37 int F4::NB_THREAD=min(8, omp_get_num_procs());
43 typedef Givaro::Modular<Givaro::Integer> Field;
44 Givaro::Integer modulo(Givaro::Integer(
"115792089237316195423570985008687907853269984665640564039457584007913129640233"));
46 typedef ElementGivaro<Field>
eltType;
48 int cyclic6F4(
bool magma)
50 cout <<
"#########################################################" << endl;
51 cout <<
"# CYCLIC 6 #" << endl;
52 cout <<
"#########################################################" << endl << endl;
64 vector<Polynomial<eltType>> polCyclic6;
67 polCyclic6.emplace_back(
"x0+x1+x2+x3+x4+x5");
68 polCyclic6.emplace_back(
"x0*x1+x1*x2+x2*x3+x3*x4+x0*x5+x4*x5");
69 polCyclic6.emplace_back(
"x0*x1*x2+x1*x2*x3+x2*x3*x4+x0*x1*x5+x0*x4*x5+x3*x4*x5");
70 polCyclic6.emplace_back(
"x0*x1*x2*x3+x1*x2*x3*x4+x0*x1*x2*x5+x0*x1*x4*x5+x0*x3*x4*x5+x2*x3*x4*x5");
71 polCyclic6.emplace_back(
"x0*x1*x2*x3*x4+x0*x1*x2*x3*x5+x0*x1*x2*x4*x5+x0*x1*x3*x4*x5+x0*x2*x3*x4*x5+x1*x2*x3*x4*x5");
72 polCyclic6.emplace_back(
"x0*x1*x2*x3*x4*x5-1");
83 cyclic6.printReducedGroebnerBasis(
"cyclic6", modulo);
89 int cyclic7F4(
bool magma)
91 cout <<
"#########################################################" << endl;
92 cout <<
"# CYCLIC 7 #" << endl;
93 cout <<
"#########################################################" << endl << endl;
105 vector<Polynomial<eltType>> polCyclic7;
108 polCyclic7.emplace_back(
"x0+x1+x2+x3+x4+x5+x6");
109 polCyclic7.emplace_back(
"x0*x1+x1*x2+x2*x3+x3*x4+x4*x5+x0*x6+x5*x6");
110 polCyclic7.emplace_back(
"x0*x1*x2+x1*x2*x3+x2*x3*x4+x3*x4*x5+x0*x1*x6+x0*x5*x6+x4*x5*x6");
111 polCyclic7.emplace_back(
"x0*x1*x2*x3+x1*x2*x3*x4+x2*x3*x4*x5+x0*x1*x2*x6+x0*x1*x5*x6+x0*x4*x5*x6+x3*x4*x5*x6");
112 polCyclic7.emplace_back(
"x0*x1*x2*x3*x4+x1*x2*x3*x4*x5+x0*x1*x2*x3*x6+x0*x1*x2*x5*x6+x0*x1*x4*x5*x6+x0*x3*x4*x5*x6+x2*x3*x4*x5*x6");
113 polCyclic7.emplace_back(
"x0*x1*x2*x3*x4*x5+x0*x1*x2*x3*x4*x6+x0*x1*x2*x3*x5*x6+x0*x1*x2*x4*x5*x6+x0*x1*x3*x4*x5*x6+x0*x2*x3*x4*x5*x6+x1*x2*x3*x4*x5*x6");
114 polCyclic7.emplace_back(
"x0*x1*x2*x3*x4*x5*x6-1");
125 cyclic7.printReducedGroebnerBasis(
"cyclic7", modulo);
131 int cyclic8F4(
bool magma)
134 cout <<
"#########################################################" << endl;
135 cout <<
"# CYCLIC 8 #" << endl;
136 cout <<
"#########################################################" << endl << endl;
139 eltType::setField(F);
148 vector<Polynomial<eltType>> polCyclic8;
151 polCyclic8.emplace_back(
"x0+x1+x2+x3+x4+x5+x6+x7");
152 polCyclic8.emplace_back(
"x0*x1+x1*x2+x2*x3+x3*x4+x4*x5+x5*x6+x0*x7+x6*x7");
153 polCyclic8.emplace_back(
"x0*x1*x2+x1*x2*x3+x2*x3*x4+x3*x4*x5+x4*x5*x6+x0*x1*x7+x0*x6*x7+x5*x6*x7");
154 polCyclic8.emplace_back(
"x0*x1*x2*x3+x1*x2*x3*x4+x2*x3*x4*x5+x3*x4*x5*x6+x0*x1*x2*x7+x0*x1*x6*x7+x0*x5*x6*x7+x4*x5*x6*x7");
