37 int F4::NB_THREAD=min(8, omp_get_num_procs());
47 int cyclic6F4(
bool magma)
49 cout <<
"#########################################################" << endl;
50 cout <<
"# CYCLIC 6 #" << endl;
51 cout <<
"#########################################################" << endl << endl;
60 vector<Polynomial<eltType>> polCyclic6;
63 polCyclic6.emplace_back(
"x0+x1+x2+x3+x4+x5");
64 polCyclic6.emplace_back(
"x0*x1+x1*x2+x2*x3+x3*x4+x0*x5+x4*x5");
65 polCyclic6.emplace_back(
"x0*x1*x2+x1*x2*x3+x2*x3*x4+x0*x1*x5+x0*x4*x5+x3*x4*x5");
66 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");
67 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");
68 polCyclic6.emplace_back(
"x0*x1*x2*x3*x4*x5-1");
79 cyclic6.printReducedGroebnerBasis(
"cyclic6", modulo);
85 int cyclic7F4(
bool magma)
87 cout <<
"#########################################################" << endl;
88 cout <<
"# CYCLIC 7 #" << endl;
89 cout <<
"#########################################################" << endl << endl;
98 vector<Polynomial<eltType>> polCyclic7;
101 polCyclic7.emplace_back(
"x0+x1+x2+x3+x4+x5+x6");
102 polCyclic7.emplace_back(
"x0*x1+x1*x2+x2*x3+x3*x4+x4*x5+x0*x6+x5*x6");
103 polCyclic7.emplace_back(
"x0*x1*x2+x1*x2*x3+x2*x3*x4+x3*x4*x5+x0*x1*x6+x0*x5*x6+x4*x5*x6");
104 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");
105 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");
106 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");
107 polCyclic7.emplace_back(
"x0*x1*x2*x3*x4*x5*x6-1");
118 cyclic7.printReducedGroebnerBasis(
"cyclic7", modulo);
124 int cyclic8F4(
bool magma)
127 cout <<
"#########################################################" << endl;
128 cout <<
"# CYCLIC 8 #" << endl;
129 cout <<
"#########################################################" << endl << endl;
138 vector<Polynomial<eltType>> polCyclic8;
141 polCyclic8.emplace_back(
"x0+x1+x2+x3+x4+x5+x6+x7");
142 polCyclic8.emplace_back(
"x0*x1+x1*x2+x2*x3+x3*x4+x4*x5+x5*x6+x0*x7+x6*x7");
143 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");
144 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");
145 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");
146 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");
147 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");
148 polCyclic8.emplace_back(
"x0*x1*x2*x3*x4*x5*x6*x7-1");
159 cyclic8.printReducedGroebnerBasis(
"cyclic8", modulo);
165 int cyclic9F4(
bool magma)
168 cout <<
"#########################################################" << endl;
169 cout <<
"# CYCLIC 9 #" << endl;
170 cout <<
"#########################################################" << endl << endl;
179 vector<Polynomial<eltType>> polCyclic9;
182 polCyclic9.emplace_back(
"x0+x1+x2+x3+x4+x5+x6+x7+x8");
183 polCyclic9.emplace_back(
"x0*x1+x1*x2+x2*x3+x3*x4+x4*x5+x5*x6+x6*x7+x0*x8+x7*x8");
184 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");
185 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");
186 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");
187 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");
188 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");
189 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");
190 polCyclic9.emplace_back(
"x0*x1*x2*x3*x4*x5*x6*x7*x8-1");
201 cyclic9.printReducedGroebnerBasis(
"cyclic9", modulo);
207 int HFE_25_96_F4(
bool magma)
209 cout <<
"#########################################################" << endl;
210 cout <<
"# HFE 25 96 #" << endl;
211 cout <<
"#########################################################" << endl << endl;
219 string * vars =
new string[25];
220 for(
int i=0; i<25; i++)
222 vars[i]=string(
string(
"x")+to_string(i+1));
227 vector<Polynomial<eltType>> polHFE_25_96;
229 polHFE_25_96.emplace_back(
"x1^2+x1");
230 polHFE_25_96.emplace_back(
"x2^2+x2");
231 polHFE_25_96.emplace_back(
"x3^2+x3");
232 polHFE_25_96.emplace_back(
"x4^2+x4");
233 polHFE_25_96.emplace_back(
"x5^2+x5");
234 polHFE_25_96.emplace_back(
"x6^2+x6");
235 polHFE_25_96.emplace_back(
"x7^2+x7");
236 polHFE_25_96.emplace_back(
"x8^2+x8");
237 polHFE_25_96.emplace_back(
"x9^2+x9");
238 polHFE_25_96.emplace_back(
"x10^2+x10");
239 polHFE_25_96.emplace_back(
"x11^2+x11");
240 polHFE_25_96.emplace_back(
"x12^2+x12");
241 polHFE_25_96.emplace_back(
"x13^2+x13");
242 polHFE_25_96.emplace_back(
"x14^2+x14");
243 polHFE_25_96.emplace_back(
"x15^2+x15");
244 polHFE_25_96.emplace_back(
"x16^2+x16");
245 polHFE_25_96.emplace_back(
"x17^2+x17");
246 polHFE_25_96.emplace_back(
"x18^2+x18");
247 polHFE_25_96.emplace_back(
"x19^2+x19");
248 polHFE_25_96.emplace_back(
"x20^2+x20");
249 polHFE_25_96.emplace_back(
"x21^2+x21");
250 polHFE_25_96.emplace_back(
"x22^2+x22");
251 polHFE_25_96.emplace_back(
"x23^2+x23");
252 polHFE_25_96.emplace_back(
"x24^2+x24");
253 polHFE_25_96.emplace_back(
"x25^2+x25");
254 polHFE_25_96.emplace_back(
"x2*x3 + x1*x4 + x2*x4 + x2*x5 + x1*x6 + x3*x6 + x4*x6 + x5*x6 + x2*x7 + x4*x7 + x6*x8 + x7*x8 + x1*x9 + x2*x9 + x3*x9 + x4*x9 + x7*x9 + x2*x10 + x4*x10 + x7*x10 + x8*x10 + x3*x11 + x4*x11 + x6*x11 + x7*x11 + x8*x11 + x9*x11 + x10*x11 + x4*x12 + x5*x12 + x6*x12 + x7*x12 + x9*x12 + x10*x12 + x11*x12 + x1*x13 + x2*x13 + x5*x13 + x6*x13 + x9*x13 + x11*x13 + x12*x13 + x5*x14 + x6*x14 + x11*x14 + x13*x14 + x6*x15 + x7*x15 + x8*x15 + x9*x15 + x10*x15 + x12*x15 + x13*x15 + x1*x16 + x2*x16 + x3*x16 + x4*x16 + x7*x16 + x9*x16 + x10*x16 + x12*x16 + x13*x16 + x14*x16 + x15*x16 + x2*x17 + x4*x17 + x6*x17 + x9*x17 + x10*x17 + x11*x17 + x15*x17 + x16*x17 + x2*x18 + x4*x18 + x5*x18 + x7*x18 + x10*x18 + x13*x18 + x14*x18 + x16*x18 + x17*x18 + x2*x19 + x3*x19 + x4*x19 + x6*x19 + x7*x19 + x8*x19 + x10*x19 + x12*x19 + x13*x19 + x15*x19 + x16*x19 + x17*x19 + x18*x19 + x2*x20 + x3*x20 + x5*x20 + x6*x20 + x11*x20 + x12*x20 + x13*x20 + x14*x20 + x17*x20 + x19*x20 + x1*x21 + x5*x21 + x7*x21 + x9*x21 + x10*x21 + x16*x21 + x17*x21 + x19*x21 + x3*x22 + x4*x22 + x6*x22 + x7*x22 + x9*x22 + x10*x22 + x12*x22 + x14*x22 + x15*x22 + x17*x22 + x18*x22 + x19*x22 + x20*x22 + x21*x22 + x1*x23 + x2*x23 + x5*x23 + x6*x23 + x8*x23 + x10*x23 + x12*x23 + x17*x23 + x18*x23 + x19*x23 + x4*x24 + x7*x24 + x8*x24 + x9*x24 + x10*x24 + x12*x24 + x13*x24 + x14*x24 + x19*x24 + x21*x24 + x3*x25 + x5*x25 + x8*x25 + x9*x25 + x11*x25 + x12*x25 + x13*x25 + x14*x25 + x15*x25 + x20*x25 + x21*x25 + x22*x25 + x23*x25 + x1 + x2 + x7 + x9 + x11 + x12 + x19 + x20 + x21 + x25");
255 polHFE_25_96.emplace_back(
"x1*x3 + x3*x4 + x1*x5 + x3*x5 + x4*x5 + x1*x6 + x4*x6 + x1*x7 + x2*x7 + x3*x7 + x1*x8 + x5*x8 + x1*x9 + x2*x9 + x3*x9 + x6*x9 + x4*x10 + x6*x10 + x1*x11 + x2*x11 + x3*x11 + x5*x11 + x7*x11 + x8*x11 + x10*x11 + x8*x12 + x10*x12 + x11*x12 + x1*x13 + x3*x13 + x5*x13 + x6*x13 + x9*x13 + x11*x13 + x12*x13 + x1*x14 + x4*x14 + x5*x14 + x6*x14 + x9*x14 + x13*x14 + x1*x15 + x2*x15 + x5*x15 + x7*x15 + x10*x15 + x13*x15 + x2*x16 + x3*x16 + x4*x16 + x8*x16 + x9*x16 + x11*x16 + x12*x16 + x1*x17 + x2*x17 + x3*x17 + x6*x17 + x7*x17 + x9*x17 + x10*x17 + x11*x17 + x13*x17 + x15*x17 + x16*x17 + x2*x18 + x4*x18 + x5*x18 + x6*x18 + x7*x18 + x10*x18 + x11*x18 + x14*x18 + x15*x18 + x1*x19 + x3*x19 + x4*x19 + x7*x19 + x8*x19 + x11*x19 + x12*x19 + x13*x19 + x15*x19 + x16*x19 + x17*x19 + x18*x19 + x1*x20 + x5*x20 + x6*x20 + x7*x20 + x13*x20 + x15*x20 + x17*x20 + x19*x20 + x1*x21 + x2*x21 + x5*x21 + x7*x21 + x8*x21 + x13*x21 + x15*x21 + x17*x21 + x18*x21 + x19*x21 + x3*x22 + x8*x22 + x9*x22 + x10*x22+ x11*x22 + x16*x22 + x17*x22 + x20*x22 + x3*x23 + x4*x23 + x5*x23 + x6*x23 + x8*x23 + x17*x23 + x19*x23 + x1*x24 + x4*x24 + x5*x24 + x7*x24 + x9*x24 + x10*x24 + x12*x24 + x13*x24 + x15*x24 + x19*x24 + x22*x24 + x23*x24 + x1*x25 + x3*x25 + x4*x25 + x5*x25 + x7*x25 + x10*x25 + x11*x25 + x14*x25 + x15*x25 + x16*x25 + x17*x25 + x19*x25 + x1 + x7 + x11 + x15 + x16 + x22 + x23 + x24");
256 polHFE_25_96.emplace_back(
"x1*x3 + x2*x3 + x1*x4 + x2*x4 + x1*x5 + x2*x5 + x3*x7 + x6*x7 + x2*x8 + x4*x8 + x1*x9 + x3*x9 + x6*x9 + x3*x10 + x4*x10 + x6*x10 + x8*x10 + x9*x10 + x1*x11 + x5*x11 + x9*x11 + x2*x12 + x3*x12 + x5*x12 +x8*x12 + x10*x12 + x11*x12 + x1*x13 + x2*x13 + x3*x13 + x6*x13 + x7*x13 + x8*x13 + x2*x14 + x3*x14 + x6*x14 + x7*x14 + x8*x14 + x9*x14 + x10*x14 + x11*x14 + x12*x14 + x13*x14 + x1*x15 + x3*x15 + x6*x15 + x7*x15 + x8*x15 + x9*x15 + x13*x15 + x1*x16 + x2*x16 + x3*x16 + x5*x16 + x9*x16 + x10*x16 + x13*x16 + x15*x16 + x1*x17 + x4*x17 + x5*x17 + x6*x17 + x9*x17 + x10*x17 + x11*x17 + x12*x17 + x13*x17 + x15*x17 + x2*x18 + x3*x18 + x4*x18 + x5*x18 + x6*x18 + x11*x18 + x12*x18 + x13*x18 + x15*x18 + x3*x19 + x4*x19 + x5*x19 + x6*x19 + x9*x19 + x10*x19 + x13*x19 + x16*x19 + x17*x19 + x3*x20 +x4*x20 + x6*x20 + x11*x20 + x13*x20 + x17*x20 + x19*x20 + x1*x21 + x3*x21 + x4*x21 + x7*x21 + x9*x21 + x11*x21 + x12*x21 + x14*x21 + x16*x21 + x17*x21 + x18*x21 + x19*x21 + x3*x22 + x4*x22 + x9*x22 + x10*x22 + x11*x22 + x18*x22 + x21*x22 + x3*x23 + x4*x23 + x5*x23 + x9*x23 + x10*x23 + x12*x23 + x13*x23 + x15*x23 + x16*x23 + x17*x23 + x21*x23 + x22*x23 + x2*x24 + x3*x24 + x4*x24 + x5*x24 + x6*x24 + x8*x24 + x11*x24 + x12*x24 + x20*x24 + x21*x24 + x22*x24 + x1*x25 + x4*x25 + x5*x25 + x6*x25 + x8*x25 + x9*x25 + x12*x25 + x13*x25 + x14*x25 + x17*x25 + x21*x25 + x22*x25 + x1 + x2 + x6 + x7 + x8 + x10 + x11 + x13 + x15 + x16 + x17 + x19 + x22 + x23 + x25");
257 polHFE_25_96.emplace_back(
"x2*x3 + x2*x4 + x1*x5 + x2*x5 + x2*x7 + x6*x7 + x1*x8 + x2*x8 + x3*x8 + x4*x8 + x5*x8 + x6*x8 + x3*x9 + x4*x9 + x5*x9 + x6*x9 + x7*x9 + x1*x10 + x2*x10 + x7*x10 + x9*x10 + x1*x11 + x3*x11 + x4*x11 + x10*x11 + x2*x12 + x3*x12 + x5*x12 + x6*x12 + x9*x12 + x11*x12 + x1*x13 + x3*x13 + x7*x13 + x1*x14 + x2*x14 + x4*x14 + x5*x14 + x9*x14 + x10*x14 + x13*x14 + x2*x15 + x3*x15 + x6*x15 + x7*x15 + x9*x15 + x13*x15 + x2*x16 + x3*x16 + x5*x16 + x10*x16 + x11*x16 + x12*x16 + x14*x16 + x15*x16 + x1*x17 + x4*x17 + x8*x17 + x9*x17 + x10*x17 + x14*x17 + x15*x17 + x16*x17 + x1*x18 + x3*x18 + x4*x18 +x6*x18 + x7*x18 + x8*x18 + x10*x18 + x11*x18 + x12*x18 + x15*x18 + x1*x19 + x7*x19 + x8*x19 + x12*x19 + x14*x19 + x17*x19 + x3*x20 + x5*x20 + x6*x20 + x7*x20 + x8*x20 + x10*x20 + x12*x20 + x13*x20 +x14*x20 + x15*x20 + x19*x20 + x3*x21 + x4*x21 + x5*x21 + x7*x21 + x9*x21 + x11*x21 + x13*x21 + x16*x21 + x17*x21 + x20*x21 + x1*x22 + x2*x22 + x3*x22 + x4*x22 + x5*x22 + x7*x22 + x8*x22 + x9*x22 + x12*x22 + x13*x22 + x15*x22 + x16*x22 + x18*x22 + x20*x22 + x21*x22 + x2*x23 + x4*x23 + x5*x23 + x7*x23 + x8*x23 + x11*x23 + x12*x23 + x15*x23 + x3*x24 + x4*x24 + x7*x24 + x9*x24 + x12*x24 + x13*x24+ x14*x24 + x15*x24 + x16*x24 + x18*x24 + x20*x24 + x2*x25 + x3*x25 + x4*x25 + x5*x25 + x10*x25 + x11*x25 + x12*x25 + x15*x25 + x17*x25 + x21*x25 + x23*x25 + x2 + x4 + x5 + x6 + x9 + x10 + x11 + x12+ x13 + x15 + x17 + x18 + x19 + x20 + x21 + x22 + x24 + x25 + 1");
258 polHFE_25_96.emplace_back(
"x1*x2 + x3*x4 + x3*x5 + x4*x6 + x1*x7 + x2*x7 + x4*x7 + x5*x7 + x6*x7 + x1*x8 + x3*x8 + x4*x8 + x6*x8 + x1*x9 + x4*x9 + x5*x9 + x6*x9 + x7*x9 + x3*x10 + x6*x10 + x9*x10 + x1*x11 + x2*x11 + x3*x11 + x4*x11 + x7*x11 + x8*x11 + x10*x11 + x5*x12 + x11*x12 + x1*x13 + x2*x13 + x3*x13 + x4*x13 + x5*x13 + x6*x13 + x7*x13 + x9*x13 + x12*x13 + x2*x14 + x3*x14 + x4*x14 + x5*x14 + x8*x14 + x10*x14 + x13*x14 + x1*x15 + x2*x15 + x3*x15 + x5*x15 + x6*x15 + x7*x15 + x13*x15 + x1*x16 + x2*x16 + x4*x16 + x10*x16 + x11*x16 + x12*x16 + x13*x16 + x14*x16 + x3*x17 + x4*x17 + x6*x17 + x7*x17 + x9*x17 + x10*x17 + x12*x17 + x13*x17 + x15*x17 + x3*x18 + x8*x18 + x17*x18 + x1*x19 + x3*x19 + x5*x19 + x8*x19 + x11*x19 + x12*x19 + x13*x19 + x14*x19 + x18*x19 + x1*x20 + x4*x20 + x5*x20 + x9*x20 + x12*x20 + x13*x20 + x14*x20 + x18*x20 + x1*x21 + x2*x21 + x3*x21 + x4*x21 + x6*x21 + x7*x21 + x9*x21 + x10*x21 + x11*x21 + x13*x21 + x17*x21 + x19*x21 + x3*x22 + x5*x22 + x8*x22 + x9*x22 + x13*x22 + x14*x22+ x16*x22 + x17*x22 + x18*x22 + x21*x22 + x2*x23 + x3*x23 + x5*x23 + x7*x23 + x9*x23 + x11*x23 + x15*x23 + x17*x23 + x18*x23 + x20*x23 + x21*x23 + x22*x23 + x2*x24 + x3*x24 + x8*x24 + x9*x24 + x10*x24 + x13*x24 + x14*x24 + x15*x24 + x16*x24 + x17*x24 + x21*x24 + x2*x25 + x3*x25 + x4*x25 + x6*x25 + x7*x25 + x8*x25 + x9*x25 + x10*x25 + x11*x25 + x17*x25 + x19*x25 + x1 + x3 + x5 + x13 + x14 + x16 + x17 + x18 + x19 + x20 + x22 + x23 + 1");
