Constant_Polynomial is a polynomial that should not change.
list< Constant_Polynomial * > buchberger(const list< Abstract_Polynomial *> &F, SPolyCreationFlags method, StrategyFlags strategy, WT_TYPE *strategy_weights)
Implementation of Buchberger’s algorithm.
Information necessary for a field modulo a prime.
Definition: fields.hpp:49
Prime_Field_Element unity()
“unity” is the multiplicative identity.
Definition: fields.cpp:188
SPolyCreationFlags
flag indicating which structure to use for an s-polynomial
Implementation of monomials.
Definition: monomial.hpp:69
Element of a field of prime characteristic.
Definition: fields.hpp:137
Encapsulates information about a polynomial ring for easy access: ground field, number of indetermina...
list< Constant_Polynomial * > buchberger_dynamic(const list< Abstract_Polynomial *> &F, SPolyCreationFlags method, StrategyFlags strategy, WT_TYPE *strategy_weights, DynamicHeuristic heuristic, DynamicSolver solver_type, bool analyze_inputs)
implementation of the dynamic Buchberger algorithm