155 polCyclic8.emplace_back(
"x0*x1*x2*x3*x4+x1*x2*x3*x4*x5+x2*x3*x4*x5*x6+x0*x1*x2*x3*x7+x0*x1*x2*x6*x7+x0*x1*x5*x6*x7+x0*x4*x5*x6*x7+x3*x4*x5*x6*x7");
156 polCyclic8.emplace_back(
"x0*x1*x2*x3*x4*x5+x1*x2*x3*x4*x5*x6+x0*x1*x2*x3*x4*x7+x0*x1*x2*x3*x6*x7+x0*x1*x2*x5*x6*x7+x0*x1*x4*x5*x6*x7+x0*x3*x4*x5*x6*x7+x2*x3*x4*x5*x6*x7");
157 polCyclic8.emplace_back(
"x0*x1*x2*x3*x4*x5*x6+x0*x1*x2*x3*x4*x5*x7+x0*x1*x2*x3*x4*x6*x7+x0*x1*x2*x3*x5*x6*x7+x0*x1*x2*x4*x5*x6*x7+x0*x1*x3*x4*x5*x6*x7+x0*x2*x3*x4*x5*x6*x7+x1*x2*x3*x4*x5*x6*x7");
158 polCyclic8.emplace_back(
"x0*x1*x2*x3*x4*x5*x6*x7-1");
169 cyclic8.printReducedGroebnerBasis(
"cyclic8", modulo);
175 int cyclic9F4(
bool magma)
178 cout <<
"#########################################################" << endl;
179 cout <<
"# CYCLIC 9 #" << endl;
180 cout <<
"#########################################################" << endl << endl;
183 eltType::setField(F);
192 vector<Polynomial<eltType>> polCyclic9;
195 polCyclic9.emplace_back(
"x0+x1+x2+x3+x4+x5+x6+x7+x8");
196 polCyclic9.emplace_back(
"x0*x1+x1*x2+x2*x3+x3*x4+x4*x5+x5*x6+x6*x7+x0*x8+x7*x8");
197 polCyclic9.emplace_back(
"x0*x1*x2+x1*x2*x3+x2*x3*x4+x3*x4*x5+x4*x5*x6+x5*x6*x7+x0*x1*x8+x0*x7*x8+x6*x7*x8");
198 polCyclic9.emplace_back(
"x0*x1*x2*x3+x1*x2*x3*x4+x2*x3*x4*x5+x3*x4*x5*x6+x4*x5*x6*x7+x0*x1*x2*x8+x0*x1*x7*x8+x0*x6*x7*x8+x5*x6*x7*x8");
199 polCyclic9.emplace_back(
"x0*x1*x2*x3*x4+x1*x2*x3*x4*x5+x2*x3*x4*x5*x6+x3*x4*x5*x6*x7+x0*x1*x2*x3*x8+x0*x1*x2*x7*x8+x0*x1*x6*x7*x8+x0*x5*x6*x7*x8+x4*x5*x6*x7*x8");
200 polCyclic9.emplace_back(
"x0*x1*x2*x3*x4*x5+x1*x2*x3*x4*x5*x6+x2*x3*x4*x5*x6*x7+x0*x1*x2*x3*x4*x8+x0*x1*x2*x3*x7*x8+x0*x1*x2*x6*x7*x8+x0*x1*x5*x6*x7*x8+x0*x4*x5*x6*x7*x8+x3*x4*x5*x6*x7*x8");
201 polCyclic9.emplace_back(
"x0*x1*x2*x3*x4*x5*x6+x1*x2*x3*x4*x5*x6*x7+x0*x1*x2*x3*x4*x5*x8+x0*x1*x2*x3*x4*x7*x8+x0*x1*x2*x3*x6*x7*x8+x0*x1*x2*x5*x6*x7*x8+x0*x1*x4*x5*x6*x7*x8+x0*x3*x4*x5*x6*x7*x8+x2*x3*x4*x5*x6*x7*x8");
202 polCyclic9.emplace_back(
"x0*x1*x2*x3*x4*x5*x6*x7+x0*x1*x2*x3*x4*x5*x6*x8+x0*x1*x2*x3*x4*x5*x7*x8+x0*x1*x2*x3*x4*x6*x7*x8+x0*x1*x2*x3*x5*x6*x7*x8+x0*x1*x2*x4*x5*x6*x7*x8+x0*x1*x3*x4*x5*x6*x7*x8+x0*x2*x3*x4*x5*x6*x7*x8+x1*x2*x3*x4*x5*x6*x7*x8");
203 polCyclic9.emplace_back(
"x0*x1*x2*x3*x4*x5*x6*x7*x8-1");
214 cyclic9.printReducedGroebnerBasis(
"cyclic9", modulo);
220 int katsura9F4(
bool magma)
222 cout <<
"#########################################################" << endl;
223 cout <<
"# KATSURA 9 #" << endl;
224 cout <<
"#########################################################" << endl << endl;
227 eltType::setField(F);
236 vector<Polynomial<eltType>> polKatsura9;
239 polKatsura9.emplace_back(
"x0+2*x1+2*x2+2*x3+2*x4+2*x5+2*x6+2*x7+2*x8-1");
240 polKatsura9.emplace_back(