259 polHFE_25_96.emplace_back(
"x1*x2 + x2*x3 + x1*x5 + x4*x5 + x1*x6 + x2*x6 + x4*x6 + x2*x7 + x1*x8 + x4*x8 + x6*x8 + x1*x9 + x2*x9 + x4*x9 + x6*x9 + x8*x9 + x2*x10 + x4*x10 + x6*x10 + x8*x10 + x4*x11 + x1*x12 + x2*x12 + x3*x12 + x5*x12 + x10*x12 + x11*x12 + x2*x13 + x3*x13 + x6*x13 + x7*x13 + x12*x13 + x1*x14 + x6*x14 + x7*x14 + x10*x14 + x12*x14 + x2*x15 + x4*x15 + x6*x15 + x7*x15 + x11*x15 + x13*x15 + x14*x15 + x2*x16 + x3*x16 + x6*x16 + x7*x16 + x9*x16 + x15*x16 + x2*x17 + x3*x17 + x5*x17 + x8*x17 + x9*x17 + x10*x17 + x15*x17 + x2*x18 + x6*x18 + x9*x18 + x13*x18 + x15*x18 + x16*x18 + x17*x18 + x3*x19 + x4*x19 + x6*x19 + x7*x19 + x8*x19 + x9*x19 + x10*x19 + x11*x19 + x12*x19 + x13*x19 + x14*x19 + x1*x20 + x2*x20 + x6*x20 + x7*x20 + x8*x20 + x10*x20 + x11*x20 + x12*x20 + x13*x20 + x17*x20 + x18*x20 + x19*x20+ x1*x21 + x2*x21 + x5*x21 + x6*x21 + x7*x21 + x8*x21 + x9*x21 + x10*x21 + x11*x21 + x12*x21 + x14*x21 + x2*x22 + x3*x22 + x5*x22 + x9*x22 + x10*x22 + x11*x22 + x13*x22 + x15*x22 + x17*x22 + x18*x22+ x19*x22 + x21*x22 + x1*x23 + x4*x23 + x5*x23 + x6*x23 + x7*x23 + x8*x23 + x10*x23 + x13*x23 + x16*x23 + x17*x23 + x1*x24 + x2*x24 + x3*x24 + x4*x24 + x6*x24 + x8*x24 + x10*x24 + x13*x24 + x17*x24 + x20*x24 + x21*x24 + x22*x24 + x23*x24 + x1*x25 + x2*x25 + x5*x25 + x6*x25 + x7*x25 + x8*x25 + x9*x25 + x10*x25 + x11*x25 + x12*x25 + x15*x25 + x16*x25 + x17*x25 + x19*x25 + x22*x25 + x24*x25 + x1 + x2 + x3 + x4 + x6 + x8 + x9 + x10 + x12 + x13 + x15 + x17 + x20 + x22 + x25 + 1");
260 polHFE_25_96.emplace_back(
"x1*x2 + x1*x4 + x3*x4 + x1*x6 + x3*x6 + x4*x6 + x1*x7 + x4*x7 + x5*x7 + x6*x7 + x1*x8 + x3*x8 + x4*x8 + x7*x8 + x1*x9 + x2*x9 + x4*x9 + x6*x9 + x3*x10 + x4*x10 + x6*x10 + x1*x11 + x2*x11 + x4*x11 + x8*x11 + x9*x11 + x10*x11 + x1*x12 + x4*x12 + x7*x12 + x9*x12 + x11*x12 + x4*x13 + x5*x13 + x9*x13 + x11*x13 + x12*x13 + x3*x14 + x5*x14 + x6*x14 + x10*x14 + x2*x15 + x3*x15 + x6*x15 + x13*x15 + x14*x15 + x1*x16 + x6*x16 + x7*x16 + x8*x16 + x12*x16 + x13*x16 + x15*x16 + x2*x17 + x3*x17 + x4*x17 + x7*x17 + x9*x17 + x11*x17 + x14*x17 + x15*x17 + x3*x18 + x10*x18 + x12*x18 + x15*x18 + x16*x18 + x2*x19 + x3*x19 + x4*x19 + x8*x19 + x13*x19 + x14*x19 + x16*x19 + x1*x20 + x5*x20 + x7*x20 + x8*x20 + x10*x20 + x11*x20 + x12*x20 + x16*x20 + x18*x20 + x3*x21 + x5*x21 + x7*x21 + x10*x21 + x11*x21+ x14*x21 + x15*x21 + x16*x21 + x19*x21 + x2*x22 + x3*x22 + x4*x22 + x7*x22 + x9*x22 + x10*x22 + x11*x22 + x12*x22 + x14*x22 + x17*x22 + x1*x23 + x2*x23 + x3*x23 + x5*x23 + x8*x23 + x10*x23 + x11*x23 + x13*x23 + x17*x23 + x19*x23 + x1*x24 + x2*x24 + x3*x24 + x4*x24 + x5*x24 + x6*x24 + x7*x24 + x8*x24 + x16*x24 + x17*x24 + x18*x24 + x19*x24 + x20*x24 + x22*x24 + x1*x25 + x3*x25 + x4*x25 +x7*x25 + x9*x25 + x11*x25 + x15*x25 + x17*x25 + x19*x25 + x21*x25 + x1 + x5 + x8 + x9 + x12 + x13 + x14 + x16 + x18 + x19 + x20 + x22 + x23 + x24");
261 polHFE_25_96.emplace_back(
"x1*x2 + x1*x3 + x2*x4 + x3*x4 + x2*x5 + x4*x5 + x1*x6 + x2*x6 + x2*x7 + x3*x7 + x4*x7 + x5*x7 + x1*x8 + x6*x8 + x1*x9 + x2*x9 + x3*x9 + x2*x10 + x3*x10 + x4*x10 + x8*x10 + x2*x11 + x3*x11 + x4*x11 + x5*x11 + x6*x11 + x7*x11 + x2*x12 + x4*x12 + x9*x12 + x11*x12 + x1*x13 + x2*x13 + x3*x13 + x5*x13 + x6*x13 + x10*x13 + x1*x14 + x4*x14 + x5*x14 + x7*x14 + x11*x14 + x12*x14 + x1*x15 + x4*x15 + x5*x15 + x6*x15 + x7*x15 + x10*x15 + x12*x15 + x13*x15 + x14*x15 + x1*x16 + x4*x16 + x5*x16 + x7*x16 + x8*x16 + x9*x16 + x12*x16 + x15*x16 + x1*x17 + x3*x17 + x4*x17 + x6*x17 + x8*x17 + x1*x18 + x3*x18 + x5*x18 + x7*x18 + x8*x18 + x10*x18 + x12*x18 + x14*x18 + x17*x18 + x1*x19 + x8*x19 + x12*x19 + x17*x19 + x1*x20 + x2*x20 + x3*x20 + x8*x20 + x13*x20 + x15*x20 + x16*x20 + x18*x20 + x3*x21 +x11*x21 + x12*x21 + x14*x21 + x15*x21 + x17*x21 + x18*x21 + x4*x22 + x5*x22 + x6*x22 + x10*x22 + x14*x22 + x15*x22 + x20*x22 + x1*x23 + x2*x23 + x4*x23 + x6*x23 + x7*x23 + x8*x23 + x10*x23 + x11*x23+ x12*x23 + x13*x23 + x15*x23 + x17*x23 + x20*x23 + x2*x24 + x3*x24 + x4*x24 + x6*x24 + x7*x24 + x8*x24 + x12*x24 + x17*x24 + x22*x24 + x3*x25 + x5*x25 + x7*x25 + x9*x25 + x11*x25 + x20*x25 + x22*x25 + x23*x25 + x24*x25 + x1 + x3 + x8 + x11 + x12 + x13 + x14 + x16 + x18 + x20 + x21 + x23 + 1");
262 polHFE_25_96.emplace_back(
"x1*x4 + x3*x4 + x1*x5 + x2*x5 + x4*x5 + x3*x6 + x4*x6 + x1*x7 + x2*x7 + x4*x7 + x5*x7 + x6*x7 + x1*x8 + x2*x8 + x4*x8 + x5*x8 + x7*x8 + x1*x9 + x5*x9 + x6*x9 + x7*x9 + x8*x9 + x1*x10 + x3*x10 + x7*x10 +x8*x10 + x4*x11 + x7*x11 + x9*x11 + x3*x12 + x7*x12 + x9*x12 + x11*x12 + x1*x13 + x2*x13 + x5*x13 + x6*x13 + x7*x13 + x8*x13 + x9*x13 + x11*x13 + x12*x13 + x4*x14 + x9*x14 + x11*x14 + x12*x14 + x1*x15 + x2*x15 + x3*x15 + x5*x15 + x6*x15 + x7*x15 + x8*x15 + x9*x15 + x10*x15 + x1*x16 + x3*x16 + x6*x16 + x7*x16 + x9*x16 + x10*x16 + x12*x16 + x13*x16 + x14*x16 + x15*x16 + x2*x17 + x6*x17 + x9*x17 + x11*x17 + x14*x17 + x16*x17 + x2*x18 + x3*x18 + x4*x18 + x7*x18 + x8*x18 + x9*x18 + x14*x18 + x15*x18 + x1*x19 + x2*x19 + x4*x19 + x5*x19 + x8*x19 + x9*x19 + x15*x19 + x1*x20 + x2*x20 + x3*x20 + x9*x20 + x10*x20 + x12*x20 + x13*x20 + x14*x20 + x18*x20 + x1*x21 + x2*x21 + x3*x21 + x6*x21 + x8*x21 + x10*x21 + x11*x21 + x13*x21 + x18*x21 + x20*x21 + x1*x22 + x7*x22 + x9*x22 + x13*x22 + x1*x23 + x3*x23 + x4*x23 + x5*x23 + x8*x23 + x9*x23 + x10*x23 + x11*x23 + x12*x23 + x14*x23 + x15*x23 + x16*x23 + x17*x23 + x18*x23 + x19*x23 + x2*x24 + x3*x24 + x6*x24 + x7*x24 + x8*x24 + x16*x24+ x19*x24 + x4*x25 + x6*x25 + x8*x25 + x10*x25 + x15*x25 + x17*x25 + x21*x25 + x22*x25 + x23*x25 + x1 + x2 + x3 + x4 + x5 + x8 + x9 + x10 + x11 + x19 + x22 + x25 + 1");
263 polHFE_25_96.emplace_back(
"x1*x3 + x1*x4 + x2*x5 + x1*x6 + x4*x6 + x5*x6 + x5*x7 + x6*x7 + x2*x8 + x3*x8 + x4*x8 + x5*x8 + x1*x10 + x4*x10 + x5*x10 + x7*x10 + x1*x11 + x2*x11 + x3*x11 + x4*x11 + x5*x11 + x7*x11 + x8*x11 + x9*x11 + x10*x11 + x2*x12 + x5*x12 + x6*x12 + x8*x12 + x9*x12 + x10*x12 + x11*x12 + x1*x13 + x6*x13 + x8*x13 + x10*x13 + x11*x13 + x12*x13 + x1*x14 + x2*x14 + x3*x14 + x6*x14 + x9*x14 + x11*x14 + x2*x15 + x4*x15 + x5*x15 + x7*x15 + x8*x15 + x11*x15 + x12*x15 + x13*x15 + x3*x16 + x5*x16 + x8*x16 + x9*x16 + x11*x16 + x12*x16 + x13*x16 + x15*x16 + x2*x17 + x3*x17 + x5*x17 + x6*x17 + x7*x17 + x8*x17 + x10*x17 + x11*x17 + x12*x17 + x13*x17 + x14*x17 + x15*x17 + x6*x18 + x7*x18 + x9*x18 + x10*x18 + x12*x18 + x13*x18 + x14*x18 + x15*x18 + x16*x18 + x17*x18 + x1*x19 + x7*x19 + x9*x19 + x10*x19 + x11*x19 + x14*x19 + x1*x20 + x2*x20 + x4*x20 + x6*x20 + x9*x20 + x10*x20 + x13*x20 + x16*x20 + x17*x20 + x18*x20 + x19*x20 + x2*x21 + x3*x21 + x4*x21 + x5*x21 + x9*x21 + x10*x21 + x14*x21 + x15*x21 + x1*x22 + x3*x22 + x6*x22 + x7*x22 + x9*x22 + x10*x22 + x11*x22 + x12*x22 + x14*x22 + x17*x22 + x18*x22 + x19*x22 + x21*x22 + x1*x23 + x2*x23 + x6*x23 + x9*x23 + x11*x23 + x12*x23 + x14*x23 + x15*x23 + x16*x23 + x19*x23 + x20*x23 + x22*x23 + x1*x24 + x4*x24 + x5*x24 + x10*x24 + x11*x24 + x12*x24 + x15*x24 + x17*x24 + x18*x24 + x20*x24 + x23*x24 + x1*x25 + x2*x25 + x3*x25 + x5*x25 + x9*x25 + x10*x25 + x15*x25 + x17*x25 + x18*x25 + x19*x25 + x20*x25 + x21*x25 + x22*x25 + x24*x25 + x2 + x6 + x7 + x10 + x11 + x14 + x16 + x17 + x18 + x19 + x24 + 1");
264 polHFE_25_96.emplace_back(
"x1*x4 + x1*x5 + x4*x5 + x1*x6 + x3*x7 + x5*x7 + x2*x8 + x4*x8 + x5*x8 + x7*x8 + x1*x9 + x2*x9 + x6*x9 + x2*x10 + x4*x10 + x7*x10 + x8*x10 + x2*x11 + x3*x11 + x5*x11 + x9*x11 + x6*x12 + x7*x12 + x8*x12 +x9*x12 + x10*x12 + x1*x13 + x4*x13 + x5*x13 + x9*x13 + x11*x13 + x12*x13 + x1*x14 + x10*x14 + x2*x15 + x7*x15 + x8*x15 + x9*x15 + x10*x15 + x11*x15 + x12*x15 + x13*x15 + x14*x15 + x2*x16 + x4*x16 + x6*x16 + x7*x16 + x10*x16 + x13*x16 + x15*x16 + x1*x17 + x4*x17 + x7*x17 + x9*x17 + x10*x17 + x14*x17 + x15*x17 + x16*x17 + x1*x18 + x2*x18 + x3*x18 + x5*x18 + x6*x18 + x8*x18 + x9*x18 + x11*x18 + x14*x18 + x15*x18 + x17*x18 + x1*x19 + x3*x19 + x4*x19 + x5*x19 + x6*x19 + x8*x19 + x10*x19 + x15*x19 + x18*x19 + x1*x20 + x2*x20 + x3*x20 + x6*x20 + x8*x20 + x10*x20 + x13*x20 + x16*x20 + x19*x20 +x4*x21 + x5*x21 + x6*x21 + x7*x21 + x8*x21 + x10*x21 + x11*x21 + x14*x21 + x15*x21 + x16*x21 + x18*x21 + x20*x21 + x1*x22 + x7*x22 + x9*x22 + x14*x22 + x15*x22 + x16*x22 + x17*x22 + x19*x22 + x1*x23+ x4*x23 + x5*x23 + x8*x23 + x10*x23 + x11*x23 + x13*x23 + x16*x23 + x17*x23 + x22*x23 + x2*x24 + x4*x24 + x5*x24 + x6*x24 + x7*x24 + x9*x24 + x13*x24 + x17*x24 + x18*x24 + x19*x24 + x20*x24 + x21*x24 + x3*x25 + x4*x25 + x6*x25 + x13*x25 + x14*x25 + x15*x25 + x17*x25 + x23*x25 + x1 + x6 + x9 + x10 + x13 + x14 + x15 + x19 + x21 + x24 + x25 + 1");
265 polHFE_25_96.emplace_back(
"x1*x2 + x1*x4 + x3*x4 + x3*x5 + x1*x6 + x3*x6 + x4*x6 + x5*x7 + x2*x8 + x5*x8 + x7*x8 + x1*x10 + x2*x10 + x7*x10 + x9*x10 + x2*x11 + x3*x11 + x4*x11 + x5*x11 + x7*x11 + x9*x11 + x1*x12 + x2*x12 + x3*x12+ x4*x12 + x5*x12 + x10*x12 + x1*x13 + x5*x13 + x6*x13 + x7*x13 + x10*x13 + x3*x14 + x4*x14 + x5*x14 + x6*x14 + x8*x14 + x10*x14 + x12*x14 + x13*x14 + x1*x15 + x3*x15 + x4*x15 + x7*x15 + x9*x15 + x11*x15 + x14*x15 + x2*x16 + x3*x16 + x4*x16 + x5*x16 + x7*x16 + x8*x16 + x9*x16 + x10*x16 + x11*x16 + x13*x16 + x1*x17 + x2*x17 + x3*x17 + x4*x17 + x7*x17 + x8*x17 + x13*x17 + x1*x18 + x2*x18 + x3*x18 + x5*x18 + x6*x18 + x10*x18 + x11*x18 + x12*x18 + x16*x18 + x17*x18 + x2*x19 + x4*x19 + x7*x19 + x9*x19 + x11*x19 + x12*x19 + x13*x19 + x14*x19 + x15*x19 + x16*x19 + x17*x19 + x18*x19 + x4*x20 + x6*x20 + x7*x20 + x10*x20 + x12*x20 + x14*x20 + x16*x20 + x19*x20 + x2*x21 + x5*x21 + x7*x21 + x8*x21 + x13*x21 + x15*x21 + x18*x21 + x19*x21 + x20*x21 + x2*x22 + x3*x22 + x5*x22 + x8*x22 +x10*x22 + x12*x22 + x14*x22 + x15*x22 + x16*x22 + x19*x22 + x20*x22 + x21*x22 + x2*x23 + x6*x23 + x7*x23 + x9*x23 + x10*x23 + x11*x23 + x15*x23 + x17*x23 + x19*x23 + x20*x23 + x3*x24 + x7*x24 + x8*x24 + x9*x24 + x10*x24 + x11*x24 + x13*x24 + x15*x24 + x18*x24 + x20*x24 + x2*x25 + x3*x25 + x5*x25 + x6*x25 + x7*x25 + x9*x25 + x13*x25 + x14*x25 + x15*x25 + x17*x25 + x19*x25 + x20*x25 + x21*x25 + x24*x25 + x1 + x2 + x3 + x7 + x9 + x10 + x11 + x15 + x16 + x17 + x18 + x19 + x20 + x21 + x22 + x23 + x25");
266 polHFE_25_96.emplace_back(
"x1*x3 + x2*x4 + x3*x4 + x2*x5 + x3*x5 + x2*x6 + x3*x6 + x1*x7 + x3*x7 + x4*x7 + x5*x7 + x3*x8 + x4*x8 + x5*x8 + x6*x8 + x5*x9 + x6*x9 + x7*x9 + x1*x10 + x4*x10 + x9*x10 + x1*x11 + x3*x11 + x4*x11 + x6*x11 + x8*x11 + x4*x12 + x5*x12 + x8*x12 + x9*x12 + x10*x12 + x11*x12 + x1*x13 + x4*x13 + x6*x13 + x7*x13 + x8*x13 + x9*x13 + x11*x13 + x1*x14 + x4*x14 + x6*x14 + x7*x14 + x8*x14 + x10*x14 + x13*x14 + x1*x15 + x4*x15 + x5*x15 + x10*x15 + x11*x15 + x14*x15 + x2*x16 + x4*x16 + x7*x16 + x10*x16 + x1*x17 + x3*x17 + x4*x17 + x6*x17 + x7*x17 + x8*x17 + x9*x17 + x10*x17 + x13*x17 + x15*x17 + x16*x17 + x3*x18 + x6*x18 + x9*x18 + x10*x18 + x11*x18 + x12*x18 + x14*x18 + x16*x18 + x1*x19 + x6*x19 + x7*x19 + x8*x19 + x10*x19 + x11*x19 + x14*x19 + x1*x20 + x2*x20 + x4*x20 + x5*x20 + x7*x20 + x8*x20 + x9*x20 + x11*x20 + x13*x20 + x16*x20 + x18*x20 + x19*x20 + x5*x21 + x8*x21 + x11*x21 + x14*x21 + x16*x21 + x17*x21 + x20*x21 + x1*x22 + x3*x22 + x6*x22 + x7*x22 + x9*x22 + x10*x22 + x12*x22+ x13*x22 + x14*x22 + x16*x22 + x17*x22 + x18*x22 + x20*x22 + x21*x22 + x1*x23 + x2*x23 + x3*x23 + x5*x23 + x11*x23 + x13*x23 + x14*x23 + x15*x23 + x16*x23 + x17*x23 + x18*x23 + x20*x23 + x21*x23 + x2*x24 + x6*x24 + x7*x24 + x9*x24 + x12*x24 + x16*x24 + x18*x24 + x19*x24 + x20*x24 + x2*x25 + x6*x25 + x12*x25 + x13*x25 + x15*x25 + x17*x25 + x18*x25 + x21*x25 + x22*x25 + x23*x25 + x1 + x2 + x3 +x4 + x5 + x6 + x7 + x9 + x11 + x13 + x14 + x17 + x18 + x20 + x22 + x24 + x25");
267 polHFE_25_96.emplace_back(