"x0^2+2*x1^2+2*x2^2+2*x3^2+2*x4^2+2*x5^2+2*x6^2+2*x7^2+2*x8^2-x0");
241 polKatsura9.emplace_back(
"2*x0*x1+2*x1*x2+2*x2*x3+2*x3*x4+2*x4*x5+2*x5*x6+2*x6*x7+2*x7*x8-x1");
242 polKatsura9.emplace_back(
"x1^2+2*x0*x2+2*x1*x3+2*x2*x4+2*x3*x5+2*x4*x6+2*x5*x7+2*x6*x8-x2");
243 polKatsura9.emplace_back(
"2*x1*x2+2*x0*x3+2*x1*x4+2*x2*x5+2*x3*x6+2*x4*x7+2*x5*x8-x3");
244 polKatsura9.emplace_back(
"x2^2+2*x1*x3+2*x0*x4+2*x1*x5+2*x2*x6+2*x3*x7+2*x4*x8-x4");
245 polKatsura9.emplace_back(
"2*x2*x3+2*x1*x4+2*x0*x5+2*x1*x6+2*x2*x7+2*x3*x8-x5");
246 polKatsura9.emplace_back(
"x3^2+2*x2*x4+2*x1*x5+2*x0*x6+2*x1*x7+2*x2*x8-x6");
247 polKatsura9.emplace_back(
"2*x3*x4+2*x2*x5+2*x1*x6+2*x0*x7+2*x1*x8-x7");
258 katsura9.printReducedGroebnerBasis(
"katsura9", modulo);
264 int katsura10F4(
bool magma)
266 cout <<
"#########################################################" << endl;
267 cout <<
"# KATSURA 10 #" << endl;
268 cout <<
"#########################################################" << endl << endl;
271 eltType::setField(F);
280 vector<Polynomial<eltType>> polKatsura10;
283 polKatsura10.emplace_back(
"x0+2*x1+2*x2+2*x3+2*x4+2*x5+2*x6+2*x7+2*x8+2*x9-1");
284 polKatsura10.emplace_back(
"x0^2+2*x1^2+2*x2^2+2*x3^2+2*x4^2+2*x5^2+2*x6^2+2*x7^2+2*x8^2+2*x9^2-x0");
285 polKatsura10.emplace_back(
"2*x0*x1+2*x1*x2+2*x2*x3+2*x3*x4+2*x4*x5+2*x5*x6+2*x6*x7+2*x7*x8+2*x8*x9-x1");
286 polKatsura10.emplace_back(
"x1^2+2*x0*x2+2*x1*x3+2*x2*x4+2*x3*x5+2*x4*x6+2*x5*x7+2*x6*x8+2*x7*x9-x2");
287 polKatsura10.emplace_back(
"2*x1*x2+2*x0*x3+2*x1*x4+2*x2*x5+2*x3*x6+2*x4*x7+2*x5*x8+2*x6*x9-x3");
288 polKatsura10.emplace_back(
"x2^2+2*x1*x3+2*x0*x4+2*x1*x5+2*x2*x6+2*x3*x7+2*x4*x8+2*x5*x9-x4");
289 polKatsura10.emplace_back(
"2*x2*x3+2*x1*x4+2*x0*x5+2*x1*x6+2*x2*x7+2*x3*x8+2*x4*x9-x5");
290 polKatsura10.emplace_back(
"x3^2+2*x2*x4+2*x1*x5+2*x0*x6+2*x1*x7+2*x2*x8+2*x3*x9-x6");
291 polKatsura10.emplace_back(
"2*x3*x4+2*x2*x5+2*x1*x6+2*x0*x7+2*x1*x8+2*x2*x9-x7");
292 polKatsura10.emplace_back(
"x4^2+2*x3*x5+2*x2*x6+2*x1*x7+2*x0*x8+2*x1*x9-x8");
298 nbGen=katsura10.f4();
303 katsura10.printReducedGroebnerBasis(
"katsura10", modulo);
308 int katsura11F4(
bool magma)
310 cout <<
"#########################################################" << endl;
311 cout <<
"# KATSURA 11 #" << endl;
312 cout <<
"#########################################################" << endl << endl;
315 eltType::setField(F);
324 vector<Polynomial<eltType>> polKatsura11;
327 polKatsura11.emplace_back(
"x0+2*x1+2*x2+2*x3+2*x4+2*x5+2*x6+2*x7+2*x8+2*x9+2*x10-1");
328 polKatsura11.emplace_back(
"x0^2+2*x1^2+2*x2^2+2*x3^2+2*x4^2+2*x5^2+2*x6^2+2*x7^2+2*x8^2+2*x9^2+2*x10^2-x0");
329 polKatsura11.emplace_back(
"2*x0*x1+2*x1*x2+2*x2*x3+2*x3*x4+2*x4*x5+2*x5*x6+2*x6*x7+2*x7*x8+2*x8*x9+2*x9*x10-x1");
330 polKatsura11.emplace_back(
"x1^2+2*x0*x2+2*x1*x3+2*x2*x4+2*x3*x5+2*x4*x6+2*x5*x7+2*x6*x8+2*x7*x9+2*x8*x10-x2");
331 polKatsura11.emplace_back(
"2*x1*x2+2*x0*x3+2*x1*x4+2*x2*x5+2*x3*x6+2*x4*x7+2*x5*x8+2*x6*x9+2*x7*x10-x3");
332 polKatsura11.emplace_back(
"x2^2+2*x1*x3+2*x0*x4+2*x1*x5+2*x2*x6+2*x3*x7+2*x4*x8+2*x5*x9+2*x6*x10-x4");
333 polKatsura11.emplace_back(
"2*x2*x3+2*x1*x4+2*x0*x5+2*x1*x6+2*x2*x7+2*x3*x8+2*x4*x9+2*x5*x10-x5");
334 polKatsura11.emplace_back(
"x3^2+2*x2*x4+2*x1*x5+2*x0*x6+2*x1*x7+2*x2*x8+2*x3*x9+2*x4*x10-x6");
335 polKatsura11.emplace_back(
"2*x3*x4+2*x2*x5+2*x1*x6+2*x0*x7+2*x1*x8+2*x2*x9+2*x3*x10-x7");
336 polKatsura11.emplace_back(
"x4^2+2*x3*x5+2*x2*x6+2*x1*x7+2*x0*x8+2*x1*x9+2*x2*x10-x8");
337 polKatsura11.emplace_back(
"2*x4*x5+2*x3*x6+2*x2*x7+2*x1*x8+2*x0*x9+2*x1*x10-x9");
343 nbGen=katsura11.f4();
348 katsura11.printReducedGroebnerBasis(
"katsura11", modulo);
353 int katsura12F4(
bool magma)
355 cout <<
"#########################################################" << endl;
356 cout <<
"# KATSURA 12 #" << endl;
357 cout <<
"#########################################################" << endl << endl;
360 eltType::setField(F);
369 vector<Polynomial<eltType>> polKatsura12;
372 polKatsura12.emplace_back(
"x0+2*x1+2*x2+2*x3+2*x4+2*x5+2*x6+2*x7+2*x8+2*x9+2*x10+2*x11-1");
373 polKatsura12.emplace_back(
"x0^2+2*x1^2+2*x2^2+2*x3^2+2*x4^2+2*x5^2+2*x6^2+2*x7^2+2*x8^2+2*x9^2+2*x10^2+2*x11^2-x0");
374 polKatsura12.emplace_back(
"2*x0*x1+2*x1*x2+2*x2*x3+2*x3*x4+2*x4*x5+2*x5*x6+2*x6*x7+2*x7*x8+2*x8*x9+2*x9*x10+2*x10*x11-x1");
375 polKatsura12.emplace_back(
"x1^2+2*x0*x2+2*x1*x3+2*x2*x4+2*x3*x5+2*x4*x6+2*x5*x7+2*x6*x8+2*x7*x9+2*x8*x10+2*x9*x11-x2");
376 polKatsura12.emplace_back(
"2*x1*x2+2*x0*x3+2*x1*x4+2*x2*x5+2*x3*x6+2*x4*x7+2*x5*x8+2*x6*x9+2*x7*x10+2*x8*x11-x3");
377 polKatsura12.emplace_back(
"x2^2+2*x1*x3+2*x0*x4+2*x1*x5+2*x2*x6+2*x3*x7+2*x4*x8+2*x5*x9+2*x6*x10+2*x7*x11-x4");
378 polKatsura12.emplace_back(
"2*x2*x3+2*x1*x4+2*x0*x5+2*x1*x6+2*x2*x7+2*x3*x8+2*x4*x9+2*x5*x10+2*x6*x11-x5");
379 polKatsura12.emplace_back(
"x3^2+2*x2*x4+2*x1*x5+2*x0*x6+2*x1*x7+2*x2*x8+2*x3*x9+2*x4*x10+2*x5*x11-x6");
380 polKatsura12.emplace_back(
"2*x3*x4+2*x2*x5+2*x1*x6+2*x0*x7+2*x1*x8+2*x2*x9+2*x3*x10+2*x4*x11-x7");
381 polKatsura12.emplace_back(
"x4^2+2*x3*x5+2*x2*x6+2*x1*x7+2*x0*x8+2*x1*x9+2*x2*x10+2*x3*x11-x8");
382 polKatsura12.emplace_back(
"2*x4*x5+2*x3*x6+2*x2*x7+2*x1*x8+2*x0*x9+2*x1*x10+2*x2*x11-x9");
383 polKatsura12.emplace_back(
"x5^2+2*x4*x6+2*x3*x7+2*x2*x8+2*x1*x9+2*x0*x10+2*x1*x11-x10");
389 nbGen=katsura12.f4();
394 katsura12.printReducedGroebnerBasis(
"katsura12", modulo);
400 int randomIdealF4(
bool magma)
402 cout <<
"#########################################################" << endl;
403 cout <<
"# RANDOM 10 #" << endl;
404 cout <<