"x1*x3 + x2*x3 + x1*x4 + x1*x5 + x3*x5 + x3*x6 + x4*x6 + x5*x6 + x2*x7 + x3*x7 + x2*x8 + x3*x8 + x5*x8 + x6*x8 + x7*x8 + x1*x9 + x3*x9 + x5*x9 + x8*x9 + x2*x10 + x3*x10 + x4*x10 + x5*x10 + x7*x10 + x8*x10 + x9*x10 + x1*x11 + x3*x11 + x6*x11 + x7*x11 + x8*x11 + x10*x11 + x1*x12 + x2*x12 + x5*x12 + x9*x12 + x11*x12 + x4*x13 + x6*x13 + x7*x13 + x9*x13 + x10*x13 + x12*x13 + x3*x14 + x5*x14 + x6*x14 + x8*x14 + x11*x14 + x12*x14 + x13*x14 + x1*x15 + x2*x15 + x5*x15 + x10*x15 + x11*x15 + x1*x16 + x3*x16 + x4*x16 + x6*x16 + x8*x16 + x9*x16 + x10*x16 + x11*x16 + x12*x16 + x14*x16 + x15*x16 +x2*x17 + x4*x17 + x6*x17 + x8*x17 + x13*x17 + x14*x17 + x15*x17 + x1*x18 + x5*x18 + x9*x18 + x10*x18 + x11*x18 + x13*x18 + x17*x18 + x1*x19 + x6*x19 + x10*x19 + x11*x19 + x12*x19 + x15*x19 + x16*x19+ x17*x19 + x18*x19 + x1*x20 + x2*x20 + x4*x20 + x5*x20 + x12*x20 + x19*x20 + x4*x21 + x5*x21 + x6*x21 + x7*x21 + x8*x21 + x12*x21 + x16*x21 + x17*x21 + x18*x21 + x19*x21 + x2*x22 + x3*x22 + x7*x22 + x8*x22 + x9*x22 + x10*x22 + x12*x22 + x13*x22 + x14*x22 + x17*x22 + x21*x22 + x1*x23 + x3*x23 + x4*x23 + x8*x23 + x12*x23 + x13*x23 + x14*x23 + x15*x23 + x16*x23 + x17*x23 + x18*x23 + x19*x23 + x22*x23 + x1*x24 + x2*x24 + x3*x24 + x4*x24 + x7*x24 + x12*x24 + x14*x24 + x15*x24 + x18*x24 + x19*x24 + x21*x24 + x22*x24 + x1*x25 + x2*x25 + x3*x25 + x4*x25 + x5*x25 + x6*x25 + x10*x25 + x12*x25 +x14*x25 + x15*x25 + x17*x25 + x21*x25 + x22*x25 + x24*x25 + x2 + x3 + x5 + x11 + x14 + x16 + x24 + x25");
268 polHFE_25_96.emplace_back(
"x2*x3 + x1*x4 + x2*x5 + x4*x5 + x1*x7 + x5*x7 + x1*x8 + x2*x8 + x1*x9 + x4*x9 + x6*x9 + x7*x9 + x1*x10 + x2*x10 + x4*x10 + x6*x10 + x8*x10 + x9*x10 + x2*x11 + x5*x11 + x6*x11 + x8*x11 + x10*x11 + x1*x12+ x2*x12 + x3*x12 + x4*x12 + x5*x12 + x6*x12 + x7*x12 + x8*x12 + x9*x12 + x11*x12 + x1*x13 + x6*x13 + x8*x13 + x11*x13 + x2*x14 + x3*x14 + x5*x14 + x10*x14 + x2*x15 + x4*x15 + x7*x15 + x8*x15 + x9*x15 + x10*x15 + x12*x15 + x13*x15 + x1*x16 + x2*x16 + x4*x16 + x9*x16 + x10*x16 + x11*x16 + x1*x17 + x2*x17 + x4*x17 + x5*x17 + x9*x17 + x10*x17 + x11*x17 + x12*x17 + x13*x17 + x14*x17 + x2*x18 +x3*x18 + x4*x18 + x5*x18 + x6*x18 + x7*x18 + x8*x18 + x12*x18 + x16*x18 + x3*x19 + x5*x19 + x6*x19 + x8*x19 + x9*x19 + x10*x19 + x13*x19 + x15*x19 + x17*x19 + x1*x20 + x3*x20 + x4*x20 + x14*x20 + x15*x20 + x16*x20 + x17*x20 + x18*x20 + x2*x21 + x4*x21 + x6*x21 + x7*x21 + x10*x21 + x13*x21 + x14*x21 + x18*x21 + x19*x21 + x1*x22 + x2*x22 + x3*x22 + x5*x22 + x12*x22 + x15*x22 + x16*x22 + x18*x22 + x21*x22 + x1*x23 + x4*x23 + x7*x23 + x10*x23 + x16*x23 + x19*x23 + x20*x23 + x1*x24 + x4*x24 + x10*x24 + x11*x24 + x15*x24 + x16*x24 + x19*x24 + x20*x24 + x21*x24 + x23*x24 + x4*x25 + x6*x25 + x10*x25 + x12*x25 + x13*x25 + x15*x25 + x21*x25 + x22*x25 + x24*x25 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x10 + x11 + x15 + x16 + x22 + x24");
269 polHFE_25_96.emplace_back(
"x1*x2 + x2*x3 + x1*x4 + x2*x4 + x3*x4 + x3*x5 + x1*x6 + x5*x6 + x1*x7 + x3*x7 + x4*x7 + x6*x7 + x1*x8 + x2*x8 + x3*x8 + x4*x8 + x2*x9 + x4*x9 + x5*x9 + x7*x9 + x4*x10 + x5*x10 + x6*x10 + x1*x11 + x2*x11+ x3*x11 + x4*x11 + x6*x11 + x7*x11 + x9*x11 + x2*x12 + x4*x12 + x6*x12 + x7*x12 + x8*x12 + x9*x12 + x10*x12 + x11*x12 + x2*x13 + x4*x13 + x5*x13 + x6*x13 + x7*x13 + x9*x13 + x11*x13 + x1*x14 + x3*x14 + x6*x14 + x8*x14 + x12*x14 + x13*x14 + x3*x15 + x5*x15 + x6*x15 + x8*x15 + x11*x15 + x12*x15 + x14*x15 + x1*x16 + x2*x16 + x3*x16 + x6*x16 + x7*x16 + x12*x16 + x1*x17 + x3*x17 + x5*x17 + x7*x17 + x11*x17 + x13*x17 + x1*x18 + x2*x18 + x4*x18 + x5*x18 + x6*x18 + x8*x18 + x10*x18 + x12*x18 + x16*x18 + x3*x19 + x4*x19 + x7*x19 + x12*x19 + x13*x19 + x18*x19 + x4*x20 + x5*x20 + x6*x20 + x7*x20 + x10*x20 + x11*x20 + x12*x20 + x14*x20 + x17*x20 + x18*x20 + x19*x20 + x3*x21 + x6*x21 + x9*x21 + x10*x21 + x11*x21 + x16*x21 + x19*x21 + x20*x21 + x5*x22 + x8*x22 + x10*x22 + x11*x22 + x12*x22 + x15*x22 + x16*x22 + x17*x22 + x19*x22 + x21*x22 + x1*x23 + x2*x23 + x3*x23 + x5*x23 + x6*x23 + x11*x23 + x13*x23 + x14*x23 + x17*x23 + x19*x23 + x22*x23 + x6*x24 + x7*x24 + x9*x24 + x11*x24 + x12*x24 + x15*x24 + x17*x24 + x19*x24 + x2*x25 + x5*x25 + x8*x25 + x11*x25 + x13*x25 + x15*x25 + x16*x25 + x17*x25 + x19*x25 + x22*x25 + x1 + x2 + x3 + x4 + x5 + x6 + x9 + x10 + x13 + x16 + x20 + x21 + x25");
270 polHFE_25_96.emplace_back(
"x1*x4 + x1*x5 + x2*x5 + x2*x6 + x3*x6 + x4*x6 + x1*x7 + x2*x7 + x3*x7 + x4*x7 + x5*x7 + x2*x8 + x4*x8 + x5*x8 + x1*x9 + x2*x9 + x3*x9 + x5*x9 + x7*x9 + x8*x9 + x3*x10 + x4*x10 + x5*x10 + x6*x10 + x8*x10+ x9*x10 + x4*x11 + x7*x11 + x9*x11 + x10*x11 + x4*x12 + x5*x12 + x8*x12 + x10*x12 + x11*x12 + x1*x13 + x4*x13 + x6*x13 + x7*x13 + x8*x13 + x9*x13 + x10*x13 + x11*x13 + x12*x13 + x1*x14 + x2*x14 + x3*x14 + x4*x14 + x5*x14 + x6*x14 + x7*x14 + x8*x14 + x9*x14 + x10*x14 + x11*x14 + x3*x15 + x5*x15 + x6*x15 + x9*x15 + x10*x15 + x11*x15 + x12*x15 + x2*x16 + x5*x16 + x6*x16 + x7*x16 + x8*x16 + x9*x16 + x11*x16 + x12*x16 + x13*x16 + x14*x16 + x3*x17 + x9*x17 + x13*x17 + x15*x17 + x2*x18 + x7*x18 + x8*x18 + x16*x18 + x17*x18 + x4*x19 + x7*x19 + x10*x19 + x11*x19 + x14*x19 + x15*x19 + x16*x19 + x17*x19 + x2*x20 + x5*x20 + x8*x20 + x9*x20 + x12*x20 + x13*x20 + x18*x20 + x1*x21 + x3*x21 + x6*x21 + x8*x21 + x9*x21 + x11*x21 + x12*x21 + x14*x21 + x16*x21 + x17*x21 + x19*x21 + x2*x22 + x3*x22 + x4*x22 + x7*x22 + x10*x22 + x11*x22 + x13*x22 + x14*x22 + x16*x22 + x19*x22 + x21*x22 + x2*x23 + x3*x23 + x4*x23 + x5*x23 + x8*x23 + x9*x23 + x11*x23 + x14*x23 + x15*x23 + x16*x23 + x17*x23 + x19*x23 + x1*x24 + x2*x24 + x3*x24 + x4*x24 + x6*x24 + x7*x24 + x10*x24 + x16*x24 + x17*x24 + x19*x24 + x1*x25 + x3*x25 + x7*x25 + x9*x25 + x12*x25 + x14*x25 + x15*x25 + x22*x25 + x24*x25 + x1 + x5 + x9 + x10 + x11 + x14 + x15 + x18 + x19 + x23 + x24 + x25");
271 polHFE_25_96.emplace_back(
"x1*x3 + x3*x4 + x1*x5 + x2*x5 + x3*x5 + x4*x6 + x5*x6 + x1*x7 + x3*x7 + x5*x7 + x3*x8 + x4*x8 + x1*x9 + x3*x9 + x5*x9 + x6*x9 + x7*x10 + x8*x10 + x9*x10 + x1*x11 + x3*x11 + x4*x11 + x7*x11 + x9*x11 + x4*x12 + x10*x12 + x1*x13 + x2*x13 + x6*x13 + x7*x13 + x11*x13 + x12*x13 + x3*x14 + x4*x14 + x7*x14 + x8*x14 + x10*x14 + x11*x14 + x2*x15 + x3*x15 + x6*x15 + x12*x15 + x13*x15 + x5*x16 + x6*x16 + x7*x16 + x8*x16 + x9*x16 + x10*x16 + x13*x16 + x14*x16 + x1*x17 + x2*x17 + x4*x17 + x6*x17 + x9*x17 + x10*x17 + x13*x17 + x14*x17 + x16*x17 + x1*x18 + x2*x18 + x5*x18 + x6*x18 + x8*x18 + x12*x18 + x14*x18 + x15*x18 + x16*x18 + x17*x18 + x1*x19 + x2*x19 + x4*x19 + x5*x19 + x6*x19 + x7*x19 + x9*x19 + x10*x19 + x12*x19 + x13*x19 + x14*x19 + x16*x19 + x18*x19 + x1*x20 + x7*x20 + x8*x20 + x10*x20 + x15*x20 + x16*x20 + x1*x21 + x5*x21 + x6*x21 + x10*x21 + x12*x21 + x13*x21 + x14*x21 + x15*x21 + x16*x21 + x17*x21 + x18*x21 + x1*x22 + x3*x22 + x4*x22 + x6*x22 + x7*x22 + x8*x22 + x9*x22 + x11*x22 + x12*x22 + x13*x22 + x15*x22 + x18*x22 + x2*x23 + x3*x23 + x6*x23 + x7*x23 + x8*x23 + x9*x23 + x10*x23 + x11*x23 + x12*x23 + x13*x23 + x15*x23 + x16*x23 + x18*x23 + x19*x23 + x22*x23 + x2*x24 + x3*x24 + x4*x24 + x5*x24 + x6*x24 + x7*x24 + x13*x24 + x14*x24 + x18*x24 + x23*x24 + x1*x25 + x2*x25 + x4*x25 + x6*x25 + x9*x25 + x11*x25 + x13*x25 + x15*x25 + x17*x25 + x19*x25 + x20*x25 + x21*x25 + x23*x25 + x24*x25 + x2 + x5 + x12 + x13 + x14 + x16 + x18 + x19 + x24 + 1");
272 polHFE_25_96.emplace_back(
"x1*x3 + x3*x4 + x2*x5 + x3*x5 + x4*x5 + x2*x6 + x3*x6 + x4*x6 + x5*x6 + x1*x7 + x3*x7 + x5*x7 + x6*x7 + x2*x8 + x4*x8 + x6*x8 + x7*x8 + x5*x9 + x8*x9 + x2*x10 + x3*x10 + x4*x10 + x5*x10 + x7*x10 + x1*x11 + x4*x11 + x5*x11 + x6*x11 + x10*x11 + x1*x12 + x2*x12 + x5*x12 + x6*x12 + x9*x12 + x2*x13 + x5*x13 + x7*x13 + x9*x13 + x12*x13 + x1*x14 + x4*x14 + x8*x14 + x10*x14 + x11*x14 + x13*x14 + x5*x15 + x10*x15 + x12*x15 + x13*x15 + x14*x15 + x1*x16 + x6*x16 + x7*x16 + x9*x16 + x10*x16 + x13*x16 + x15*x16 + x1*x17 + x2*x17 + x3*x17 + x4*x17 + x7*x17 + x12*x17 + x14*x17 + x16*x17 + x2*x18 +x4*x18 + x7*x18 + x15*x18 + x16*x18 + x2*x19 + x3*x19 + x6*x19 + x12*x19 + x14*x19 + x17*x19 + x1*x20 + x4*x20 + x9*x20 + x13*x20 + x14*x20 + x15*x20 + x16*x20 + x3*x21 + x10*x21 + x12*x21 + x13*x21+ x14*x21 + x15*x21 + x16*x21 + x19*x21 + x20*x21 + x2*x22 + x3*x22 + x5*x22 + x6*x22 + x8*x22 + x9*x22 + x10*x22 + x11*x22 + x12*x22 + x13*x22 + x14*x22 + x17*x22 + x18*x22 + x4*x23 + x5*x23 + x6*x23 + x12*x23 + x18*x23 + x19*x23 + x20*x23 + x21*x23 + x22*x23 + x1*x24 + x2*x24 + x4*x24 + x7*x24 + x8*x24 + x9*x24 + x10*x24 + x11*x24 + x12*x24 + x13*x24 + x16*x24 + x17*x24 + x21*x24 + x22*x24 + x2*x25 + x3*x25 + x4*x25 + x5*x25 + x8*x25 + x12*x25 + x15*x25 + x20*x25 + x22*x25 + x4 + x6 + x8 + x10 + x12 + x13 + x15 + x16 + x21 + x22 + x23 + x24 + x25 + 1");
273 polHFE_25_96.emplace_back(
"x1*x2 + x1*x3 + x2*x3 + x3*x4 + x3*x6 + x4*x6 + x1*x7 + x2*x7 + x4*x7 + x5*x7 + x1*x8 + x5*x8 + x6*x8 + x1*x9 + x3*x9 + x5*x9 + x6*x9 + x7*x9 + x2*x10 + x7*x10 + x9*x10 + x1*x11 + x5*x11 + x8*x11 + x9*x11 + x10*x11 + x1*x12 + x3*x12 + x4*x12 + x8*x12 + x9*x12 + x2*x13 + x3*x13 + x4*x13 + x5*x13 + x6*x13 + x11*x13 + x1*x14 + x2*x14 + x3*x14 + x4*x14 + x5*x14 + x8*x14 + x9*x14 + x10*x14 + x11*x14 + x13*x14 + x2*x15 + x4*x15 + x5*x15 + x6*x15 + x8*x15 + x12*x15 + x13*x15 + x14*x15 + x2*x16 + x4*x16 + x6*x16 + x8*x16 + x11*x16 + x12*x16 + x15*x16 + x3*x17 + x4*x17 + x8*x17 + x10*x17 + x12*x17 + x13*x17 + x16*x17 + x5*x18 + x6*x18 + x7*x18 + x8*x18 + x9*x18 + x12*x18 + x14*x18 + x17*x18 + x3*x19 + x4*x19 + x5*x19 + x7*x19 + x9*x19 + x12*x19 + x14*x19 + x15*x19 + x17*x19 + x4*x20 +x5*x20 + x6*x20 + x7*x20 + x14*x20 + x15*x20 + x16*x20 + x17*x20 + x18*x20 + x4*x21 + x6*x21 + x7*x21 + x11*x21 + x12*x21 + x15*x21 + x17*x21 + x18*x21 + x19*x21 + x20*x21 + x3*x22 + x4*x22 + x7*x22 + x10*x22 + x11*x22 + x13*x22 + x14*x22 + x18*x22 + x20*x22 + x21*x22 + x1*x23 + x3*x23 + x7*x23 + x9*x23 + x10*x23 + x13*x23 + x15*x23 + x16*x23 + x17*x23 + x19*x23 + x20*x23 + x21*x23 + x1*x24 + x3*x24 + x5*x24 + x7*x24 + x9*x24 + x10*x24 + x12*x24 + x14*x24 + x16*x24 + x20*x24 + x22*x24 + x1*x25 + x2*x25 + x3*x25 + x4*x25 + x5*x25 + x11*x25 + x14*x25 + x19*x25 + x21*x25 + x24*x25 + x2 + x6+ x7 + x8 + x9 + x14 + x15 + x18 + x19 + x24");
274 polHFE_25_96.emplace_back(
"x2*x4 + x1*x5 + x3*x5 + x4*x5 + x3*x6 + x4*x6 + x5*x6 + x1*x7 + x2*x7 + x3*x7 + x4*x8 + x5*x8 + x7*x8 + x3*x9 + x5*x9 + x6*x9 + x5*x10 + x7*x10 + x1*x11 + x5*x11 + x8*x11 + x1*x12 + x2*x12 + x3*x12 + x5*x12 + x6*x12 + x7*x12 + x9*x12 + x11*x12 + x4*x13 + x5*x13 + x7*x13 + x9*x13 + x10*x13 + x12*x13 + x2*x14 + x4*x14 + x5*x14 + x7*x14 + x8*x14 + x9*x14 + x10*x14 + x13*x14 + x3*x15 + x4*x15 + x5*x15 + x6*x15 + x7*x15 + x1*x16 + x2*x16 + x5*x16 + x6*x16 + x8*x16 + x9*x16 + x11*x16 + x13*x16 + x14*x16 + x15*x16 + x1*x17 + x3*x17 + x13*x17 + x16*x17 + x3*x18 + x5*x18 + x6*x18 + x9*x18 + x12*x18 + x15*x18 + x16*x18 + x1*x19 + x2*x19 + x3*x19 + x4*x19 + x6*x19 + x7*x19 + x9*x19 + x10*x19 + x11*x19 + x12*x19 + x14*x19 + x1*x20 + x2*x20 + x4*x20 + x8*x20 + x10*x20 + x12*x20 + x14*x20 +x15*x20 + x18*x20 + x19*x20 + x1*x21 + x7*x21 + x8*x21 + x9*x21 + x10*x21 + x11*x21 + x12*x21 + x14*x21 + x17*x21 + x18*x21 + x1*x22 + x5*x22 + x7*x22 + x8*x22 + x9*x22 + x10*x22 + x15*x22 + x18*x22+ x19*x22 + x20*x22 + x1*x23 + x2*x23 + x4*x23 + x5*x23 + x10*x23 + x14*x23 + x15*x23 + x18*x23 + x19*x23 + x21*x23 + x4*x24 + x5*x24 + x12*x24 + x13*x24 + x14*x24 + x18*x24 + x21*x24 + x23*x24 + x2*x25 + x3*x25 + x7*x25 + x8*x25 + x9*x25 + x13*x25 + x16*x25 + x18*x25 + x22*x25 + x23*x25 + x1 + x2 + x4 + x5 + x8 + x10 + x13 + x15 + x16 + x18 + x21 + x23 + x25 + 1");
275 polHFE_25_96.emplace_back(
"x1*x3 + x1*x4 + x2*x4 + x3*x5 + x4*x5 + x3*x6 + x4*x6 + x4*x7 + x5*x7 + x1*x8 + x2*x8 + x3*x8 + x4*x8 + x5*x8 + x7*x8 + x4*x9 + x6*x9 + x8*x9 + x1*x10 + x3*x10 + x4*x10 + x5*x10 + x6*x10 + x8*x10 + x9*x10 + x1*x11 + x6*x11 + x9*x11 + x10*x11 + x3*x12 + x5*x12 + x6*x12 + x4*x13 + x5*x13 + x7*x13 + x9*x13 + x10*x13 + x11*x13 + x2*x14 + x3*x14 + x6*x14 + x7*x14 + x8*x14 + x10*x14 + x11*x14 + x12*x14 + x1*x15 + x2*x15 + x3*x15 + x5*x15 + x8*x15 + x9*x15 + x1*x16 + x4*x16 + x7*x16 + x8*x16 + x10*x16 + x13*x16 + x15*x16 + x1*x17 + x3*x17 + x5*x17 + x7*x17 + x10*x17 + x11*x17 + x13*x17 + x15*x17 + x16*x17 + x3*x18 + x4*x18 + x5*x18 + x7*x18 + x8*x18 + x9*x18 + x10*x18 + x11*x18 + x12*x18 + x15*x18 + x2*x19 + x5*x19 + x6*x19 + x7*x19 + x9*x19 + x11*x19 + x13*x19 + x18*x19 + x2*x20 + x4*x20 + x5*x20 + x6*x20 + x8*x20 + x15*x20 + x19*x20 + x2*x21 + x3*x21 + x10*x21 + x11*x21 + x14*x21 + x15*x21 + x18*x21 + x19*x21 + x20*x21 + x2*x22 + x3*x22 + x4*x22 + x5*x22 + x6*x22 + x7*x22 + x9*x22 + x15*x22 + x16*x22 + x18*x22 + x3*x23 + x4*x23 + x5*x23 + x7*x23 + x8*x23 + x10*x23 + x11*x23 + x12*x23 + x13*x23 + x14*x23 + x22*x23 + x5*x24 + x6*x24 + x8*x24 + x12*x24 + x13*x24 + x15*x24+ x16*x24 + x18*x24 + x21*x24 + x23*x24 + x2*x25 + x4*x25 + x5*x25 + x6*x25 + x7*x25 + x8*x25 + x10*x25 + x12*x25 + x13*x25 + x20*x25 + x1 + x2 + x6 + x7 + x8 + x12 + x13 + x14 + x15 + x16 + x22 + x23 + 1");
276 polHFE_25_96.emplace_back(
"x1*x3 + x2*x3 + x2*x4 + x1*x5 + x2*x5 + x4*x5 + x1*x6 + x3*x6 + x4*x6 + x3*x7 + x5*x7 + x6*x7 + x1*x8 + x2*x8 + x7*x8 + x1*x9 + x3*x9 + x4*x9 + x5*x9 + x6*x9 + x8*x9 + x2*x10 + x3*x10 + x6*x10 + x8*x10 + x9*x10 + x1*x11 + x3*x11 + x4*x11 + x6*x11 + x8*x11 + x9*x11 + x10*x11 + x1*x12 + x3*x12 + x4*x12 + x8*x12 + x9*x12 + x11*x12 + x1*x13 + x3*x13 + x10*x13 + x11*x13 + x12*x13 + x4*x14 + x5*x14 + x6*x14 + x9*x14 + x10*x14 + x11*x14 + x13*x14 + x1*x15 + x2*x15 + x5*x15 + x7*x15 + x9*x15 + x10*x15 + x11*x15 + x13*x15 + x14*x15 + x1*x16 + x8*x16 + x12*x16 + x14*x16 + x15*x16 + x3*x17 + x7*x17 +x9*x17 + x10*x17 + x11*x17 + x12*x17 + x13*x17 + x16*x17 + x1*x18 + x3*x18 + x5*x18 + x6*x18 + x7*x18 + x10*x18 + x11*x18 + x12*x18 + x14*x18 + x15*x18 + x16*x18 + x1*x19 + x2*x19 + x3*x19 + x6*x19 + x7*x19 + x8*x19 + x9*x19 + x10*x19 + x17*x19 + x18*x19 + x2*x20 + x4*x20 + x5*x20 + x7*x20 + x8*x20 + x9*x20 + x12*x20 + x13*x20 + x15*x20 + x16*x20 + x18*x20 + x4*x21 + x6*x21 + x12*x21 + x14*x21+ x16*x21 + x17*x21 + x18*x21 + x19*x21 + x20*x21 + x1*x22 + x2*x22 + x3*x22 + x5*x22 + x6*x22 + x8*x22 + x9*x22 + x10*x22 + x13*x22 + x14*x22 + x15*x22 + x16*x22 + x19*x22 + x20*x22 + x3*x23 + x5*x23 + x6*x23 + x7*x23 + x9*x23 + x10*x23 + x11*x23 + x14*x23 + x15*x23 + x16*x23 + x19*x23 + x21*x23 + x22*x23 + x4*x24 + x5*x24 + x7*x24 + x8*x24 + x10*x24 + x13*x24 + x14*x24 + x15*x24 + x16*x24 + x17*x24 + x19*x24 + x20*x24 + x22*x24 + x23*x24 + x1*x25 + x2*x25 + x3*x25 + x5*x25 + x11*x25 + x13*x25 + x15*x25 + x16*x25 + x17*x25 + x18*x25 + x19*x25 + x20*x25 + x21*x25 + x23*x25 + x24*x25 + x1 + x2 + x3 + x4 + x5 + x6 + x8 + x9 + x10 + x11 + x12 + x16 + x19 + x21 + x22 + x24");
277 polHFE_25_96.emplace_back(
"x1*x2 + x1*x4 + x2*x4 + x2*x6 + x4*x6 + x5*x6 + x2*x7 + x5*x7 + x6*x7 + x1*x8 + x4*x8 + x6*x8 + x5*x9 + x7*x9 + x1*x10 + x2*x10 + x4*x10 + x5*x10 + x6*x10 + x8*x10 + x9*x10 + x3*x11 + x4*x11 + x5*x11 + x6*x11 + x7*x11 + x9*x11 + x1*x12 + x3*x12 + x4*x12 + x5*x12 + x6*x12 + x7*x12 + x10*x12 + x1*x13 + x3*x13 + x4*x13 + x5*x13 + x8*x13 + x9*x13 + x10*x13 + x11*x13 + x2*x14 + x5*x14 + x9*x14 + x11*x14 + x12*x14 + x4*x15 + x5*x15 + x6*x15 + x8*x15 + x9*x15 + x12*x15 + x14*x15 + x1*x16 + x6*x16 + x8*x16 + x9*x16 + x1*x17 + x3*x17 + x5*x17 + x6*x17 + x7*x17 + x9*x17 + x10*x17 + x12*x17 + x13*x17 + x15*x17 + x3*x18 + x5*x18 + x7*x18 + x9*x18 + x12*x18 + x15*x18 + x17*x18 + x1*x19 + x2*x19 + x3*x19 + x7*x19 + x8*x19 + x10*x19 + x12*x19 + x14*x19 + x16*x19 + x1*x20 + x2*x20 + x8*x20 + x11*x20 + x12*x20 + x15*x20 + x17*x20 + x19*x20 + x2*x21 + x6*x21 + x13*x21 + x16*x21 + x17*x21 + x18*x21 + x20*x21 + x1*x22 + x2*x22 + x4*x22 + x7*x22 + x10*x22 + x14*x22 + x16*x22 + x18*x22 + x19*x22 + x21*x22 + x2*x23 + x3*x23 + x5*x23 + x7*x23 + x11*x23 + x15*x23 + x17*x23 + x20*x23 + x21*x23 + x22*x23 + x1*x24 + x2*x24 + x6*x24 + x7*x24 + x8*x24 + x9*x24 + x10*x24 + x11*x24 + x12*x24 + x14*x24 + x20*x24 + x21*x24 + x22*x24 + x1*x25 + x2*x25 + x8*x25 + x9*x25 + x10*x25 + x11*x25 + x14*x25 + x16*x25 + x17*x25 + x18*x25 + x20*x25 + x21*x25 + x23*x25 + x1 + x3 + x5 + x6 + x9 + x11 +x12 + x15 + x16 + x17 + x21 + x22 + x23 + x25");
278 polHFE_25_96.emplace_back(
"x1*x2 + x2*x3 + x1*x4 + x3*x4 + x1*x5 + x1*x6 + x1*x7 + x4*x7 + x5*x7 + x6*x7 + x1*x8 + x2*x8 + x6*x8 + x5*x9 + x6*x9 + x2*x10 + x6*x10 + x7*x10 + x9*x10 + x1*x11 + x3*x11 + x4*x11 + x6*x11 + x8*x11 + x3*x12 + x5*x12 + x7*x12 + x8*x12 + x10*x12 + x2*x13 + x3*x13 + x4*x13 + x6*x13 + x8*x13 + x10*x13 + x3*x14 + x5*x14 + x11*x14 + x1*x15 + x2*x15 + x6*x15 + x7*x15 + x9*x15 + x13*x15 + x14*x15 + x1*x16 + x3*x16 + x7*x16 + x8*x16 + x9*x16 + x10*x16 + x15*x16 + x1*x17 + x2*x17 + x5*x17 + x8*x17 + x13*x17 + x15*x17 + x16*x17 + x3*x18 + x4*x18 + x7*x18 + x12*x18 + x13*x18 + x1*x19 + x8*x19 + x10*x19 + x15*x19 + x16*x19 + x1*x20 + x3*x20 + x4*x20 + x6*x20 + x7*x20 + x9*x20 + x10*x20 + x11*x20 + x13*x20 + x15*x20 + x19*x20 + x2*x21 + x3*x21 + x6*x21 + x8*x21 + x11*x21 + x13*x21 + x14*x21 + x15*x21 + x17*x21 + x18*x21 + x2*x22 + x3*x22 + x4*x22 + x6*x22 + x7*x22 + x10*x22 + x11*x22 + x12*x22 + x15*x22 + x16*x22 + x17*x22 + x19*x22 + x20*x22 + x1*x23 + x2*x23 + x7*x23 + x9*x23 + x10*x23 + x11*x23 + x12*x23 + x13*x23 + x14*x23 + x15*x23 + x16*x23 + x17*x23 + x20*x23 + x22*x23 + x4*x24 + x6*x24 + x10*x24 + x11*x24 + x13*x24 + x16*x24 + x17*x24 + x19*x24 + x20*x24 + x21*x24 + x22*x24 + x23*x24 + x2*x25 + x3*x25 + x4*x25 + x7*x25 + x11*x25 + x13*x25 + x14*x25 + x20*x25 + x22*x25 + x23*x25 + x1 + x2 + x5 + x6 + x8 + x9 + x10 + x16 + x19 + x21 + x22 + x23 + x24 + x25 ");
284 nbGen=HFE_25_96.f4();
289 HFE_25_96.printReducedGroebnerBasis(
"HFE_25_96", modulo);
295 int HFE_30_96_F4(
bool magma)
297 cout <<
"#########################################################" << endl;
298 cout <<
"# HFE 30 96 #" << endl;
299 cout <<
"#########################################################" << endl << endl;
307 string * vars =
new string[30];
308 for(
int i=0; i<30; i++)
310 vars[i]=string(
string(
"x")+to_string(i+1));
315 vector<Polynomial<eltType>> polHFE_30_96;
318 polHFE_30_96.emplace_back(
"x1^2+x1");
319 polHFE_30_96.emplace_back(
"x2^2+x2");
320 polHFE_30_96.emplace_back(
"x3^2+x3");
321 polHFE_30_96.emplace_back(
"x4^2+x4");
322 polHFE_30_96.emplace_back(
"x5^2+x5");
323 polHFE_30_96.emplace_back(
"x6^2+x6");
324 polHFE_30_96.emplace_back(
"x7^2+x7");
325 polHFE_30_96.emplace_back(
"x8^2+x8");
326 polHFE_30_96.emplace_back(
"x9^2+x9");
327 polHFE_30_96.emplace_back(
"x10^2+x10");
328 polHFE_30_96.emplace_back(
"x11^2+x11");
329 polHFE_30_96.emplace_back(
"x12^2+x12");
330 polHFE_30_96.emplace_back(
"x13^2+x13");
331 polHFE_30_96.emplace_back(
"x14^2+x14");
332 polHFE_30_96.emplace_back(
"x15^2+x15");
333 polHFE_30_96.emplace_back(
"x16^2+x16");
334 polHFE_30_96.emplace_back(
"x17^2+x17");
335 polHFE_30_96.emplace_back(
"x18^2+x18");
336 polHFE_30_96.emplace_back(
"x19^2+x19");
337 polHFE_30_96.emplace_back(
"x20^2+x20");
338 polHFE_30_96.emplace_back(
"x21^2+x21");
339 polHFE_30_96.emplace_back(
"x22^2+x22");
340 polHFE_30_96.emplace_back(
"x23^2+x23");
341 polHFE_30_96.emplace_back(
"x24^2+x24");
342 polHFE_30_96.emplace_back(
"x25^2+x25");
343 polHFE_30_96.emplace_back(
"x26^2+x26");
344 polHFE_30_96.emplace_back(
"x27^2+x27");
345 polHFE_30_96.emplace_back(
"x28^2+x28");
346 polHFE_30_96.emplace_back(
"x29^2+x29");
347 polHFE_30_96.emplace_back(
"x30^2+x30");
348 polHFE_30_96.emplace_back(
"x2+x4+x5+x9+x11+x12+x14+x18+x19+x24+x25+x26+x28+x29+x1*x2+x1*x3+x1*x7+x1*x8+x1*x9+x1*x11+x1*x12+x1*x15+x1*x16+x1*x21+x1*x25+x1*x27+x1*x28+x1*x29+x1*x30+x2*x3+x2*x7+x2*x8+x2*x11+x2*x12+x2*x14+x2*x17+x2*x18+x2*x19+x2*x20+x2*x21+x2*x22+x2*x24+x2*x27+x2*x28+x2*x30+x3*x4+x3*x5+x3*x9+x3*x12+x3*x14+x3*x16+x3*x17+x3*x18+x3*x19+x3*x21+x3*x24+x3*x29+x3*x30+x4*x5+x4*x6+x4*x16+x4*x19+x4*x20+x4*x21+x4*x22+x4*x23+x4*x24+x4*x28+x4*x30+x5*x9+x5*x11+x5*x15+x5*x17+x5*x18+x5*x19+x5*x20+x5*x22+x5*x23+x5*x24+x5*x25+x5*x29+x5*x30+x6*x9+x6*x10+x6*x12+x6*x13+x6*x15+x6*x18+x6*x19+x6*x20+x6*x21+x6*x24+x6*x26+x6*x28+x6*x29+x6*x30+x7*x10+x7*x12+x7*x13+x7*x15+x7*x17+x7*x18+x7*x19+x7*x21+x7*x22+x7*x26+x7*x28+x7*x30+x8*x9+x8*x12+x8*x13+x8*x14+x8*x17+x8*x18+x8*x19+x8*x21+x8*x22+x8*x27+x8*x28+x9*x11+x9*x14+x9*x15+x9*x18+x9*x19+x9*x24+x9*x26+x9*x28+x9*x29+x10*x14+x10*x15+x10*x16+x10*x18+x10*x19+x10*x21+x10*x23+x10*x24+x10*x28+x10*x30+x11*x12+x11*x13+x11*x14+x11*x15+x11*x16+x11*x18+x11*x20+x11*x22+x11*x25+x11*x26+x11*x27+x11*x29+x11*x30+x12*x16+x12*x19+x12*x20+x12*x22+x12*x24+x12*x25+x12*x26+x12*x28+x13*x17+x13*x18+x13*x19+x13*x21+x13*x26+x13*x27+x13*x28+x13*x29+x14*x16+x14*x17+x14*x18+x14*x20+x14*x23+x14*x25+x14*x26+x14*x30+x15*x16+x15*x19+x15*x21+x15*x22+x15*x24+x15*x26+x15*x28+x15*x30+x16*x17+x16*x19+x16*x20+x16*x21+x16*x24+x16*x26+x16*x27+x16*x30+x17*x18+x17*x21+x17*x22+x17*x24+x17*x26+x17*x28+x17*x29+x17*x30+x18*x19+x18*x20+x18*x21+x18*x24+x18*x25+x18*x27+x18*x29+x19*x20+x19*x21+x19*x22+x19*x23+x19*x27+x19*x29+x19*x30+x20*x21+x20*x22+x20*x23+x20*x27+x20*x28+x20*x29+x21*x22+x21*x27+x21*x28+x21*x30+x22*x25+x22*x28+x22*x29+x22*x30+x23*x24+x23*x26+x23*x27+x23*x28+x24*x29+x25*x26+x25*x27+x25*x28+x26*x30+x27*x30+x28*x29+x29*x30");
349 polHFE_30_96.emplace_back(
"x3+x5+x7+x9+x10+x12+x13+x18+x19+x20+x21+x22+x23+x28+x29+x1*x4+x1*x5+x1*x6+x1*x8+x1*x9+x1*x11+x1*x12+x1*x13+x1*x14+x1*x15+x1*x16+x1*x19+x1*x22+x1*x24+x1*x25+x1*x26+x1*x27+x1*x28+x1*x29+x1*x30+x2*x13+x2*x14+x2*x16+x2*x17+x2*x19+x2*x21+x2*x22+x2*x26+x2*x27+x2*x28+x2*x29+x3*x4+x3*x5+x3*x6+x3*x7+x3*x8+x3*x9+x3*x14+x3*x15+x3*x17+x3*x21+x3*x22+x3*x25+x3*x29+x4*x5+x4*x10+x4*x11+x4*x14+x4*x17+x4*x20+x5*x6+x5*x8+x5*x10+x5*x13+x5*x14+x5*x17+x5*x19+x5*x20+x5*x21+x5*x22+x5*x26+x5*x27+x6*x8+x6*x12+x6*x13+x6*x14+x6*x15+x6*x17+x6*x20+x6*x23+x6*x24+x6*x25+x6*x26+x6*x27+x6*x29+x6*x30+x7*x8+x7*x10+x7*x11+x7*x12+x7*x13+x7*x15+x7*x16+x7*x21+x7*x23+x7*x24+x7*x26+x7*x27+x7*x28+x7*x29+x7*x30+x8*x14+x8*x16+x8*x17+x8*x18+x8*x21+x8*x23+x8*x24+x8*x25+x8*x26+x8*x27+x8*x30+x9*x11+x9*x12+x9*x13+x9*x14+x9*x17+x9*x19+x9*x23+x9*x24+x9*x26+x10*x11+x10*x13+x10*x15+x10*x16+x10*x17+x10*x18+x10*x19+x10*x20+x10*x21+x10*x22+x10*x25+x10*x26+x11*x13+x11*x15+x11*x16+x11*x17+x11*x20+x11*x21+x11*x22+x11*x23+x11*x24+x11*x25+x11*x27+x11*x28+x11*x29+x12*x17+x12*x22+x12*x23+x12*x24+x12*x26+x12*x27+x12*x28+x12*x30+x13*x14+x13*x15+x13*x20+x13*x22+x13*x23+x13*x24+x13*x25+x13*x28+x14*x15+x14*x19+x14*x23+x14*x27+x14*x29+x15*x17+x15*x20+x15*x22+x15*x23+x15*x25+x16*x17+x16*x23+x16*x24+x16*x26+x16*x27+x16*x28+x16*x29+x16*x30+x17*x18+x17*x20+x17*x22+x17*x23+x17*x24+x17*x25+x17*x26+x17*x28+x17*x30+x18*x19+x18*x20+x18*x21+x18*x22+x18*x24+x18*x25+x18*x26+x18*x28+x19*x20+x19*x23+x19*x25+x20*x23+x20*x26+x20*x27+x21*x24+x21*x25+x21*x26+x21*x27+x21*x28+x21*x29+x21*x30+x22*x24+x22*x25+x23*x24+x23*x25+x23*x28+x24*x28+x24*x29+x24*x30+x25*x28+x26*x30+x27*x29+x27*x30");
350 polHFE_30_96.emplace_back(
"x3+x4+x5+x6+x9+x10+x13+x16+x21+x22+x23+x24+x26+x27+x28+x30+x1*x5+x1*x8+x1*x10+x1*x11+x1*x15+x1*x17+x1*x19+x1*x23+x1*x30+x2*x3+x2*x7+x2*x8+x2*x9+x2*x11+x2*x12+x2*x15+x2*x16+x2*x17+x2*x18+x2*x19+x2*x20+x2*x21+x2*x22+x2*x25+x2*x27+x2*x28+x2*x29+x3*x4+x3*x5+x3*x7+x3*x9+x3*x12+x3*x15+x3*x16+x3*x17+x3*x19+x3*x23+x3*x25+x3*x27+x3*x29+x4*x6+x4*x8+x4*x9+x4*x11+x4*x13+x4*x14+x4*x16+x4*x20+x4*x22+x4*x25+x4*x27+x4*x29+x4*x30+x5*x6+x5*x11+x5*x14+x5*x16+x5*x19+x5*x20+x5*x21+x5*x23+x5*x27+x5*x28+x6*x7+x6*x8+x6*x9+x6*x12+x6*x13+x6*x15+x6*x17+x6*x18+x6*x23+x6*x25+x7*x9+x7*x11+x7*x13+x7*x20+x7*x21+x7*x22+x7*x23+x7*x24+x7*x25+x7*x26+x7*x27+x7*x28+x7*x29+x7*x30+x8*x9+x8*x10+x8*x12+x8*x13+x8*x14+x8*x15+x8*x18+x8*x19+x8*x20+x8*x21+x8*x22+x8*x25+x8*x27+x8*x28+x8*x29+x8*x30+x9*x10+x9*x13+x9*x15+x9*x16+x9*x19+x9*x20+x9*x22+x9*x23+x9*x29+x10*x11+x10*x13+x10*x16+x10*x20+x10*x22+x10*x23+x10*x24+x10*x26+x10*x29+x10*x30+x11*x12+x11*x13+x11*x14+x11*x15+x11*x16+x11*x17+x11*x18+x11*x19+x11*x22+x11*x25+x11*x26+x11*x30+x12*x14+x12*x16+x12*x17+x12*x19+x12*x21+x12*x22+x12*x23+x12*x24+x12*x25+x12*x27+x12*x29+x13*x14+x13*x16+x13*x19+x13*x21+x13*x23+x13*x29+x13*x30+x14*x17+x14*x18+x14*x19+x14*x20+x14*x21+x14*x22+x14*x24+x14*x25+x14*x26+x14*x29+x14*x30+x15*x16+x15*x17+x15*x20+x15*x23+x15*x26+x15*x27+x15*x30+x16*x18+x16*x20+x16*x21+x16*x22+x16*x25+x16*x28+x16*x29+x17*x18+x17*x19+x17*x21+x17*x22+x17*x26+x17*x27+x17*x28+x17*x29+x18*x23+x18*x25+x18*x26+x18*x29+x19*x24+x19*x25+x19*x26+x19*x27+x19*x30+x20*x21+x20*x23+x20*x26+x20*x27+x20*x28+x20*x29+x21*x22+x21*x24+x21*x26+x21*x28+x21*x29+x22*x23+x22*x24+x22*x25+x22*x26+x22*x27+x22*x28+x22*x29+x22*x30+x23*x24+x23*x25+x23*x27+x23*x29+x23*x30+x24*x25+x25*x26+x25*x29+x26*x28+x26*x29+x26*x30+x27*x28+x27*x29+x28*x29+x28*x30");
351 polHFE_30_96.emplace_back(