"#########################################################" << endl << endl;
407 eltType::setField(F);
416 vector<Polynomial<eltType>> polRandomIdeal;
419 polRandomIdeal.emplace_back(
"24597339625910113576177812194822250879537888983662139157054688348207021034423*x0*x2^3*x3 + 7151588983918886554522549736197912065523665823784056349692045272366005788565*x0^2*x2*x3^2 + 95599032154676572226640446287059550522243931209485035728481004109380836179795*x0*x1^2*x3*x4 + 80882266569802612115142178105069880712235080346583360326358277892681539845732*x0^3*x3*x5 + 101864944527580784908102973651636073902143046328060199850906610091806947685022*x0*x3^2*x4*x5 + 104729712827144379217380985817333309181450988946645646697114354205618456582492*x0^2*x4*x5^2 + 52302434696683789707660417227753471409142053519740797962753625864564463811375*x1^2*x5^3 + 17351950912516853579762997039599589425266549548666687814496665086694694159586*x0*x1^2*x3 + 57227991936024998238525433049119252484044400932298334640398545161720853774944*x2*x3*x4^2 + 38511682104007724413948279389864784831862930925142964452301117791670531282410*x4");
420 polRandomIdeal.emplace_back(
"86346388292488249693869354105874299384790680682194436292372522278549507768591*x3^2*x4^3 + 8560263876613706064403723240653698444937439375423776730755015899158932842647*x1^2*x3^2*x5 + 114724691048080175315386081552620657520918558817449626896120724453969617140460*x2^2*x3*x4*x5 + 40878117764229528421408904940423898833248553959986663655083414549083339596552*x0*x1*x4^2*x5 + 29331944903965444678929349681346850658980582826770917817437252786162390253711*x2*x4^3*x5 + 87607904220986147695088733307722614252715606105143772697170967808308305165752*x0*x1*x5^3 + 65596215877552473724063874933319504303306707295349647359211407346928426648221*x2*x3*x5^3 + 56669973593023066605257462537515724309040997310759397676506125179995947207805*x1*x2*x3^2 + 89782880725008317979230645836251624558567904255006493194084628222595510888312*x1^2*x5^2 + 103674841782615880557579059147217301083806806039093159135639389165583018130578*x3^2");
421 polRandomIdeal.emplace_back(
"20555372959538263695300487972318050811409584461989901476892596135795399007972*x0*x2^3*x4 + 5934883841580475383464077425056051853720558922314186953741822652041312229861*x0*x1^2*x4^2 + 17710328902511891669230229596735065270173524867878787745829992603487297107510*x2^2*x3*x4^2 + 70404710174534786665778251066204965060179971987897435343713576428374740408256*x0*x4^4 + 58426575736174100224339841770010585175567236430388827167224449807299941566077*x0*x2*x3^2*x5 + 30924715140590657501911767836863937316255060662617400020818103627533478901229*x0^3*x5^2 + 39500461401725546193800195222441711243433837945025353320818490293478989705375*x1^2*x2*x3 + 64240298741364943418471687622389504568349868475893951422615715204540247474855*x0*x4^2*x5 + 65820732534870169140028008687678098817567316157097444187709680681916368484914*x4*x5^3 + 17272453016442962442302752791953060985176759042717911629687645606592891860888*x4*x5");
422 polRandomIdeal.emplace_back(
"12384393892417675961175644242218445795611270141536380862841430355542048945085*x1^4*x3 + 62117470929065963636773146246593970394763704726641029743988220795495717410803*x1^3*x3^2 + 85619266736706628749218187296710103779188326378690946812602186116779762130986*x1*x2^2*x3^2 + 78777699432899971447463849098828646733245461242068819366140165453034019618264*x1*x2^2*x3*x4 + 60532401626170308029709934649599544595568150628715306147854909931133932052790*x0^2*x4^3 + 71822141816384506883608511920275736927595134162667327611607722341197820116110*x0*x2*x4^3 + 37098078751644219974002508996700695086621623357192113467047119767669799270965*x1^2*x2*x4*x5 + 63912960464413836237227794975572970151536793396077872846928677515156238102473*x3*x4^3 + 35312782757171746885185524802919703708611850096516153058825836129727838715106*x2*x4*x5 + 1343217275458213949398887747305351360705055910323149933135594844254487693698*x4*x5");
423 polRandomIdeal.emplace_back(
"28381607648242478091145546569738942138490135373130646389457403625175172311248*x0^2*x1^3 + 97629891473294042452534075850587001679173377545311155140176153692564089928974*x0*x1^2*x2^2 + 26563855492181492863726541015290497720634690978340399702372536173601777578991*x1^2*x2^3 + 94418967799063888112199911973141289579879737901092393135865628433426320213508*x0*x2^3*x3 + 75904322816224886498948320053011705672627274171263473501967112349188186065915*x1^2*x2^2*x4 + 4211364562071041806690191029623605410137554183422577681706484078158419251640*x0^3*x3*x4 + 91613731288563016881346819513246567701509323051875994794659318808230283066460*x1^2*x3*x5^2 + 89803895793131901997696630423649455067510213320346896852691998335464227790294*x0^2*x4^2 + 75236829790691047060918314537432780193922926192907772789500111625658582524194*x0*x1*x4*x5 + 88214290422334784207736225415065448927133778554493575039918313349055750449376*x0*x4^2");
424 polRandomIdeal.emplace_back(
"36819072232725910256455616092735238942832580357061287151935045000104711104411*x0^3*x1*x3 + 92291875768826133686313407982369359745050073458651281392130985753191759709555*x0*x1*x2*x3^2 + 101938393329103051382592541594609110833699156858188605831660754891793011921846*x0*x1*x3*x4*x5 + 78518394770627757449165376995944664714763318337121096642895914042049946334065*x0*x3^3 + 105540139497579157022475500477406241172092810961640031984154318748048515678792*x4^3*x5 + 84774161335942515317743013157128228128841107642095399345126979227940275346840*x1^2*x5 + 28913909478286876522946234334944523118995435566050167225895704836461177828945*x2*x5^2 + 106937289130333317810026636145567706868904407646348007959878422922013786734185*x0*x3 + 63666212440767596437341393306731648918103562050621587961742006659395222409375*x1*x3 + 83996307259878859577055366727974705831495419710797565080759747834770898783875*x5");