"1+x1+x2+x4+x8+x10+x13+x16+x20+x21+x22+x24+x29+x30+x1*x2+x1*x3+x1*x4+x1*x5+x1*x6+x1*x7+x1*x8+x1*x9+x1*x12+x1*x13+x1*x14+x1*x17+x1*x19+x1*x20+x1*x21+x1*x22+x1*x24+x1*x26+x1*x27+x1*x28+x1*x30+x2*x8+x2*x9+x2*x10+x2*x11+x2*x14+x2*x15+x2*x16+x2*x18+x2*x19+x2*x21+x2*x25+x2*x27+x2*x30+x3*x4+x3*x5+x3*x6+x3*x7+x3*x8+x3*x11+x3*x12+x3*x13+x3*x16+x3*x18+x3*x20+x3*x21+x3*x22+x3*x25+x3*x28+x3*x29+x4*x5+x4*x6+x4*x7+x4*x8+x4*x9+x4*x14+x4*x15+x4*x17+x4*x18+x4*x24+x4*x25+x4*x28+x4*x29+x4*x30+x5*x6+x5*x7+x5*x8+x5*x11+x5*x13+x5*x15+x5*x16+x5*x20+x5*x21+x5*x22+x5*x23+x5*x24+x5*x25+x5*x26+x6*x8+x6*x9+x6*x10+x6*x12+x6*x16+x6*x17+x6*x18+x6*x19+x6*x20+x6*x21+x6*x23+x6*x25+x6*x28+x6*x30+x7*x8+x7*x9+x7*x12+x7*x14+x7*x16+x7*x19+x7*x25+x7*x27+x7*x28+x8*x9+x8*x10+x8*x14+x8*x16+x8*x17+x8*x21+x8*x22+x8*x23+x8*x24+x8*x25+x8*x26+x8*x27+x9*x10+x9*x11+x9*x13+x9*x14+x9*x15+x9*x16+x9*x26+x9*x27+x9*x29+x10*x11+x10*x13+x10*x15+x10*x16+x10*x17+x10*x20+x10*x21+x10*x22+x10*x24+x10*x25+x10*x29+x11*x13+x11*x14+x11*x15+x11*x17+x11*x20+x11*x22+x11*x25+x11*x28+x11*x29+x11*x30+x12*x13+x12*x14+x12*x15+x12*x16+x12*x17+x12*x20+x12*x21+x12*x22+x12*x23+x12*x24+x12*x27+x12*x28+x12*x30+x13*x17+x13*x18+x13*x20+x13*x25+x13*x26+x13*x28+x13*x30+x14*x15+x14*x16+x14*x17+x14*x18+x14*x20+x14*x22+x14*x23+x14*x25+x14*x28+x14*x29+x15*x21+x15*x24+x15*x25+x15*x27+x15*x28+x15*x29+x15*x30+x16*x17+x16*x22+x16*x26+x16*x28+x16*x30+x17*x18+x17*x20+x17*x23+x17*x24+x17*x25+x17*x26+x17*x27+x17*x30+x18*x19+x18*x20+x18*x23+x18*x26+x18*x30+x19*x20+x19*x24+x19*x26+x19*x27+x19*x28+x19*x30+x20*x25+x20*x27+x20*x30+x21*x22+x21*x24+x21*x25+x21*x30+x22*x24+x22*x26+x22*x27+x22*x28+x23*x26+x23*x27+x24*x25+x24*x27+x24*x29+x25*x26+x25*x27+x25*x28+x27*x29+x28*x29+x28*x30");
352 polHFE_30_96.emplace_back(
"1+x1+x2+x4+x12+x14+x15+x17+x18+x20+x21+x22+x25+x26+x1*x3+x1*x4+x1*x5+x1*x10+x1*x11+x1*x13+x1*x14+x1*x15+x1*x16+x1*x21+x1*x24+x1*x26+x1*x27+x2*x5+x2*x6+x2*x7+x2*x8+x2*x9+x2*x14+x2*x19+x2*x20+x2*x21+x2*x23+x2*x24+x2*x27+x2*x28+x2*x29+x2*x30+x3*x5+x3*x6+x3*x10+x3*x11+x3*x12+x3*x15+x3*x16+x3*x17+x3*x21+x3*x22+x3*x23+x3*x24+x3*x26+x3*x27+x3*x28+x4*x6+x4*x8+x4*x11+x4*x12+x4*x13+x4*x17+x4*x18+x4*x21+x4*x25+x4*x27+x4*x28+x5*x6+x5*x7+x5*x13+x5*x14+x5*x15+x5*x16+x5*x18+x5*x20+x5*x21+x5*x22+x5*x23+x5*x24+x5*x26+x5*x27+x5*x30+x6*x9+x6*x11+x6*x13+x6*x16+x6*x17+x6*x20+x6*x24+x6*x25+x6*x29+x7*x8+x7*x15+x7*x16+x7*x17+x7*x20+x7*x21+x7*x22+x7*x24+x7*x25+x7*x27+x7*x28+x8*x9+x8*x10+x8*x12+x8*x13+x8*x16+x8*x17+x8*x19+x8*x23+x8*x27+x8*x30+x9*x10+x9*x11+x9*x12+x9*x14+x9*x15+x9*x16+x9*x20+x9*x23+x9*x24+x9*x25+x9*x27+x9*x28+x10*x13+x10*x15+x10*x18+x10*x21+x10*x22+x10*x24+x10*x28+x10*x29+x11*x15+x11*x16+x11*x17+x11*x18+x11*x20+x11*x23+x11*x24+x11*x25+x11*x26+x11*x27+x11*x28+x11*x30+x12*x13+x12*x14+x12*x18+x12*x19+x12*x20+x12*x23+x12*x25+x12*x28+x12*x29+x12*x30+x13*x14+x13*x15+x13*x17+x13*x20+x13*x21+x14*x16+x14*x17+x14*x18+x14*x19+x14*x20+x14*x26+x14*x27+x14*x28+x15*x16+x15*x17+x15*x20+x15*x21+x15*x22+x15*x24+x15*x25+x15*x30+x16*x17+x16*x19+x16*x20+x16*x21+x16*x22+x16*x23+x16*x25+x16*x26+x16*x27+x16*x28+x16*x30+x17*x18+x17*x19+x17*x23+x17*x28+x17*x30+x18*x19+x18*x20+x18*x23+x18*x24+x18*x25+x18*x27+x18*x29+x18*x30+x19*x21+x19*x23+x19*x24+x19*x25+x19*x26+x19*x28+x19*x29+x20*x21+x20*x22+x20*x23+x20*x24+x20*x26+x20*x27+x20*x28+x20*x29+x21*x23+x21*x24+x21*x25+x21*x26+x22*x23+x22*x25+x22*x27+x22*x30+x23*x26+x23*x28+x23*x30+x24*x26+x24*x27+x24*x28+x24*x29+x25*x26+x25*x28+x25*x29+x26*x27+x26*x28+x27*x28+x28*x30");
353 polHFE_30_96.emplace_back(
"1+x1+x3+x5+x6+x7+x8+x9+x13+x16+x17+x18+x19+x21+x23+x27+x28+x29+x1*x2+x1*x3+x1*x4+x1*x5+x1*x6+x1*x7+x1*x9+x1*x12+x1*x13+x1*x14+x1*x15+x1*x16+x1*x18+x1*x19+x1*x20+x1*x22+x1*x25+x1*x27+x1*x28+x1*x29+x2*x4+x2*x6+x2*x7+x2*x8+x2*x9+x2*x11+x2*x12+x2*x15+x2*x16+x2*x18+x2*x19+x2*x20+x2*x21+x2*x22+x2*x26+x2*x27+x2*x28+x3*x4+x3*x12+x3*x13+x3*x14+x3*x18+x3*x20+x3*x21+x3*x26+x3*x28+x4*x5+x4*x6+x4*x8+x4*x9+x4*x11+x4*x12+x4*x13+x4*x14+x4*x16+x4*x17+x4*x19+x4*x20+x4*x21+x4*x23+x4*x24+x4*x27+x5*x7+x5*x8+x5*x10+x5*x11+x5*x13+x5*x15+x5*x17+x5*x18+x5*x20+x5*x21+x5*x22+x5*x24+x5*x25+x5*x28+x5*x29+x6*x7+x6*x9+x6*x11+x6*x12+x6*x13+x6*x16+x6*x18+x6*x21+x6*x23+x6*x28+x6*x29+x7*x8+x7*x9+x7*x12+x7*x14+x7*x16+x7*x18+x7*x19+x7*x20+x7*x21+x7*x24+x7*x25+x7*x26+x7*x27+x8*x14+x8*x15+x8*x17+x8*x22+x8*x25+x8*x27+x8*x28+x9*x11+x9*x12+x9*x13+x9*x16+x9*x18+x9*x23+x9*x24+x9*x26+x9*x30+x10*x13+x10*x14+x10*x15+x10*x16+x10*x19+x10*x20+x10*x25+x10*x26+x10*x28+x10*x30+x11*x13+x11*x19+x11*x21+x11*x23+x11*x24+x11*x25+x11*x26+x11*x27+x11*x28+x11*x29+x12*x15+x12*x20+x12*x21+x12*x26+x12*x28+x13*x14+x13*x17+x13*x20+x13*x21+x13*x23+x13*x25+x13*x28+x13*x29+x13*x30+x14*x15+x14*x16+x14*x17+x14*x18+x14*x22+x14*x23+x14*x28+x14*x29+x15*x16+x15*x17+x15*x18+x15*x21+x15*x22+x15*x23+x15*x27+x15*x29+x16*x17+x16*x23+x16*x24+x16*x25+x16*x27+x16*x28+x17*x22+x17*x23+x17*x26+x17*x29+x18*x19+x18*x20+x18*x22+x18*x23+x18*x24+x18*x25+x18*x27+x18*x30+x19*x22+x19*x23+x19*x24+x19*x28+x19*x29+x20*x23+x20*x24+x20*x25+x20*x27+x21*x24+x21*x25+x21*x27+x21*x28+x21*x29+x21*x30+x22*x27+x22*x28+x22*x29+x23*x24+x23*x27+x23*x28+x24*x25+x24*x27+x24*x30+x25*x28+x25*x29+x25*x30+x26*x27+x27*x30+x28*x30");
354 polHFE_30_96.emplace_back(
"x7+x9+x10+x12+x13+x14+x18+x19+x20+x27+x28+x29+x30+x1*x4+x1*x6+x1*x7+x1*x8+x1*x9+x1*x17+x1*x19+x1*x20+x1*x22+x1*x25+x1*x26+x1*x27+x2*x3+x2*x6+x2*x8+x2*x9+x2*x10+x2*x14+x2*x15+x2*x16+x2*x17+x2*x18+x2*x19+x2*x20+x2*x21+x2*x23+x2*x25+x2*x30+x3*x5+x3*x6+x3*x10+x3*x12+x3*x13+x3*x17+x3*x18+x3*x23+x3*x25+x3*x26+x3*x28+x3*x29+x3*x30+x4*x8+x4*x9+x4*x12+x4*x15+x4*x16+x4*x17+x4*x19+x4*x21+x4*x25+x4*x27+x4*x28+x4*x29+x4*x30+x5*x6+x5*x8+x5*x9+x5*x15+x5*x16+x5*x17+x5*x19+x5*x21+x5*x25+x5*x26+x5*x27+x5*x28+x6*x7+x6*x8+x6*x9+x6*x11+x6*x12+x6*x18+x6*x20+x6*x21+x6*x22+x6*x24+x6*x25+x6*x26+x6*x28+x7*x10+x7*x12+x7*x13+x7*x15+x7*x18+x7*x19+x7*x20+x7*x22+x7*x23+x7*x24+x7*x25+x7*x26+x7*x27+x7*x28+x7*x29+x8*x10+x8*x20+x8*x21+x8*x28+x9*x10+x9*x11+x9*x16+x9*x17+x9*x18+x9*x22+x9*x25+x9*x29+x10*x12+x10*x14+x10*x16+x10*x17+x10*x20+x10*x22+x10*x23+x10*x25+x10*x26+x10*x30+x11*x12+x11*x15+x11*x16+x11*x20+x11*x21+x11*x23+x11*x25+x11*x26+x11*x30+x12*x14+x12*x15+x12*x19+x12*x22+x12*x24+x12*x26+x12*x27+x12*x29+x13*x14+x13*x15+x13*x18+x13*x20+x13*x21+x13*x23+x13*x26+x13*x27+x13*x29+x14*x20+x14*x21+x14*x24+x14*x26+x14*x27+x14*x29+x15*x20+x15*x21+x15*x22+x15*x23+x15*x26+x15*x27+x15*x29+x15*x30+x16*x17+x16*x20+x16*x21+x16*x22+x16*x23+x16*x26+x16*x27+x16*x29+x16*x30+x17*x18+x17*x21+x17*x26+x17*x27+x17*x28+x18*x19+x18*x21+x18*x22+x18*x23+x18*x25+x18*x26+x18*x27+x18*x28+x18*x29+x19*x20+x19*x21+x19*x23+x19*x24+x19*x25+x20*x23+x20*x24+x20*x25+x20*x26+x21*x22+x21*x24+x21*x25+x21*x26+x22*x25+x22*x26+x22*x27+x22*x28+x23*x26+x23*x28+x23*x29+x23*x30+x24*x25+x24*x26+x24*x27+x25*x26+x25*x28+x25*x29+x25*x30+x27*x28+x27*x30+x29*x30");
355 polHFE_30_96.emplace_back(
"x1+x2+x6+x7+x8+x11+x15+x17+x18+x19+x20+x21+x25+x28+x30+x1*x2+x1*x3+x1*x4+x1*x5+x1*x9+x1*x11+x1*x12+x1*x13+x1*x15+x1*x16+x1*x17+x1*x18+x1*x19+x1*x20+x1*x22+x1*x25+x1*x26+x1*x29+x1*x30+x2*x5+x2*x7+x2*x14+x2*x15+x2*x17+x2*x18+x2*x20+x2*x22+x2*x24+x2*x25+x2*x29+x2*x30+x3*x6+x3*x7+x3*x8+x3*x9+x3*x13+x3*x14+x3*x15+x3*x19+x3*x20+x3*x21+x3*x22+x3*x23+x3*x24+x3*x28+x3*x29+x4*x11+x4*x15+x4*x18+x4*x19+x4*x20+x4*x21+x4*x22+x4*x23+x4*x26+x4*x28+x4*x30+x5*x8+x5*x9+x5*x12+x5*x15+x5*x18+x5*x20+x5*x24+x5*x25+x5*x26+x5*x28+x5*x30+x6*x8+x6*x9+x6*x10+x6*x12+x6*x13+x6*x18+x6*x21+x6*x23+x6*x24+x6*x25+x6*x27+x6*x29+x7*x9+x7*x11+x7*x12+x7*x15+x7*x16+x7*x19+x7*x24+x7*x25+x7*x28+x8*x9+x8*x11+x8*x16+x8*x18+x8*x19+x8*x20+x8*x23+x8*x24+x8*x27+x8*x30+x9*x14+x9*x16+x9*x17+x9*x18+x9*x22+x9*x23+x9*x24+x9*x25+x9*x26+x9*x27+x9*x30+x10*x11+x10*x13+x10*x14+x10*x17+x10*x19+x10*x22+x10*x23+x10*x24+x10*x26+x10*x29+x10*x30+x11*x12+x11*x15+x11*x16+x11*x17+x11*x22+x11*x27+x12*x13+x12*x14+x12*x15+x12*x16+x12*x17+x12*x18+x12*x22+x12*x23+x12*x24+x12*x25+x12*x26+x12*x28+x12*x29+x12*x30+x13*x14+x13*x15+x13*x18+x13*x22+x13*x25+x13*x26+x13*x29+x13*x30+x14*x16+x14*x21+x14*x24+x14*x26+x14*x30+x15*x17+x15*x22+x15*x24+x15*x25+x16*x19+x16*x20+x16*x24+x16*x26+x16*x28+x16*x29+x16*x30+x17*x18+x17*x19+x17*x23+x17*x24+x17*x29+x17*x30+x18*x20+x18*x22+x18*x28+x18*x30+x19*x21+x19*x22+x19*x28+x19*x30+x20*x23+x20*x25+x20*x26+x20*x27+x20*x30+x21*x24+x21*x28+x21*x29+x22*x23+x22*x24+x22*x25+x22*x26+x22*x27+x22*x28+x22*x30+x23*x24+x23*x25+x23*x27+x23*x28+x23*x29+x24*x28+x24*x29+x25*x26+x25*x29+x26*x28+x26*x29+x27*x28+x27*x29+x28*x30");
356 polHFE_30_96.emplace_back(
"x2+x3+x4+x5+x6+x9+x10+x17+x18+x19+x20+x23+x24+x25+x28+x29+x1*x2+x1*x3+x1*x6+x1*x9+x1*x13+x1*x14+x1*x15+x1*x18+x1*x20+x1*x21+x1*x22+x1*x23+x1*x25+x1*x26+x1*x29+x1*x30+x2*x3+x2*x4+x2*x5+x2*x6+x2*x11+x2*x13+x2*x18+x2*x20+x2*x22+x2*x24+x2*x25+x2*x28+x2*x30+x3*x6+x3*x8+x3*x9+x3*x11+x3*x13+x3*x19+x3*x23+x3*x26+x3*x27+x3*x28+x3*x29+x4*x6+x4*x10+x4*x12+x4*x13+x4*x14+x4*x17+x4*x19+x4*x20+x4*x21+x4*x22+x4*x23+x4*x24+x4*x25+x4*x26+x4*x27+x4*x28+x4*x30+x5*x7+x5*x8+x5*x11+x5*x13+x5*x14+x5*x15+x5*x16+x5*x17+x5*x21+x5*x26+x5*x27+x5*x29+x6*x7+x6*x8+x6*x9+x6*x10+x6*x14+x6*x15+x6*x17+x6*x19+x6*x20+x6*x24+x6*x26+x7*x9+x7*x11+x7*x13+x7*x15+x7*x18+x7*x19+x7*x20+x7*x21+x7*x22+x7*x24+x7*x26+x8*x11+x8*x13+x8*x15+x8*x16+x8*x17+x8*x18+x8*x19+x8*x21+x8*x23+x8*x26+x8*x29+x8*x30+x9*x10+x9*x13+x9*x15+x9*x16+x9*x17+x9*x18+x9*x22+x9*x23+x9*x24+x9*x25+x9*x30+x10*x12+x10*x13+x10*x15+x10*x17+x10*x18+x10*x20+x10*x22+x10*x27+x10*x30+x11*x12+x11*x13+x11*x14+x11*x15+x11*x17+x11*x18+x11*x21+x11*x25+x11*x27+x11*x29+x12*x14+x12*x18+x12*x20+x12*x21+x12*x23+x12*x24+x12*x26+x12*x27+x12*x28+x12*x30+x13*x14+x13*x21+x13*x23+x13*x24+x13*x25+x13*x27+x13*x30+x14*x16+x14*x17+x14*x19+x14*x25+x14*x27+x14*x28+x14*x29+x15*x16+x15*x17+x15*x18+x15*x19+x15*x24+x15*x25+x15*x29+x16*x17+x16*x19+x16*x20+x16*x22+x16*x23+x16*x24+x16*x25+x16*x28+x16*x29+x16*x30+x17*x20+x17*x21+x17*x22+x17*x23+x17*x24+x17*x28+x17*x29+x18*x19+x18*x20+x18*x24+x18*x26+x18*x28+x18*x29+x19*x20+x19*x21+x19*x22+x19*x23+x19*x25+x19*x28+x19*x30+x20*x23+x20*x25+x20*x27+x20*x28+x21*x22+x21*x23+x21*x25+x21*x26+x21*x29+x21*x30+x22*x23+x22*x28+x23*x24+x23*x26+x23*x30+x24*x25+x25*x27+x25*x28+x27*x28+x27*x29+x28*x29+x28*x30+x29*x30");
357 polHFE_30_96.emplace_back(
"1+x1+x2+x4+x5+x8+x9+x12+x13+x15+x16+x20+x21+x22+x23+x24+x25+x26+x28+x1*x2+x1*x3+x1*x6+x1*x7+x1*x8+x1*x9+x1*x12+x1*x13+x1*x14+x1*x15+x1*x18+x1*x19+x1*x20+x1*x23+x1*x27+x1*x29+x1*x30+x2*x3+x2*x5+x2*x9+x2*x12+x2*x15+x2*x17+x2*x18+x2*x19+x2*x21+x2*x22+x2*x23+x2*x27+x2*x29+x2*x30+x3*x4+x3*x5+x3*x6+x3*x7+x3*x8+x3*x9+x3*x10+x3*x11+x3*x12+x3*x14+x3*x15+x3*x16+x3*x19+x3*x20+x3*x23+x3*x24+x3*x25+x3*x26+x3*x28+x3*x29+x3*x30+x4*x5+x4*x6+x4*x9+x4*x12+x4*x13+x4*x14+x4*x17+x4*x18+x4*x19+x4*x22+x4*x26+x4*x27+x4*x28+x4*x29+x5*x6+x5*x7+x5*x9+x5*x10+x5*x15+x5*x16+x5*x20+x5*x21+x5*x23+x5*x28+x5*x29+x6*x10+x6*x11+x6*x12+x6*x13+x6*x15+x6*x16+x6*x21+x6*x22+x6*x23+x6*x25+x6*x26+x6*x27+x7*x13+x7*x14+x7*x15+x7*x16+x7*x18+x7*x19+x7*x21+x7*x25+x7*x28+x7*x29+x8*x10+x8*x11+x8*x12+x8*x19+x8*x20+x8*x22+x8*x23+x8*x25+x8*x28+x8*x30+x9*x10+x9*x11+x9*x13+x9*x14+x9*x17+x9*x18+x9*x20+x9*x22+x9*x24+x9*x28+x9*x30+x10*x14+x10*x15+x10*x24+x10*x26+x10*x27+x10*x28+x10*x30+x11*x18+x11*x20+x11*x22+x11*x24+x11*x25+x11*x26+x11*x28+x11*x29+x12*x13+x12*x15+x12*x17+x12*x18+x12*x19+x12*x21+x12*x22+x12*x23+x12*x25+x12*x27+x12*x30+x13*x15+x13*x16+x13*x18+x13*x20+x13*x21+x13*x23+x13*x24+x13*x26+x13*x27+x13*x28+x14*x16+x14*x17+x14*x19+x14*x20+x14*x21+x14*x24+x14*x25+x14*x26+x14*x28+x14*x30+x15*x17+x15*x18+x15*x20+x15*x24+x15*x25+x15*x26+x15*x27+x15*x28+x15*x30+x16*x18+x16*x20+x16*x21+x16*x24+x16*x25+x16*x26+x16*x28+x16*x30+x17*x20+x17*x21+x17*x24+x17*x25+x17*x26+x17*x27+x18*x20+x18*x21+x18*x23+x18*x25+x18*x26+x18*x28+x19*x20+x19*x21+x19*x23+x19*x25+x19*x26+x20*x21+x20*x22+x20*x23+x20*x24+x20*x25+x20*x26+x20*x27+x20*x29+x21*x25+x21*x30+x22*x24+x22*x26+x22*x27+x22*x28+x23*x28+x24*x26+x24*x27+x24*x30+x25*x28+x25*x29+x26*x27+x26*x30");
358 polHFE_30_96.emplace_back(