425 polRandomIdeal.emplace_back(
"95136961029579226839637332012775663846115938875849099068708963080153370687870*x0^4*x1 + 76661948597477609517006426019266647328314089124644038885570980154181394767045*x0^2*x1*x2^2 + 27648974455310197157642464629672364390288189790420888726061791111455930492175*x0*x1^2*x4^2 + 99920868693778594352975463016494289879012074085347132032153078814030759868224*x2*x3^2*x4^2 + 114576007790549395302027460749852743178287491103989645103656698251762797956277*x0*x1*x2*x5^2 + 43153777207871533863124675741671309793892255338939927520368389402438237387200*x1^2*x2*x5^2 + 110318690252357714779958276568104661106261376891832416580120755279823049887113*x3*x4^2*x5^2 + 45799078731622712232945448991759430123294657671582099449044877222550442558738*x0*x2^2*x4 + 100277677872859926645680483411379280810471168956065420170667425387985565806433*x3^2*x4 + 68644070924152146278996255474255655652298183872273530921674643251905127029128*x4*x5");
426 polRandomIdeal.emplace_back(
"87978767156577336556423273498613521678164709661646440569923905722446974932580*x0*x1^3*x2 + 70199507444825230647493402897761692537994351870483255214231224774601251297974*x0*x1*x4^3 + 10499470273219641798942672785992918744734361231209730859900373933910949161692*x2*x3^3*x5 + 10578305965849220536418224538586043663097136242388818907836369052306903906601*x0*x1*x4^2*x5 + 32249366203262097372573463349641203429995781989381112500573426781212335279118*x0*x1*x2*x3 + 68965782969450373459926970875762316518136291840379380514392013450011450721038*x0*x1*x3*x4 + 106629938451314744237236927474319652055736870796645986260679888340450464841026*x1^2*x4*x5 + 88351726336724052112084554771705971133037039282167216023462500471200318288497*x0*x3*x5^2 + 84046176579642600973999519206384583444257671151834634463273585411955530393954*x0*x1*x4 + 2932552305743391062700434765772653160158777010296451457377134869842474189579*x0*x5");
427 polRandomIdeal.emplace_back(
"96175621691556224386088482294073036284237851574485948577108659192463312510712*x0^2*x2^3 + 16095887211020898803806210526133834612853130933198816810948682148899139349600*x0^2*x3*x4^2 + 98747250666492396295286689772042224509297294109856664554352878419198232617521*x0*x3^3*x5 + 52569893992386578310288654986310745632795983936543823080780536063381889538173*x0*x1^2*x5^2 + 36070712509652751546201022316199583998607010198219874113379048155683684512939*x2*x3^3 + 38459960562537420353680404430137735268833402366364859536583425875504311849535*x4^3*x5 + 113265414726720472996579440938493403137255422517872281489764072963845855836208*x0*x2^2 + 33031201838571091233829098061859824402045327050874566178073169835546536449040*x1^2*x3 + 77060949484187104215934343083327162793888599177091130574481647315933319100248*x0*x3*x4 + 3155394989270135101201445442533082844433454102552047565792654883026176768937*x0*x1");
428 polRandomIdeal.emplace_back(
"100307018005733281728228439480689303268611563644292865992483825902060219306155*x0^2*x2^3 + 105212694999612411994109856290944335059209993707016399450156734493741925982223*x0^2*x1*x3*x4 + 58140815460156743900993549079587138617713837063726348071633359223936496336099*x0*x1*x3^2*x4 + 8951532369766415191105325162452055460388676698962191148548481629695483289115*x1^2*x3*x4^2 + 69954737050315706014137404090624170387633458271507253876540354269572114628457*x0*x3^2*x5^2 + 21769110896144960056125376434972489426599777661038130833468146359769606682708*x2*x4^3 + 88454000542334193985275053321689469577999258427270074292622316785230589464978*x3*x4^3 + 23329368668390090437170212328783556103331009522530474701480630589364702028429*x1*x4*x5^2 + 14452449608795143101201599761577715436126915563168593823066496214782963561358*x2*x5^2 + 88082782885434895653280422218839066097313430921228053271593271806651074773006*x1");
434 nbGen=randomIdeal.f4();
439 randomIdeal.printReducedGroebnerBasis(
"randomIdeal", modulo);
447 int main (
int argc,
char **argv)
449 cout <<
"#########################################################" << endl;
450 cout <<
"# BENCHMARK GMP #" << endl;
451 cout <<
"#########################################################" << endl << endl;
454 chrono::steady_clock::time_point start;
455 typedef chrono::duration<int,milli> millisecs_t;
458 cout << NB_THREAD <<
" threads used " << endl << endl;
467 ofstream file(
"benchmark-big-integer.txt");
470 file <<
"Benchmark for ideal with integer type coefficient." << endl << endl << endl;
473 start=chrono::steady_clock::now();
474 nbGen=randomIdealF4(magma);
477 file <<
"Random 10 : " << chrono::duration_cast<millisecs_t>(chrono::steady_clock::now()-start).count() <<
" ms (" << nbGen <<
" generators)" << endl << endl;
494 start=chrono::steady_clock::now();
495 nbGen=cyclic8F4(magma);
498 file <<
"Cyclic 8 : " << chrono::duration_cast<millisecs_t>(chrono::steady_clock::now()-start).count() <<
" ms (" << nbGen <<
" generators)" << endl << endl;
529 start=chrono::steady_clock::now();
530 nbGen=katsura12F4(magma);
533 file <<
"Katsura 12 : " << chrono::duration_cast<millisecs_t>(chrono::steady_clock::now()-start).count() <<
" ms (" << nbGen <<
" generators)" << endl << endl;
static void initMonomial(int nbVariable, short degree=0)
Initialise the static parameters of Monomial.
Represent an element of an extension of GF2, this class is a POD (Plain Old Data) because of the alig...
Declaration of class F4 methods.