"1+x2+x3+x4+x13+x14+x15+x16+x20+x22+x24+x27+x28+x1*x3+x1*x4+x1*x10+x1*x11+x1*x12+x1*x17+x1*x19+x1*x24+x1*x26+x1*x28+x1*x29+x1*x30+x2*x3+x2*x4+x2*x5+x2*x6+x2*x8+x2*x9+x2*x11+x2*x12+x2*x13+x2*x14+x2*x16+x2*x17+x2*x22+x2*x23+x2*x27+x2*x28+x2*x30+x3*x4+x3*x5+x3*x8+x3*x9+x3*x13+x3*x14+x3*x15+x3*x16+x3*x17+x3*x22+x3*x23+x3*x24+x3*x27+x3*x28+x4*x6+x4*x8+x4*x9+x4*x15+x4*x17+x4*x18+x4*x19+x4*x20+x4*x21+x4*x27+x4*x29+x5*x6+x5*x8+x5*x10+x5*x14+x5*x17+x5*x19+x5*x21+x5*x24+x5*x26+x5*x27+x5*x30+x6*x7+x6*x10+x6*x12+x6*x15+x6*x19+x6*x21+x6*x22+x6*x23+x6*x24+x6*x25+x6*x28+x6*x30+x7*x9+x7*x12+x7*x16+x7*x18+x7*x19+x7*x25+x8*x10+x8*x11+x8*x12+x8*x14+x8*x15+x8*x17+x8*x18+x8*x19+x8*x20+x8*x23+x8*x24+x8*x26+x8*x27+x8*x30+x9*x11+x9*x12+x9*x13+x9*x14+x9*x16+x9*x17+x9*x19+x9*x21+x9*x22+x9*x23+x9*x25+x9*x28+x9*x30+x10*x12+x10*x15+x10*x16+x10*x17+x10*x22+x10*x25+x10*x29+x10*x30+x11*x13+x11*x14+x11*x15+x11*x16+x11*x17+x11*x19+x11*x20+x11*x22+x11*x23+x11*x24+x11*x25+x11*x26+x11*x27+x11*x28+x11*x30+x12*x15+x12*x20+x12*x21+x12*x24+x12*x25+x12*x28+x12*x29+x12*x30+x13*x14+x13*x15+x13*x16+x13*x17+x13*x18+x13*x23+x13*x24+x13*x27+x14*x16+x14*x17+x14*x20+x14*x21+x14*x23+x14*x25+x14*x29+x14*x30+x15*x17+x15*x20+x15*x21+x15*x24+x15*x25+x15*x26+x15*x29+x16*x17+x16*x18+x16*x19+x16*x20+x16*x23+x16*x28+x16*x29+x16*x30+x17*x18+x17*x20+x17*x21+x17*x23+x17*x27+x18*x23+x18*x25+x18*x27+x18*x28+x18*x29+x19*x20+x19*x21+x19*x24+x19*x28+x20*x21+x20*x22+x20*x23+x20*x24+x20*x25+x20*x27+x20*x30+x21*x24+x21*x25+x21*x29+x22*x23+x22*x27+x22*x29+x22*x30+x23*x25+x23*x26+x23*x29+x23*x30+x24*x26+x24*x30+x25*x27+x25*x28+x25*x29+x25*x30+x26*x27+x26*x28+x26*x29+x26*x30+x28*x29+x28*x30+x29*x30");
359 polHFE_30_96.emplace_back(
"x1+x6+x9+x10+x12+x14+x16+x17+x18+x19+x21+x26+x27+x1*x7+x1*x8+x1*x20+x1*x22+x1*x24+x1*x26+x1*x27+x1*x28+x1*x30+x2*x3+x2*x5+x2*x7+x2*x8+x2*x11+x2*x15+x2*x16+x2*x17+x2*x18+x2*x19+x2*x20+x2*x21+x2*x24+x2*x25+x2*x27+x2*x28+x2*x30+x3*x6+x3*x7+x3*x8+x3*x12+x3*x13+x3*x14+x3*x15+x3*x16+x3*x18+x3*x20+x3*x21+x3*x22+x3*x25+x3*x26+x3*x28+x3*x29+x4*x7+x4*x8+x4*x10+x4*x13+x4*x16+x4*x18+x4*x20+x4*x21+x4*x22+x4*x23+x4*x25+x4*x27+x5*x7+x5*x9+x5*x12+x5*x14+x5*x18+x5*x19+x5*x20+x5*x23+x5*x28+x5*x30+x6*x7+x6*x10+x6*x12+x6*x17+x6*x21+x6*x22+x6*x24+x6*x25+x6*x26+x7*x8+x7*x10+x7*x12+x7*x14+x7*x18+x7*x20+x7*x22+x7*x23+x7*x24+x7*x26+x7*x29+x7*x30+x8*x12+x8*x14+x8*x16+x8*x17+x8*x18+x8*x19+x8*x21+x8*x22+x8*x23+x8*x24+x8*x26+x8*x27+x8*x28+x8*x29+x8*x30+x9*x14+x9*x15+x9*x16+x9*x22+x9*x25+x9*x27+x9*x29+x9*x30+x10*x11+x10*x12+x10*x13+x10*x17+x10*x21+x10*x23+x10*x24+x10*x26+x10*x27+x10*x28+x11*x12+x11*x14+x11*x15+x11*x17+x11*x21+x11*x22+x11*x23+x11*x25+x11*x26+x11*x28+x12*x14+x12*x18+x12*x20+x12*x21+x12*x22+x12*x23+x12*x27+x12*x28+x12*x29+x13*x15+x13*x16+x13*x17+x13*x20+x13*x23+x13*x25+x13*x27+x13*x28+x13*x30+x14*x15+x14*x16+x14*x17+x14*x18+x14*x20+x14*x22+x14*x24+x14*x30+x15*x17+x15*x19+x15*x21+x15*x22+x15*x23+x15*x24+x15*x25+x15*x26+x15*x27+x15*x28+x16*x19+x16*x20+x16*x21+x16*x24+x16*x26+x16*x27+x16*x29+x17*x18+x17*x21+x17*x23+x17*x25+x17*x30+x18*x20+x18*x21+x18*x25+x18*x26+x18*x29+x19*x21+x19*x24+x19*x25+x19*x26+x19*x28+x19*x30+x20*x22+x20*x24+x20*x27+x20*x28+x20*x29+x20*x30+x21*x22+x21*x27+x22*x23+x22*x24+x22*x25+x22*x28+x23*x26+x23*x27+x24*x26+x24*x27+x24*x28+x24*x29+x24*x30+x25*x26+x25*x28+x25*x30+x26*x27+x27*x28");
360 polHFE_30_96.emplace_back(
"1+x2+x4+x5+x6+x7+x8+x9+x13+x15+x16+x21+x23+x24+x25+x29+x30+x1*x2+x1*x3+x1*x4+x1*x6+x1*x9+x1*x10+x1*x11+x1*x12+x1*x16+x1*x18+x1*x21+x1*x22+x1*x24+x1*x25+x1*x26+x1*x29+x1*x30+x2*x3+x2*x4+x2*x5+x2*x6+x2*x7+x2*x8+x2*x10+x2*x11+x2*x12+x2*x14+x2*x15+x2*x18+x2*x22+x3*x6+x3*x7+x3*x8+x3*x12+x3*x13+x3*x14+x3*x15+x3*x18+x3*x21+x3*x22+x3*x23+x3*x24+x3*x25+x4*x8+x4*x9+x4*x10+x4*x11+x4*x12+x4*x14+x4*x16+x4*x18+x4*x19+x4*x24+x4*x25+x4*x30+x5*x8+x5*x10+x5*x11+x5*x12+x5*x15+x5*x18+x5*x20+x5*x22+x5*x23+x5*x25+x5*x26+x5*x27+x5*x28+x6*x9+x6*x10+x6*x11+x6*x12+x6*x14+x6*x15+x6*x17+x6*x19+x6*x20+x6*x23+x6*x24+x6*x25+x7*x8+x7*x9+x7*x10+x7*x17+x7*x19+x7*x21+x7*x25+x7*x27+x7*x30+x8*x9+x8*x15+x8*x16+x8*x17+x8*x19+x8*x27+x8*x28+x8*x30+x9*x12+x9*x14+x9*x15+x9*x17+x9*x18+x9*x19+x9*x24+x9*x26+x9*x27+x9*x28+x10*x11+x10*x12+x10*x13+x10*x15+x10*x16+x10*x18+x10*x19+x10*x21+x10*x22+x10*x25+x10*x27+x10*x28+x11*x13+x11*x14+x11*x15+x11*x16+x11*x17+x11*x18+x11*x19+x11*x20+x11*x25+x11*x26+x11*x27+x11*x30+x12*x13+x12*x23+x12*x24+x12*x25+x12*x29+x13*x17+x13*x19+x13*x24+x13*x25+x13*x26+x13*x27+x13*x29+x13*x30+x14*x18+x14*x19+x14*x21+x14*x24+x14*x27+x14*x29+x14*x30+x15*x16+x15*x18+x15*x20+x15*x21+x15*x24+x15*x25+x15*x26+x15*x28+x16*x17+x16*x18+x16*x22+x16*x24+x16*x25+x16*x27+x16*x28+x16*x29+x17*x19+x17*x21+x17*x24+x17*x27+x17*x28+x18*x20+x18*x26+x18*x28+x18*x30+x19*x22+x19*x23+x19*x26+x19*x30+x20*x22+x20*x23+x20*x24+x20*x25+x20*x27+x21*x22+x21*x30+x22*x24+x22*x26+x22*x28+x23*x24+x23*x29+x23*x30+x24*x26+x24*x27+x24*x29+x25*x26+x25*x27+x26*x27+x26*x28+x26*x30+x27*x28+x27*x30");
361 polHFE_30_96.emplace_back(
"1+x1+x4+x5+x6+x8+x9+x11+x12+x16+x20+x23+x24+x28+x29+x30+x1*x4+x1*x6+x1*x7+x1*x13+x1*x15+x1*x16+x1*x17+x1*x19+x1*x23+x1*x26+x1*x27+x1*x28+x1*x29+x1*x30+x2*x3+x2*x4+x2*x9+x2*x10+x2*x11+x2*x13+x2*x14+x2*x18+x2*x28+x2*x30+x3*x5+x3*x13+x3*x14+x3*x17+x3*x19+x3*x20+x3*x21+x3*x22+x3*x28+x3*x30+x4*x7+x4*x9+x4*x12+x4*x16+x4*x19+x4*x20+x4*x22+x4*x23+x4*x24+x4*x28+x4*x29+x4*x30+x5*x6+x5*x7+x5*x10+x5*x13+x5*x14+x5*x16+x5*x18+x5*x20+x5*x22+x5*x24+x5*x28+x5*x29+x5*x30+x6*x7+x6*x8+x6*x11+x6*x15+x6*x16+x6*x17+x6*x18+x6*x19+x6*x22+x6*x23+x6*x24+x6*x28+x6*x29+x7*x9+x7*x11+x7*x13+x7*x14+x7*x20+x7*x21+x7*x24+x7*x26+x7*x28+x7*x29+x7*x30+x8*x9+x8*x10+x8*x11+x8*x12+x8*x13+x8*x17+x8*x18+x8*x21+x8*x22+x8*x24+x8*x30+x9*x10+x9*x16+x9*x17+x9*x19+x9*x23+x9*x25+x9*x28+x9*x29+x9*x30+x10*x11+x10*x14+x10*x17+x10*x19+x10*x20+x10*x21+x10*x23+x10*x24+x10*x27+x10*x30+x11*x14+x11*x17+x11*x18+x11*x20+x11*x26+x11*x28+x11*x29+x11*x30+x12*x15+x12*x18+x12*x19+x12*x21+x12*x22+x12*x24+x12*x26+x12*x29+x13*x14+x13*x15+x13*x16+x13*x19+x13*x20+x13*x23+x13*x25+x13*x29+x14*x15+x14*x16+x14*x19+x14*x20+x14*x22+x14*x23+x14*x24+x14*x25+x14*x28+x14*x29+x15*x17+x15*x19+x15*x20+x15*x23+x15*x26+x15*x27+x15*x28+x15*x30+x16*x17+x16*x18+x16*x19+x16*x21+x16*x22+x16*x27+x17*x20+x17*x21+x17*x23+x17*x26+x17*x28+x17*x30+x18*x22+x18*x25+x18*x26+x18*x27+x18*x28+x18*x29+x18*x30+x19*x22+x19*x25+x19*x26+x19*x28+x19*x29+x19*x30+x20*x21+x20*x23+x20*x24+x20*x27+x20*x28+x20*x29+x20*x30+x21*x22+x21*x28+x21*x30+x22*x24+x22*x28+x22*x30+x23*x24+x23*x25+x23*x29+x24*x26+x25*x26+x25*x27+x25*x28+x25*x29+x26*x27+x26*x29+x27*x28");
362 polHFE_30_96.emplace_back(
"x2+x4+x6+x8+x12+x14+x15+x16+x17+x20+x21+x23+x25+x28+x30+x1*x2+x1*x3+x1*x4+x1*x5+x1*x8+x1*x10+x1*x11+x1*x17+x1*x19+x1*x21+x1*x22+x1*x23+x1*x24+x1*x27+x1*x28+x1*x29+x1*x30+x2*x6+x2*x7+x2*x8+x2*x11+x2*x12+x2*x13+x2*x14+x2*x16+x2*x22+x2*x23+x2*x24+x2*x25+x2*x30+x3*x4+x3*x5+x3*x6+x3*x7+x3*x8+x3*x9+x3*x10+x3*x12+x3*x13+x3*x14+x3*x15+x3*x16+x3*x17+x3*x18+x3*x19+x3*x20+x3*x21+x3*x22+x3*x24+x3*x26+x3*x28+x3*x29+x3*x30+x4*x6+x4*x9+x4*x10+x4*x11+x4*x20+x4*x23+x4*x24+x4*x26+x4*x27+x4*x29+x4*x30+x5*x9+x5*x10+x5*x11+x5*x12+x5*x15+x5*x17+x5*x19+x5*x20+x5*x21+x5*x22+x5*x24+x5*x27+x5*x28+x5*x30+x6*x8+x6*x9+x6*x12+x6*x13+x6*x15+x6*x17+x6*x18+x6*x19+x6*x21+x6*x22+x6*x26+x6*x29+x7*x11+x7*x16+x7*x17+x7*x19+x7*x20+x7*x22+x7*x23+x7*x25+x7*x27+x7*x28+x7*x29+x8*x9+x8*x10+x8*x12+x8*x15+x8*x16+x8*x21+x8*x23+x8*x24+x8*x28+x8*x30+x9*x10+x9*x11+x9*x12+x9*x13+x9*x16+x9*x19+x9*x22+x9*x23+x9*x24+x9*x27+x9*x28+x9*x30+x10*x11+x10*x12+x10*x13+x10*x14+x10*x17+x10*x20+x10*x25+x10*x28+x11*x13+x11*x14+x11*x15+x11*x17+x11*x20+x11*x22+x11*x23+x11*x24+x11*x25+x11*x26+x11*x27+x11*x29+x12*x13+x12*x14+x12*x15+x12*x16+x12*x18+x12*x28+x12*x29+x13*x14+x13*x15+x13*x16+x13*x17+x13*x18+x13*x19+x13*x22+x13*x24+x13*x29+x14*x15+x14*x16+x14*x17+x14*x18+x14*x19+x14*x20+x14*x24+x14*x25+x14*x29+x14*x30+x15*x16+x15*x17+x15*x19+x15*x20+x15*x21+x15*x22+x15*x24+x15*x30+x16*x18+x16*x19+x16*x20+x16*x22+x16*x24+x16*x26+x16*x27+x16*x28+x16*x29+x17*x21+x17*x23+x17*x25+x17*x27+x17*x28+x18*x22+x18*x25+x18*x26+x18*x28+x18*x29+x18*x30+x19*x20+x19*x23+x19*x25+x19*x27+x19*x28+x20*x21+x20*x22+x20*x23+x20*x24+x20*x25+x20*x26+x21*x22+x21*x25+x21*x26+x21*x27+x21*x28+x21*x30+x22*x24+x22*x25+x22*x26+x22*x27+x22*x28+x22*x29+x22*x30+x23*x24+x23*x28+x24*x25+x24*x26+x24*x27+x24*x29+x24*x30+x25*x29+x26*x27+x26*x28+x27*x28+x27*x30+x28*x30+x29*x30");
363 polHFE_30_96.emplace_back(
"1+x1+x3+x5+x6+x7+x10+x11+x20+x21+x22+x24+x25+x26+x27+x28+x1*x2+x1*x4+x1*x7+x1*x9+x1*x10+x1*x11+x1*x12+x1*x13+x1*x14+x1*x15+x1*x21+x1*x22+x1*x24+x1*x27+x1*x28+x2*x3+x2*x5+x2*x7+x2*x8+x2*x11+x2*x12+x2*x14+x2*x17+x2*x18+x2*x20+x2*x24+x2*x26+x2*x27+x2*x28+x2*x30+x3*x4+x3*x7+x3*x8+x3*x9+x3*x11+x3*x12+x3*x19+x3*x21+x3*x23+x3*x29+x4*x5+x4*x6+x4*x8+x4*x9+x4*x10+x4*x11+x4*x12+x4*x15+x4*x17+x4*x19+x4*x23+x4*x24+x4*x25+x4*x26+x4*x27+x4*x28+x4*x29+x5*x8+x5*x10+x5*x11+x5*x12+x5*x13+x5*x14+x5*x15+x5*x20+x5*x24+x5*x25+x5*x28+x5*x29+x5*x30+x6*x7+x6*x9+x6*x14+x6*x15+x6*x16+x6*x18+x6*x19+x6*x20+x6*x22+x6*x23+x6*x25+x6*x27+x6*x28+x6*x30+x7*x8+x7*x11+x7*x14+x7*x15+x7*x21+x7*x23+x7*x24+x7*x25+x7*x27+x7*x28+x7*x29+x7*x30+x8*x9+x8*x11+x8*x17+x8*x18+x8*x19+x8*x22+x8*x23+x8*x25+x8*x27+x9*x10+x9*x11+x9*x13+x9*x16+x9*x19+x9*x24+x9*x25+x9*x26+x9*x27+x9*x29+x10*x12+x10*x13+x10*x14+x10*x16+x10*x18+x10*x20+x10*x21+x10*x22+x10*x23+x10*x24+x10*x26+x10*x28+x10*x29+x10*x30+x11*x13+x11*x14+x11*x15+x11*x16+x11*x17+x11*x19+x11*x22+x11*x26+x11*x28+x11*x29+x11*x30+x12*x15+x12*x18+x12*x19+x12*x21+x12*x27+x12*x28+x12*x29+x13*x15+x13*x16+x13*x17+x13*x18+x13*x21+x13*x22+x13*x23+x13*x24+x13*x25+x13*x26+x13*x27+x13*x28+x13*x30+x14*x16+x14*x18+x14*x19+x14*x23+x14*x24+x14*x27+x14*x30+x15*x16+x15*x17+x15*x18+x15*x19+x15*x20+x15*x21+x15*x22+x15*x26+x15*x28+x15*x29+x15*x30+x16*x17+x16*x19+x16*x21+x16*x23+x16*x26+x16*x27+x16*x29+x17*x18+x17*x20+x17*x22+x17*x27+x18*x19+x18*x20+x18*x21+x18*x25+x18*x27+x18*x28+x19*x20+x19*x21+x19*x24+x19*x25+x19*x26+x19*x27+x19*x29+x20*x21+x20*x23+x20*x25+x20*x26+x20*x28+x20*x29+x20*x30+x21*x24+x21*x26+x21*x28+x21*x29+x22*x24+x22*x28+x22*x29+x22*x30+x23*x24+x23*x25+x23*x26+x23*x28+x23*x29+x23*x30+x24*x27+x24*x28+x24*x29+x25*x29+x25*x30+x26*x27+x26*x28+x26*x30+x27*x28+x27*x29+x27*x30+x28*x29+x28*x30");
364 polHFE_30_96.emplace_back(
"x3+x4+x6+x7+x9+x11+x13+x14+x15+x18+x19+x23+x26+x27+x28+x29+x30+x1*x2+x1*x4+x1*x8+x1*x10+x1*x11+x1*x13+x1*x15+x1*x19+x1*x20+x1*x24+x1*x25+x2*x3+x2*x4+x2*x6+x2*x9+x2*x11+x2*x12+x2*x13+x2*x14+x2*x17+x2*x18+x2*x19+x2*x20+x2*x25+x2*x28+x2*x29+x2*x30+x3*x5+x3*x8+x3*x9+x3*x11+x3*x12+x3*x13+x3*x14+x3*x16+x3*x17+x3*x20+x3*x21+x3*x22+x3*x23+x3*x24+x4*x7+x4*x8+x4*x9+x4*x11+x4*x15+x4*x16+x4*x18+x4*x22+x4*x25+x4*x27+x4*x28+x4*x29+x5*x9+x5*x11+x5*x12+x5*x14+x5*x16+x5*x18+x5*x19+x5*x20+x5*x21+x5*x25+x5*x27+x5*x28+x5*x29+x5*x30+x6*x11+x6*x12+x6*x15+x6*x16+x6*x18+x6*x21+x6*x27+x6*x28+x6*x29+x6*x30+x7*x8+x7*x9+x7*x11+x7*x12+x7*x13+x7*x15+x7*x16+x7*x18+x7*x20+x7*x27+x7*x28+x7*x29+x8*x9+x8*x10+x8*x14+x8*x17+x8*x20+x8*x22+x8*x23+x8*x25+x8*x28+x8*x29+x8*x30+x9*x14+x9*x15+x9*x19+x9*x20+x9*x21+x9*x23+x9*x24+x9*x25+x9*x26+x9*x27+x9*x28+x9*x29+x10*x11+x10*x13+x10*x14+x10*x17+x10*x20+x10*x23+x10*x24+x10*x27+x10*x28+x11*x12+x11*x13+x11*x14+x11*x16+x11*x17+x11*x19+x11*x20+x11*x21+x11*x22+x11*x23+x11*x25+x11*x26+x11*x28+x11*x30+x12*x13+x12*x19+x12*x26+x12*x27+x12*x28+x12*x29+x13*x14+x13*x16+x13*x18+x13*x20+x13*x21+x13*x22+x13*x26+x13*x27+x13*x28+x14*x19+x14*x21+x14*x23+x14*x24+x14*x25+x14*x27+x14*x28+x14*x29+x15*x20+x15*x21+x15*x22+x15*x23+x15*x25+x15*x27+x15*x28+x16*x20+x16*x25+x16*x26+x16*x29+x17*x20+x17*x21+x17*x22+x17*x27+x17*x30+x18*x20+x18*x24+x18*x25+x18*x26+x18*x29+x18*x30+x19*x22+x19*x25+x19*x26+x19*x27+x19*x28+x20*x26+x20*x29+x21*x22+x21*x23+x21*x28+x21*x30+x22*x24+x22*x27+x22*x28+x23*x25+x23*x26+x23*x29+x23*x30+x24*x25+x24*x26+x24*x27+x24*x28+x24*x30+x25*x26+x25*x27+x25*x28+x25*x30+x26*x27+x26*x28+x26*x30+x27*x29+x28*x30");
365 polHFE_30_96.emplace_back(
"1+x3+x5+x6+x11+x12+x13+x15+x16+x17+x21+x22+x23+x25+x27+x29+x30+x1*x3+x1*x5+x1*x10+x1*x11+x1*x12+x1*x13+x1*x14+x1*x15+x1*x17+x1*x19+x1*x20+x1*x21+x1*x22+x1*x25+x1*x28+x2*x6+x2*x12+x2*x14+x2*x17+x2*x18+x2*x20+x2*x23+x2*x25+x2*x26+x2*x27+x2*x28+x2*x29+x2*x30+x3*x4+x3*x6+x3*x8+x3*x9+x3*x10+x3*x11+x3*x13+x3*x16+x3*x19+x3*x20+x3*x21+x3*x22+x3*x23+x3*x28+x3*x29+x3*x30+x4*x6+x4*x7+x4*x8+x4*x9+x4*x13+x4*x15+x4*x20+x4*x25+x4*x26+x4*x29+x4*x30+x5*x7+x5*x8+x5*x11+x5*x12+x5*x14+x5*x16+x5*x18+x5*x19+x5*x23+x5*x24+x5*x25+x5*x28+x5*x29+x5*x30+x6*x7+x6*x8+x6*x15+x6*x16+x6*x20+x6*x22+x6*x24+x6*x25+x6*x26+x6*x28+x6*x29+x7*x8+x7*x12+x7*x13+x7*x14+x7*x15+x7*x16+x7*x17+x7*x19+x7*x20+x7*x21+x7*x22+x7*x24+x7*x25+x7*x29+x8*x9+x8*x11+x8*x12+x8*x17+x8*x18+x8*x21+x8*x22+x8*x25+x8*x26+x8*x27+x8*x28+x8*x29+x9*x10+x9*x12+x9*x13+x9*x17+x9*x19+x9*x20+x9*x22+x9*x24+x9*x26+x9*x28+x9*x30+x10*x13+x10*x14+x10*x16+x10*x18+x10*x19+x10*x20+x10*x22+x10*x24+x10*x25+x10*x29+x10*x30+x11*x12+x11*x14+x11*x15+x11*x18+x11*x20+x11*x27+x11*x28+x11*x29+x11*x30+x12*x14+x12*x15+x12*x17+x12*x18+x12*x20+x12*x22+x12*x25+x12*x28+x12*x29+x12*x30+x13*x14+x13*x15+x13*x17+x13*x18+x13*x21+x13*x22+x13*x23+x13*x25+x13*x26+x13*x27+x13*x28+x13*x29+x14*x15+x14*x20+x14*x21+x14*x26+x14*x28+x14*x30+x15*x17+x15*x18+x15*x19+x15*x20+x15*x26+x15*x27+x15*x28+x15*x30+x16*x22+x16*x23+x16*x25+x16*x26+x16*x28+x16*x29+x16*x30+x17*x18+x17*x20+x17*x23+x17*x25+x17*x27+x17*x28+x18*x20+x18*x22+x18*x26+x18*x28+x18*x30+x19*x22+x19*x23+x19*x24+x19*x29+x20*x21+x20*x23+x20*x24+x20*x25+x20*x27+x20*x28+x20*x29+x20*x30+x21*x24+x21*x25+x21*x29+x22*x24+x22*x25+x22*x26+x22*x27+x22*x28+x23*x25+x23*x26+x23*x27+x24*x26+x24*x27+x24*x28+x24*x30+x25*x26+x25*x28+x25*x30+x26*x27+x26*x29+x26*x30");
366 polHFE_30_96.emplace_back(
"x1+x2+x4+x5+x6+x9+x10+x11+x12+x13+x14+x20+x24+x25+x26+x27+x1*x3+x1*x4+x1*x5+x1*x7+x1*x8+x1*x10+x1*x15+x1*x20+x1*x21+x1*x22+x1*x25+x1*x26+x1*x27+x1*x28+x1*x30+x2*x3+x2*x4+x2*x5+x2*x6+x2*x8+x2*x9+x2*x12+x2*x16+x2*x18+x2*x19+x2*x20+x2*x21+x2*x22+x2*x24+x2*x25+x2*x26+x2*x27+x2*x30+x3*x5+x3*x7+x3*x8+x3*x9+x3*x12+x3*x15+x3*x16+x3*x18+x3*x20+x3*x25+x3*x27+x3*x28+x3*x29+x4*x8+x4*x9+x4*x11+x4*x12+x4*x13+x4*x14+x4*x15+x4*x17+x4*x19+x4*x20+x4*x23+x4*x25+x4*x28+x4*x29+x5*x7+x5*x8+x5*x11+x5*x12+x5*x13+x5*x14+x5*x15+x5*x16+x5*x17+x5*x20+x5*x21+x5*x24+x5*x26+x5*x27+x5*x28+x5*x29+x5*x30+x6*x9+x6*x10+x6*x12+x6*x13+x6*x19+x6*x20+x6*x21+x6*x22+x6*x24+x6*x26+x6*x27+x7*x8+x7*x10+x7*x11+x7*x14+x7*x15+x7*x16+x7*x17+x7*x20+x7*x21+x7*x26+x7*x28+x7*x29+x8*x11+x8*x14+x8*x16+x8*x17+x8*x19+x8*x20+x8*x22+x8*x24+x8*x25+x8*x27+x8*x28+x8*x29+x8*x30+x9*x10+x9*x11+x9*x12+x9*x13+x9*x14+x9*x15+x9*x17+x9*x19+x9*x20+x9*x23+x9*x25+x9*x26+x9*x27+x9*x28+x9*x29+x9*x30+x10*x11+x10*x12+x10*x15+x10*x17+x10*x18+x10*x21+x10*x22+x10*x23+x10*x24+x10*x25+x10*x30+x11*x15+x11*x16+x11*x18+x11*x20+x11*x21+x11*x22+x11*x23+x11*x25+x11*x27+x11*x28+x11*x30+x12*x14+x12*x15+x12*x16+x12*x18+x12*x20+x12*x22+x12*x24+x12*x25+x12*x27+x13*x14+x13*x16+x13*x18+x13*x24+x13*x25+x13*x26+x13*x27+x13*x28+x13*x29+x14*x15+x14*x16+x14*x18+x14*x23+x14*x24+x14*x25+x15*x16+x15*x18+x15*x21+x15*x23+x15*x28+x15*x30+x16*x18+x16*x19+x16*x20+x16*x21+x16*x22+x16*x27+x16*x29+x17*x19+x17*x23+x17*x25+x18*x19+x18*x26+x19*x20+x19*x21+x19*x23+x19*x26+x19*x28+x19*x29+x20*x21+x20*x24+x21*x22+x21*x24+x21*x25+x21*x26+x21*x27+x21*x28+x21*x29+x22*x23+x22*x26+x22*x27+x22*x29+x22*x30+x23*x27+x23*x28+x23*x30+x24*x26+x24*x28+x24*x30+x25*x27+x25*x28+x25*x30+x26*x27+x26*x29+x27*x28+x28*x29+x29*x30");
367 polHFE_30_96.emplace_back(
"1+x2+x3+x6+x7+x8+x9+x12+x14+x15+x17+x19+x20+x24+x27+x29+x1*x4+x1*x6+x1*x10+x1*x12+x1*x15+x1*x16+x1*x18+x1*x22+x1*x27+x1*x29+x2*x3+x2*x6+x2*x7+x2*x10+x2*x11+x2*x13+x2*x15+x2*x20+x2*x26+x2*x28+x2*x30+x3*x8+x3*x11+x3*x16+x3*x18+x3*x19+x3*x23+x3*x25+x3*x26+x3*x30+x4*x5+x4*x7+x4*x10+x4*x12+x4*x13+x4*x14+x4*x17+x4*x18+x4*x23+x4*x24+x4*x25+x4*x26+x4*x27+x4*x28+x4*x29+x5*x7+x5*x9+x5*x10+x5*x11+x5*x12+x5*x14+x5*x16+x5*x18+x5*x19+x5*x20+x5*x24+x5*x28+x5*x30+x6*x8+x6*x9+x6*x10+x6*x11+x6*x12+x6*x13+x6*x14+x6*x15+x6*x16+x6*x19+x6*x20+x6*x21+x6*x23+x6*x26+x6*x30+x7*x10+x7*x12+x7*x16+x7*x18+x7*x20+x7*x25+x7*x26+x7*x27+x7*x29+x8*x9+x8*x10+x8*x11+x8*x12+x8*x16+x8*x19+x8*x21+x8*x22+x8*x23+x8*x24+x8*x25+x8*x27+x8*x28+x8*x29+x9*x10+x9*x12+x9*x13+x9*x17+x9*x19+x9*x22+x9*x24+x9*x26+x9*x28+x9*x29+x10*x12+x10*x15+x10*x17+x10*x18+x10*x19+x10*x21+x10*x23+x10*x24+x10*x25+x10*x26+x10*x28+x10*x29+x11*x12+x11*x13+x11*x15+x11*x17+x11*x18+x11*x20+x11*x21+x11*x22+x11*x23+x11*x25+x11*x27+x11*x29+x12*x15+x12*x17+x12*x18+x12*x20+x12*x21+x12*x24+x12*x30+x13*x16+x13*x18+x13*x20+x13*x23+x13*x30+x14*x16+x14*x18+x14*x19+x14*x26+x14*x27+x14*x28+x14*x30+x15*x17+x15*x19+x15*x22+x15*x24+x15*x25+x15*x28+x16*x17+x16*x19+x16*x23+x16*x24+x16*x25+x16*x27+x16*x29+x17*x18+x17*x20+x17*x22+x17*x23+x17*x26+x17*x27+x17*x28+x17*x30+x18*x19+x18*x20+x18*x22+x18*x23+x18*x24+x18*x27+x18*x28+x18*x30+x19*x20+x19*x22+x19*x23+x19*x25+x19*x26+x19*x29+x19*x30+x20*x21+x20*x23+x20*x26+x20*x27+x20*x30+x21*x24+x21*x25+x21*x27+x21*x28+x21*x30+x22*x23+x22*x27+x22*x28+x22*x29+x23*x24+x23*x25+x23*x26+x23*x27+x23*x29+x23*x30+x24*x25+x24*x27+x24*x29+x24*x30+x25*x26+x25*x27+x25*x29+x26*x27+x26*x28+x26*x29+x27*x30+x28*x30");
368 polHFE_30_96.emplace_back(
"1+x1+x3+x4+x6+x9+x10+x11+x15+x16+x20+x21+x22+x25+x28+x29+x1*x2+x1*x6+x1*x7+x1*x8+x1*x11+x1*x12+x1*x15+x1*x20+x1*x22+x1*x23+x1*x26+x1*x27+x1*x28+x1*x29+x1*x30+x2*x3+x2*x4+x2*x6+x2*x9+x2*x11+x2*x12+x2*x14+x2*x20+x2*x21+x2*x22+x2*x24+x2*x25+x2*x26+x2*x29+x3*x4+x3*x5+x3*x7+x3*x11+x3*x14+x3*x16+x3*x18+x3*x20+x3*x23+x3*x25+x3*x28+x3*x30+x4*x5+x4*x7+x4*x8+x4*x9+x4*x16+x4*x17+x4*x19+x4*x20+x4*x21+x4*x23+x4*x28+x4*x29+x4*x30+x5*x6+x5*x7+x5*x8+x5*x10+x5*x11+x5*x12+x5*x14+x5*x16+x5*x17+x5*x18+x5*x19+x5*x23+x5*x29+x6*x8+x6*x10+x6*x15+x6*x18+x6*x19+x6*x21+x6*x24+x6*x26+x6*x27+x6*x29+x6*x30+x7*x10+x7*x11+x7*x13+x7*x14+x7*x15+x7*x17+x7*x20+x7*x21+x7*x25+x7*x27+x7*x28+x8*x11+x8*x12+x8*x13+x8*x15+x8*x24+x8*x26+x8*x29+x8*x30+x9*x11+x9*x13+x9*x16+x9*x17+x9*x18+x9*x20+x9*x24+x9*x26+x9*x27+x9*x28+x10*x12+x10*x15+x10*x17+x10*x20+x10*x21+x10*x22+x10*x23+x10*x25+x10*x28+x11*x12+x11*x13+x11*x14+x11*x22+x11*x25+x11*x26+x11*x27+x11*x28+x11*x29+x11*x30+x12*x13+x12*x15+x12*x17+x12*x20+x12*x21+x12*x22+x12*x23+x12*x25+x12*x27+x12*x28+x12*x29+x12*x30+x13*x14+x13*x15+x13*x17+x13*x20+x13*x22+x13*x24+x13*x25+x13*x26+x13*x27+x13*x28+x13*x29+x14*x16+x14*x18+x14*x19+x14*x20+x14*x21+x14*x22+x14*x24+x14*x26+x15*x17+x15*x19+x15*x21+x15*x22+x15*x26+x15*x29+x15*x30+x16*x20+x16*x22+x16*x23+x16*x24+x16*x26+x17*x19+x17*x20+x17*x21+x17*x23+x17*x24+x17*x26+x17*x29+x18*x22+x18*x23+x18*x26+x18*x27+x18*x28+x18*x30+x19*x20+x19*x21+x19*x22+x19*x23+x19*x24+x19*x26+x19*x28+x19*x29+x19*x30+x20*x21+x20*x26+x20*x28+x20*x29+x21*x22+x21*x24+x21*x29+x22*x23+x22*x26+x22*x29+x22*x30+x23*x27+x23*x28+x23*x29+x23*x30+x24*x26+x24*x27+x24*x28+x25*x27+x25*x29+x26*x30+x27*x28+x27*x29+x27*x30+x28*x30+x29*x30");
369 polHFE_30_96.emplace_back(
"1+x2+x4+x7+x9+x10+x11+x12+x15+x18+x22+x23+x25+x26+x1*x4+x1*x5+x1*x9+x1*x10+x1*x11+x1*x14+x1*x15+x1*x17+x1*x19+x1*x22+x1*x23+x1*x25+x1*x26+x1*x27+x1*x29+x1*x30+x2*x3+x2*x4+x2*x9+x2*x10+x2*x12+x2*x14+x2*x15+x2*x19+x2*x20+x2*x21+x2*x22+x2*x23+x2*x24+x2*x27+x2*x30+x3*x6+x3*x7+x3*x8+x3*x9+x3*x10+x3*x11+x3*x13+x3*x15+x3*x16+x3*x17+x3*x23+x3*x26+x3*x27+x3*x29+x3*x30+x4*x5+x4*x6+x4*x7+x4*x8+x4*x10+x4*x11+x4*x15+x4*x16+x4*x17+x4*x19+x4*x20+x4*x24+x4*x26+x4*x27+x4*x28+x4*x29+x5*x8+x5*x10+x5*x11+x5*x12+x5*x14+x5*x16+x5*x17+x5*x18+x5*x23+x5*x24+x5*x25+x5*x26+x5*x28+x5*x29+x6*x7+x6*x12+x6*x13+x6*x15+x6*x18+x6*x20+x6*x21+x6*x22+x6*x24+x6*x25+x6*x27+x7*x8+x7*x12+x7*x16+x7*x17+x7*x21+x7*x23+x7*x24+x7*x25+x7*x26+x8*x10+x8*x15+x8*x18+x8*x22+x8*x23+x8*x25+x8*x30+x9*x11+x9*x12+x9*x14+x9*x17+x9*x18+x9*x20+x9*x22+x9*x23+x9*x24+x9*x25+x9*x26+x9*x27+x9*x29+x10*x13+x10*x19+x10*x21+x10*x25+x10*x26+x10*x27+x10*x28+x10*x30+x11*x12+x11*x14+x11*x18+x11*x22+x11*x26+x11*x27+x11*x28+x11*x29+x11*x30+x12*x14+x12*x18+x12*x19+x12*x20+x12*x22+x12*x23+x12*x24+x12*x29+x13*x14+x13*x16+x13*x18+x13*x19+x13*x23+x13*x24+x13*x25+x13*x30+x14*x15+x14*x17+x14*x19+x14*x21+x14*x22+x14*x23+x14*x28+x15*x17+x15*x18+x15*x19+x15*x20+x15*x24+x15*x26+x15*x29+x15*x30+x16*x21+x16*x22+x16*x23+x16*x27+x16*x28+x16*x30+x17*x19+x17*x20+x17*x23+x17*x24+x17*x25+x17*x26+x17*x29+x18*x23+x18*x24+x18*x26+x18*x29+x18*x30+x19*x20+x19*x23+x19*x24+x19*x29+x20*x24+x20*x25+x21*x22+x21*x24+x21*x26+x21*x28+x21*x29+x21*x30+x22*x23+x22*x24+x22*x25+x22*x29+x23*x24+x23*x25+x23*x26+x23*x27+x23*x29+x24*x26+x24*x27+x24*x29+x25*x26+x25*x30+x26*x27+x27*x28+x27*x29+x27*x30+x28*x29+x28*x30");
370 polHFE_30_96.emplace_back(
"1+x6+x7+x9+x10+x12+x13+x14+x16+x17+x18+x23+x28+x1*x2+x1*x3+x1*x8+x1*x9+x1*x10+x1*x12+x1*x13+x1*x15+x1*x16+x1*x21+x1*x22+x1*x23+x1*x25+x1*x26+x1*x28+x1*x29+x1*x30+x2*x3+x2*x5+x2*x7+x2*x9+x2*x11+x2*x12+x2*x14+x2*x15+x2*x16+x2*x17+x2*x20+x2*x23+x2*x25+x2*x26+x2*x28+x3*x5+x3*x6+x3*x7+x3*x9+x3*x10+x3*x11+x3*x12+x3*x15+x3*x16+x3*x17+x3*x18+x3*x19+x3*x22+x3*x23+x3*x25+x3*x28+x4*x5+x4*x7+x4*x8+x4*x9+x4*x14+x4*x15+x4*x17+x4*x22+x4*x23+x4*x27+x4*x28+x5*x6+x5*x7+x5*x8+x5*x9+x5*x12+x5*x13+x5*x14+x5*x18+x5*x19+x5*x20+x5*x21+x5*x22+x5*x23+x5*x28+x6*x7+x6*x11+x6*x12+x6*x14+x6*x15+x6*x17+x6*x19+x6*x21+x6*x22+x6*x23+x6*x24+x6*x25+x6*x27+x6*x28+x6*x29+x6*x30+x7*x9+x7*x11+x7*x12+x7*x13+x7*x15+x7*x17+x7*x18+x7*x20+x7*x21+x7*x22+x7*x23+x7*x27+x7*x28+x8*x9+x8*x11+x8*x12+x8*x16+x8*x17+x8*x21+x8*x22+x8*x23+x8*x24+x8*x25+x8*x26+x8*x29+x9*x10+x9*x11+x9*x13+x9*x16+x9*x21+x9*x22+x9*x23+x9*x26+x9*x30+x10*x12+x10*x15+x10*x17+x10*x20+x10*x25+x10*x27+x10*x29+x11*x12+x11*x16+x11*x18+x11*x22+x11*x24+x11*x25+x11*x27+x11*x28+x12*x15+x12*x16+x12*x21+x12*x22+x12*x25+x12*x26+x12*x28+x13*x14+x13*x15+x13*x16+x13*x17+x13*x25+x13*x26+x13*x27+x13*x30+x14*x22+x14*x23+x14*x24+x14*x27+x14*x28+x14*x30+x15*x16+x15*x18+x15*x20+x15*x21+x15*x22+x15*x24+x15*x25+x15*x27+x15*x28+x16*x17+x16*x18+x16*x19+x16*x20+x16*x21+x16*x23+x16*x24+x16*x26+x16*x30+x17*x18+x17*x20+x17*x21+x17*x23+x17*x25+x17*x26+x17*x28+x17*x30+x18*x19+x18*x20+x18*x24+x18*x25+x18*x27+x18*x28+x18*x29+x19*x20+x19*x21+x19*x23+x19*x24+x19*x26+x19*x27+x19*x28+x20*x22+x20*x23+x20*x24+x20*x28+x20*x30+x21*x23+x21*x28+x21*x30+x22*x23+x22*x24+x22*x25+x22*x27+x22*x28+x23*x24+x23*x26+x23*x28+x24*x25+x24*x26+x24*x30+x25*x27+x25*x29+x25*x30+x26*x28+x27*x30+x28*x29+x28*x30+x29*x30");
371 polHFE_30_96.emplace_back(
"1+x2+x6+x8+x9+x14+x22+x23+x25+x28+x29+x1*x2+x1*x3+x1*x4+x1*x5+x1*x6+x1*x8+x1*x9+x1*x11+x1*x12+x1*x15+x1*x18+x1*x19+x1*x26+x1*x30+x2*x4+x2*x9+x2*x10+x2*x14+x2*x17+x2*x18+x2*x19+x2*x22+x2*x24+x2*x25+x2*x26+x2*x27+x2*x28+x2*x29+x3*x5+x3*x6+x3*x7+x3*x9+x3*x13+x3*x15+x3*x16+x3*x17+x3*x19+x3*x20+x3*x21+x3*x22+x3*x23+x3*x27+x4*x5+x4*x6+x4*x16+x4*x18+x4*x19+x4*x20+x4*x21+x4*x23+x4*x26+x4*x27+x4*x29+x5*x6+x5*x7+x5*x9+x5*x10+x5*x17+x5*x18+x5*x22+x5*x27+x5*x29+x6*x7+x6*x9+x6*x13+x6*x14+x6*x18+x6*x20+x6*x27+x6*x28+x6*x30+x7*x11+x7*x13+x7*x14+x7*x15+x7*x21+x7*x22+x7*x23+x7*x24+x7*x26+x7*x27+x8*x9+x8*x10+x8*x11+x8*x12+x8*x13+x8*x15+x8*x16+x8*x19+x8*x21+x8*x26+x8*x27+x8*x29+x9*x10+x9*x11+x9*x12+x9*x15+x9*x16+x9*x17+x9*x24+x9*x26+x9*x27+x9*x28+x9*x29+x10*x11+x10*x12+x10*x15+x10*x20+x10*x21+x11*x12+x11*x14+x11*x15+x11*x17+x11*x24+x11*x26+x11*x27+x11*x28+x11*x29+x12*x14+x12*x18+x12*x19+x12*x20+x12*x24+x12*x25+x12*x26+x12*x27+x12*x28+x13*x18+x13*x20+x13*x22+x13*x23+x13*x26+x13*x27+x13*x29+x14*x17+x14*x18+x14*x23+x14*x25+x14*x26+x14*x28+x15*x16+x15*x17+x15*x21+x15*x23+x15*x24+x15*x26+x15*x28+x15*x30+x16*x19+x16*x20+x16*x21+x16*x25+x16*x26+x16*x30+x17*x23+x17*x25+x17*x26+x17*x27+x17*x28+x17*x29+x18*x19+x18*x25+x18*x27+x19*x20+x19*x21+x19*x22+x19*x25+x19*x26+x19*x28+x19*x29+x20*x22+x20*x23+x20*x25+x20*x30+x21*x25+x21*x26+x21*x27+x22*x24+x22*x25+x22*x27+x22*x28+x23*x28+x23*x29+x24*x28+x24*x29+x24*x30+x25*x28+x26*x29+x27*x29+x28*x30+x29*x30");
372 polHFE_30_96.emplace_back(
"x1+x5+x6+x9+x10+x13+x14+x15+x16+x17+x18+x19+x20+x28+x29+x30+x1*x2+x1*x3+x1*x5+x1*x7+x1*x9+x1*x10+x1*x15+x1*x16+x1*x18+x1*x20+x1*x24+x1*x25+x1*x27+x1*x28+x1*x29+x2*x3+x2*x7+x2*x8+x2*x10+x2*x11+x2*x12+x2*x14+x2*x15+x2*x17+x2*x18+x2*x21+x2*x22+x2*x24+x2*x26+x2*x27+x2*x28+x2*x29+x2*x30+x3*x4+x3*x7+x3*x9+x3*x11+x3*x15+x3*x16+x3*x17+x3*x19+x3*x21+x3*x22+x3*x23+x3*x25+x4*x5+x4*x7+x4*x8+x4*x9+x4*x10+x4*x11+x4*x18+x4*x19+x4*x20+x4*x23+x4*x24+x4*x26+x4*x28+x5*x9+x5*x11+x5*x13+x5*x14+x5*x16+x5*x19+x5*x20+x5*x23+x5*x24+x5*x25+x5*x26+x5*x28+x5*x29+x5*x30+x6*x8+x6*x10+x6*x11+x6*x12+x6*x13+x6*x16+x6*x17+x6*x20+x6*x22+x6*x23+x6*x27+x6*x28+x6*x30+x7*x12+x7*x14+x7*x15+x7*x17+x7*x19+x7*x22+x7*x23+x7*x25+x7*x26+x7*x28+x7*x30+x8*x9+x8*x10+x8*x11+x8*x12+x8*x13+x8*x17+x8*x20+x8*x22+x8*x27+x8*x28+x8*x29+x8*x30+x9*x11+x9*x16+x9*x18+x9*x19+x9*x23+x9*x25+x9*x26+x9*x28+x9*x30+x10*x11+x10*x12+x10*x13+x10*x14+x10*x15+x10*x18+x10*x23+x10*x26+x10*x27+x10*x29+x11*x13+x11*x15+x11*x16+x11*x18+x11*x19+x11*x25+x11*x27+x12*x13+x12*x15+x12*x17+x12*x18+x12*x20+x12*x21+x12*x25+x12*x27+x13*x14+x13*x15+x13*x20+x13*x21+x13*x22+x13*x25+x13*x26+x13*x29+x14*x15+x14*x17+x14*x19+x14*x20+x14*x21+x14*x22+x14*x27+x14*x29+x15*x17+x15*x20+x15*x21+x15*x23+x15*x24+x15*x25+x15*x28+x15*x29+x15*x30+x16*x18+x16*x20+x16*x22+x16*x23+x16*x24+x16*x26+x16*x27+x16*x28+x16*x29+x16*x30+x17*x21+x17*x24+x17*x25+x17*x26+x17*x27+x17*x28+x18*x19+x18*x20+x18*x21+x18*x22+x18*x23+x18*x24+x18*x27+x18*x30+x19*x20+x19*x22+x19*x24+x19*x25+x19*x26+x19*x28+x20*x21+x20*x26+x20*x27+x20*x28+x20*x30+x21*x25+x21*x27+x21*x28+x21*x30+x22*x26+x22*x28+x23*x24+x23*x27+x23*x28+x24*x25+x24*x26+x24*x30+x25*x27+x25*x30+x26*x27+x26*x28+x26*x29+x26*x30+x27*x28+x27*x29+x28*x30");
373 polHFE_30_96.emplace_back(
"x2+x3+x9+x10+x11+x15+x17+x18+x19+x21+x22+x24+x25+x28+x1*x7+x1*x10+x1*x13+x1*x16+x1*x17+x1*x20+x1*x21+x1*x23+x1*x24+x1*x25+x1*x28+x1*x29+x1*x30+x2*x4+x2*x5+x2*x6+x2*x7+x2*x9+x2*x10+x2*x11+x2*x12+x2*x13+x2*x14+x2*x17+x2*x18+x2*x21+x2*x22+x2*x26+x2*x27+x2*x28+x3*x5+x3*x6+x3*x8+x3*x9+x3*x12+x3*x13+x3*x15+x3*x16+x3*x17+x3*x18+x3*x20+x3*x21+x3*x22+x3*x23+x3*x25+x3*x26+x3*x28+x3*x29+x3*x30+x4*x7+x4*x11+x4*x14+x4*x17+x4*x19+x4*x20+x4*x21+x4*x25+x4*x26+x4*x28+x4*x29+x5*x6+x5*x7+x5*x9+x5*x12+x5*x13+x5*x14+x5*x17+x5*x18+x5*x19+x5*x21+x5*x22+x5*x23+x5*x24+x5*x26+x5*x27+x5*x29+x6*x11+x6*x12+x6*x15+x6*x17+x6*x18+x6*x20+x6*x24+x6*x26+x6*x27+x6*x30+x7*x8+x7*x10+x7*x12+x7*x15+x7*x16+x7*x17+x7*x20+x7*x21+x7*x23+x7*x24+x7*x25+x7*x28+x7*x30+x8*x10+x8*x14+x8*x15+x8*x18+x8*x24+x8*x26+x9*x11+x9*x12+x9*x13+x9*x14+x9*x16+x9*x19+x9*x21+x9*x22+x9*x24+x9*x26+x9*x29+x10*x11+x10*x12+x10*x13+x10*x17+x10*x20+x10*x23+x10*x24+x10*x25+x10*x26+x11*x12+x11*x14+x11*x15+x11*x17+x11*x18+x11*x19+x11*x21+x11*x23+x11*x24+x11*x26+x11*x27+x11*x30+x12*x14+x12*x15+x12*x17+x12*x20+x12*x21+x12*x22+x12*x25+x12*x28+x12*x29+x13*x17+x13*x18+x13*x21+x13*x24+x13*x27+x13*x28+x13*x29+x13*x30+x14*x17+x14*x20+x14*x24+x14*x25+x14*x26+x15*x20+x15*x21+x15*x22+x15*x25+x15*x27+x15*x29+x15*x30+x16*x18+x16*x19+x16*x20+x16*x26+x16*x27+x16*x29+x17*x20+x17*x26+x17*x27+x17*x29+x18*x20+x18*x25+x18*x26+x18*x27+x18*x30+x19*x20+x19*x24+x19*x25+x19*x29+x20*x25+x20*x27+x20*x28+x21*x23+x21*x24+x21*x29+x21*x30+x22*x24+x22*x27+x22*x29+x23*x24+x23*x25+x23*x29+x24*x25+x24*x26+x24*x29+x24*x30+x25*x26+x25*x27+x25*x28+x25*x29+x25*x30+x26*x28+x27*x28+x27*x30+x28*x29+x28*x30");
374 polHFE_30_96.emplace_back(
"1+x1+x3+x7+x11+x12+x14+x15+x17+x21+x25+x27+x28+x30+x1*x3+x1*x7+x1*x12+x1*x16+x1*x18+x1*x19+x1*x20+x1*x22+x1*x24+x1*x25+x1*x26+x1*x27+x1*x30+x2*x3+x2*x6+x2*x7+x2*x8+x2*x9+x2*x10+x2*x11+x2*x13+x2*x14+x2*x16+x2*x19+x2*x20+x2*x22+x2*x25+x2*x26+x2*x27+x3*x6+x3*x9+x3*x12+x3*x14+x3*x19+x3*x22+x3*x24+x3*x25+x3*x27+x4*x7+x4*x10+x4*x13+x4*x16+x4*x18+x4*x20+x4*x23+x4*x26+x4*x27+x4*x28+x4*x30+x5*x8+x5*x10+x5*x13+x5*x14+x5*x18+x5*x19+x5*x20+x5*x22+x5*x26+x5*x28+x5*x29+x5*x30+x6*x11+x6*x12+x6*x13+x6*x15+x6*x17+x6*x19+x6*x21+x6*x23+x6*x25+x6*x27+x6*x30+x7*x8+x7*x9+x7*x10+x7*x14+x7*x15+x7*x16+x7*x20+x7*x21+x7*x22+x7*x25+x7*x28+x7*x29+x8*x11+x8*x12+x8*x13+x8*x14+x8*x15+x8*x16+x8*x18+x8*x19+x8*x20+x8*x23+x8*x25+x8*x29+x9*x10+x9*x14+x9*x15+x9*x17+x9*x18+x9*x19+x9*x21+x9*x22+x9*x23+x9*x24+x9*x25+x9*x27+x9*x28+x9*x30+x10*x13+x10*x15+x10*x17+x10*x18+x10*x19+x10*x20+x10*x21+x10*x23+x10*x25+x10*x28+x10*x29+x10*x30+x11*x13+x11*x14+x11*x19+x11*x20+x11*x22+x11*x25+x12*x15+x12*x17+x12*x18+x12*x19+x12*x22+x12*x24+x12*x29+x13*x14+x13*x15+x13*x18+x13*x19+x13*x20+x13*x23+x13*x24+x13*x26+x13*x27+x13*x28+x13*x29+x14*x16+x14*x17+x14*x19+x14*x22+x14*x23+x14*x29+x15*x16+x15*x17+x15*x19+x15*x20+x15*x21+x15*x22+x15*x23+x15*x26+x15*x27+x15*x28+x15*x30+x16*x19+x16*x23+x16*x24+x16*x25+x16*x27+x16*x29+x17*x19+x17*x20+x17*x21+x17*x22+x17*x23+x17*x24+x17*x25+x17*x27+x17*x30+x18*x19+x18*x21+x18*x24+x18*x25+x18*x27+x19*x23+x19*x25+x19*x26+x19*x29+x20*x21+x20*x26+x20*x30+x21*x23+x21*x24+x21*x25+x21*x26+x21*x27+x21*x28+x22*x23+x22*x24+x23*x25+x24*x25+x24*x29+x24*x30+x25*x27+x25*x30+x26*x27+x26*x29+x27*x28+x27*x30+x28*x29+x28*x30");
375 polHFE_30_96.emplace_back(
"x1+x2+x3+x4+x5+x6+x8+x10+x11+x12+x13+x14+x15+x20+x22+x24+x25+x29+x1*x3+x1*x4+x1*x7+x1*x8+x1*x11+x1*x12+x1*x13+x1*x14+x1*x16+x1*x17+x1*x18+x1*x20+x1*x24+x1*x25+x1*x26+x1*x27+x1*x28+x1*x29+x1*x30+x2*x4+x2*x8+x2*x9+x2*x11+x2*x13+x2*x18+x2*x20+x2*x23+x2*x25+x2*x27+x2*x28+x3*x7+x3*x8+x3*x12+x3*x14+x3*x15+x3*x16+x3*x17+x3*x18+x3*x19+x3*x21+x3*x22+x3*x23+x3*x25+x3*x26+x3*x27+x3*x28+x3*x29+x3*x30+x4*x7+x4*x10+x4*x11+x4*x14+x4*x15+x4*x16+x4*x18+x4*x20+x4*x21+x4*x22+x4*x25+x4*x28+x5*x6+x5*x7+x5*x8+x5*x10+x5*x11+x5*x19+x5*x20+x5*x21+x5*x22+x5*x25+x5*x26+x5*x27+x5*x28+x5*x29+x6*x8+x6*x9+x6*x11+x6*x12+x6*x14+x6*x15+x6*x17+x6*x18+x6*x28+x7*x8+x7*x13+x7*x14+x7*x16+x7*x19+x7*x24+x7*x26+x7*x27+x7*x29+x8*x12+x8*x13+x8*x14+x8*x15+x8*x16+x8*x17+x8*x18+x8*x19+x8*x21+x8*x22+x8*x25+x8*x27+x8*x30+x9*x10+x9*x13+x9*x20+x9*x23+x9*x24+x9*x26+x10*x12+x10*x13+x10*x15+x10*x17+x10*x19+x10*x20+x10*x21+x10*x22+x10*x23+x10*x25+x10*x26+x10*x27+x10*x29+x11*x12+x11*x13+x11*x14+x11*x16+x11*x17+x11*x21+x11*x22+x11*x23+x11*x26+x11*x27+x11*x28+x12*x13+x12*x14+x12*x15+x12*x16+x12*x17+x12*x23+x12*x24+x12*x28+x12*x29+x13*x17+x13*x18+x13*x19+x13*x23+x13*x24+x13*x26+x13*x29+x14*x15+x14*x16+x14*x18+x14*x19+x14*x21+x14*x23+x14*x28+x14*x29+x14*x30+x15*x16+x15*x19+x15*x21+x15*x22+x15*x23+x15*x24+x15*x25+x15*x27+x15*x28+x16*x17+x16*x20+x16*x22+x16*x23+x16*x24+x16*x25+x16*x26+x16*x30+x17*x19+x17*x20+x17*x22+x17*x23+x17*x25+x17*x27+x17*x29+x17*x30+x18*x19+x18*x25+x18*x27+x18*x28+x18*x29+x19*x20+x19*x24+x19*x25+x19*x29+x20*x21+x20*x23+x20*x25+x20*x28+x20*x29+x20*x30+x21*x24+x21*x25+x21*x28+x21*x30+x22*x25+x22*x26+x22*x30+x23*x24+x23*x27+x23*x28+x23*x29+x24*x27+x24*x29+x25*x26+x25*x27+x25*x28+x26*x27+x26*x28+x26*x30+x27*x28+x27*x30+x28*x30");
376 polHFE_30_96.emplace_back(
"1+x1+x5+x7+x8+x9+x10+x13+x15+x17+x18+x21+x22+x24+x25+x29+x1*x2+x1*x3+x1*x6+x1*x9+x1*x11+x1*x12+x1*x13+x1*x17+x1*x20+x1*x23+x1*x24+x1*x25+x1*x27+x1*x28+x2*x3+x2*x6+x2*x8+x2*x9+x2*x11+x2*x12+x2*x15+x2*x19+x2*x22+x2*x25+x2*x29+x3*x5+x3*x6+x3*x8+x3*x11+x3*x13+x3*x21+x3*x23+x3*x24+x3*x26+x3*x27+x3*x29+x3*x30+x4*x6+x4*x7+x4*x8+x4*x9+x4*x10+x4*x13+x4*x20+x4*x21+x4*x23+x4*x24+x4*x26+x4*x27+x4*x28+x4*x30+x5*x6+x5*x9+x5*x10+x5*x13+x5*x14+x5*x15+x5*x16+x5*x19+x5*x20+x5*x23+x5*x24+x5*x29+x5*x30+x6*x8+x6*x10+x6*x11+x6*x14+x6*x15+x6*x16+x6*x17+x6*x21+x6*x22+x6*x23+x6*x25+x6*x26+x7*x9+x7*x10+x7*x15+x7*x16+x7*x19+x7*x20+x7*x25+x7*x29+x7*x30+x8*x10+x8*x11+x8*x12+x8*x13+x8*x16+x8*x19+x8*x20+x8*x22+x8*x25+x8*x27+x8*x30+x9*x10+x9*x12+x9*x16+x9*x18+x9*x19+x9*x21+x9*x22+x9*x24+x9*x28+x9*x29+x10*x11+x10*x13+x10*x17+x10*x19+x10*x21+x10*x22+x10*x23+x10*x24+x10*x28+x11*x12+x11*x13+x11*x14+x11*x21+x11*x23+x11*x24+x11*x25+x11*x28+x11*x30+x12*x13+x12*x15+x12*x16+x12*x21+x12*x22+x12*x23+x12*x24+x12*x29+x12*x30+x13*x16+x13*x18+x13*x19+x13*x20+x13*x22+x13*x23+x13*x26+x13*x27+x13*x30+x14*x16+x14*x18+x14*x19+x14*x20+x14*x22+x14*x24+x14*x25+x14*x27+x14*x28+x14*x29+x14*x30+x15*x16+x15*x17+x15*x18+x15*x19+x15*x21+x15*x24+x16*x19+x16*x20+x16*x21+x16*x22+x16*x23+x16*x27+x16*x30+x17*x18+x17*x21+x17*x22+x17*x23+x17*x25+x17*x26+x17*x27+x17*x28+x17*x29+x17*x30+x18*x19+x18*x23+x18*x24+x18*x25+x18*x26+x18*x28+x18*x30+x19*x21+x19*x22+x19*x24+x19*x25+x19*x27+x19*x28+x20*x22+x20*x23+x20*x28+x21*x26+x21*x30+x22*x23+x22*x26+x22*x28+x22*x29+x23*x24+x23*x26+x23*x27+x23*x28+x23*x29+x23*x30+x24*x25+x24*x26+x25*x28+x25*x29+x25*x30+x26*x27+x26*x28+x26*x29+x27*x29+x27*x30+x29*x30");
377 polHFE_30_96.emplace_back(
"x2+x4+x5+x6+x8+x9+x10+x14+x15+x16+x17+x19+x20+x22+x24+x25+x26+x27+x28+x1*x2+x1*x3+x1*x4+x1*x6+x1*x8+x1*x9+x1*x10+x1*x12+x1*x13+x1*x14+x1*x20+x1*x21+x1*x23+x1*x26+x1*x27+x1*x29+x1*x30+x2*x3+x2*x5+x2*x6+x2*x9+x2*x12+x2*x14+x2*x15+x2*x16+x2*x17+x2*x19+x2*x20+x2*x21+x2*x22+x2*x28+x2*x30+x3*x4+x3*x5+x3*x6+x3*x8+x3*x10+x3*x13+x3*x15+x3*x17+x3*x18+x3*x22+x3*x23+x3*x24+x3*x25+x3*x26+x3*x27+x3*x29+x4*x5+x4*x7+x4*x8+x4*x13+x4*x15+x4*x17+x4*x19+x4*x24+x4*x29+x5*x6+x5*x9+x5*x11+x5*x15+x5*x16+x5*x19+x5*x20+x5*x22+x5*x23+x5*x25+x5*x26+x5*x29+x5*x30+x6*x8+x6*x9+x6*x10+x6*x12+x6*x13+x6*x14+x6*x15+x6*x16+x6*x17+x6*x19+x6*x20+x6*x21+x6*x22+x6*x25+x6*x26+x7*x8+x7*x11+x7*x12+x7*x13+x7*x15+x7*x16+x7*x19+x7*x20+x7*x21+x7*x22+x7*x23+x7*x24+x7*x27+x7*x28+x7*x30+x8*x10+x8*x14+x8*x15+x8*x16+x8*x17+x8*x19+x8*x21+x8*x22+x8*x23+x8*x27+x8*x28+x8*x29+x9*x10+x9*x13+x9*x14+x9*x15+x9*x16+x9*x17+x9*x18+x9*x20+x9*x21+x9*x22+x9*x27+x10*x11+x10*x13+x10*x14+x10*x16+x10*x17+x10*x18+x10*x19+x10*x20+x10*x21+x10*x23+x10*x24+x10*x26+x10*x28+x11*x12+x11*x13+x11*x15+x11*x16+x11*x17+x11*x19+x11*x21+x11*x24+x11*x28+x11*x29+x12*x13+x12*x15+x12*x16+x12*x17+x12*x18+x12*x19+x12*x21+x12*x24+x12*x25+x12*x26+x12*x27+x12*x30+x13*x15+x13*x17+x13*x19+x13*x25+x13*x29+x14*x19+x14*x20+x14*x21+x14*x23+x14*x24+x14*x26+x14*x27+x14*x29+x14*x30+x15*x18+x15*x20+x15*x22+x15*x23+x15*x24+x15*x25+x15*x27+x15*x28+x15*x30+x16*x17+x16*x18+x16*x19+x16*x22+x16*x23+x16*x25+x16*x29+x16*x30+x17*x18+x17*x21+x17*x22+x17*x23+x17*x24+x17*x26+x17*x28+x17*x29+x18*x19+x18*x21+x18*x25+x18*x28+x18*x30+x19*x23+x19*x24+x19*x27+x19*x28+x19*x30+x20*x21+x20*x23+x20*x24+x20*x25+x20*x26+x20*x27+x20*x28+x20*x29+x20*x30+x21*x23+x22*x24+x22*x25+x22*x26+x22*x28+x23*x24+x23*x26+x23*x27+x23*x28+x24*x29+x25*x26+x25*x27+x25*x28+x26*x27+x26*x28+x26*x29+x27*x28+x29*x30");
383 nbGen=HFE_30_96.f4();
388 HFE_30_96.printReducedGroebnerBasis(
"HFE_30_96", modulo);
394 int randomIdealF4(
bool magma)
396 cout <<
"#########################################################" << endl;
397 cout <<
"# RANDOM 10 #" << endl;
398 cout <<
"#########################################################" << endl << endl;
407 vector<Polynomial<eltType>> polRandomIdeal;
410 polRandomIdeal.emplace_back(
"x0*x2^2*x3*x4 + x2^2*x5^3 + x1*x2*x4^2 + x1*x2^2 + x0");
411 polRandomIdeal.emplace_back(
"x2*x4*x5^3 + x1^3 + x1*x5");
412 polRandomIdeal.emplace_back(
"x3*x4^3");
413 polRandomIdeal.emplace_back(
"x0*x1^4 + x1*x2*x3*x4 + x1^2*x3*x5");
414 polRandomIdeal.emplace_back(
"x0^3*x3^2 + x0^3*x2*x5 + x0*x2^2*x3*x5 + x2^3*x4 + x1*x3*x5^2 + x1^2*x3");
415 polRandomIdeal.emplace_back(
"x0^3*x3*x4 + x2^3*x4^2 + x0*x1^2*x3 + x0*x3");
416 polRandomIdeal.emplace_back(
"x0*x1^3*x5 + x1^3*x3*x5 + x1^2*x4^2*x5 + x1*x4*x5^2");
417 polRandomIdeal.emplace_back(
"x1*x2^3*x3 + x0^2*x1*x3*x4 + x1^2*x3^2*x4 + x1^2*x3*x4^2 + x0*x1*x2^2*x5 + x0^2*x5 + x0*x3*x5 + x1*x4*x5");
418 polRandomIdeal.emplace_back(
"x0*x1^2*x4*x5");
419 polRandomIdeal.emplace_back(
"x1*x2*x3^3 + x1^3*x2*x4 + x1^2*x4*x5^2 + x0^3*x5 + x2*x5^3 + x1^2*x2");
425 nbGen=randomIdeal.f4();
430 randomIdeal.printReducedGroebnerBasis(
"randomIdeal", modulo);
437 int main (
int argc,
char **argv)
439 cout <<
"#########################################################" << endl;
440 cout <<
"# BENCHMARK GF(2) #" << endl;
441 cout <<
"#########################################################" << endl << endl;
444 chrono::steady_clock::time_point start;
445 typedef chrono::duration<int,milli> millisecs_t;
448 cout << NB_THREAD <<
" threads used " << endl << endl;
457 ofstream file(
"benchmark-gf2.txt");
460 file <<
"Benchmark for ideal with bool type coefficient." << endl << endl << endl;
463 start=chrono::steady_clock::now();
464 nbGen=randomIdealF4(magma);
467 file <<
"Random 10 : " << chrono::duration_cast<millisecs_t>(chrono::steady_clock::now()-start).count() <<
" ms (" << nbGen <<
" generators)" << endl << endl;
484 start=chrono::steady_clock::now();
485 nbGen=cyclic8F4(magma);
488 file <<
"Cyclic 8 : " << chrono::duration_cast<millisecs_t>(chrono::steady_clock::now()-start).count() <<
" ms (" << nbGen <<
" generators)" << endl << endl;
498 start=chrono::steady_clock::now();
499 nbGen=HFE_25_96_F4(magma);
502 file <<
"HFE 25 96 : " << 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...
static void setVariable(std::string const *vars)
Modify the static variable VARS.
Represent an element of the field GF(2), this class is a POD (Plain Old Data) because of the aligneme...
Declaration of class F4 methods.