1gap> START_TEST(""); 2 3# 4gap> sc := rec( dim := 3, prime := 2, tab := [] );; 5gap> L := LiePRingBySCTable(sc); 6<LiePRing of dimension 3 over prime 2> 7gap> l := BasisOfLiePRing(L); 8[ l1, l2, l3 ] 9gap> l[1]*l[2]; 100 11gap> 2*l[1]; 120 13gap> l[1] + l[2]; 14l1 + l2 15gap> sc := rec( dim := 4, prime := 5, tab := [ [], [3, 1], [], [4, 1]]);; 16gap> L := LiePRingBySCTableNC(sc);; 17gap> ViewPCPresentation(L); 18[l2,l1] = l3 19[l3,l1] = l4 20gap> p := IndeterminateByName("p");; 21gap> x := IndeterminateByName("x");; 22gap> S := rec( dim := 5, 23> param := [ x ], 24> prime := p, 25> tab := [ [ 4, 1 ], [ 3, 1 ], [ 5, x ], [ 4, 1 ], [ 5, 1 ] ] );; 26gap> L := LiePRingBySCTable(S); 27<LiePRing of dimension 5 over prime p with parameters [ x ]> 28gap> ViewPCPresentation(L); 29p*l1 = l4 30p*l2 = x*l5 31[l2,l1] = l3 32[l3,l1] = l4 33[l3,l2] = l5 34gap> l := BasisOfLiePRing(L); 35[ l1, l2, l3, l4, l5 ] 36gap> p*l[1]; 37l4 38gap> l[1]+l[2]; 39l1 + l2 40gap> l[1]*l[2]; 41-1*l3 42gap> p := IndeterminateByName("p");; 43gap> w := IndeterminateByName("w");; 44gap> x := IndeterminateByName("x");; 45gap> y := IndeterminateByName("y");; 46gap> S := rec( dim := 7, 47> param := [ w, x, y ], 48> prime := p, 49> tab := [ [ ], [ 6, 1 ], [ 6, 1 ], [ 7, 1 ], [ ], 50> [ 6, x, 7, y ], [ ], [ 7, 1 ], [ 6, w ] ] );; 51gap> L := LiePRingBySCTable(S); 52<LiePRing of dimension 7 over prime p with parameters [ w, x, y ]> 53gap> ViewPCPresentation(L); 54p*l2 = l6 55p*l3 = x*l6 + y*l7 56[l2,l1] = l6 57[l3,l1] = l7 58[l4,l2] = l7 59[l4,l3] = w*l6 60gap> 61gap> SpecialiseLiePRing(L, 7, [x, y], [0,0]); 62<LiePRing of dimension 7 over prime 7> 63gap> ViewPCPresentation(last); 647*l2 = l6 65[l2,l1] = l6 66[l3,l1] = l7 67[l4,l2] = l7 68[l4,l3] = 3*l6 69gap> 70gap> SpecialiseLiePRing(L, 11, [x, y], [0,10]); 71<LiePRing of dimension 7 over prime 11> 72gap> ViewPCPresentation(last); 7311*l2 = l6 7411*l3 = 10*l7 75[l2,l1] = l6 76[l3,l1] = l7 77[l4,l2] = l7 78[l4,l3] = 2*l6 79gap> 80gap> Cartesian([0,1],[0,1]); 81[ [ 0, 0 ], [ 0, 1 ], [ 1, 0 ], [ 1, 1 ] ] 82gap> List(last, v -> SpecialiseLiePRing(L, 2, [x,y], v)); 83[ <LiePRing of dimension 7 over prime 2>, <LiePRing of dimension 7 over prime 84 2>, <LiePRing of dimension 7 over prime 2>, 85 <LiePRing of dimension 7 over prime 2> ] 86gap> SpecialiseLiePRing(L, p, [x], [0]); 87<LiePRing of dimension 7 over prime p with parameters [ y, w ]> 88gap> ViewPCPresentation(last); 89p*l2 = l6 90p*l3 = y*l7 91[l2,l1] = l6 92[l3,l1] = l7 93[l4,l2] = l7 94[l4,l3] = w*l6 95gap> SpecialiseLiePRing(L, p, [y], [3]); 96<LiePRing of dimension 7 over prime p with parameters [ x, w ]> 97gap> ViewPCPresentation(last); 98p*l2 = l6 99p*l3 = x*l6 + 3*l7 100[l2,l1] = l6 101[l3,l1] = l7 102[l4,l2] = l7 103[l4,l3] = w*l6 104gap> SpecialisePrimeOfLiePRing(L, 29); 105<LiePRing of dimension 7 over prime 29 with parameters [ y, x ]> 106gap> ViewPCPresentation(last); 10729*l2 = l6 10829*l3 = x*l6 + y*l7 109[l2,l1] = l6 110[l3,l1] = l7 111[l4,l2] = l7 112[l4,l3] = 2*l6 113gap> L := LiePRingsByLibrary(6)[14]; 114<LiePRing of dimension 6 over prime p with parameters [ x ]> 115gap> K := SpecialisePrimeOfLiePRing(L, 5); 116<LiePRing of dimension 6 over prime 5 with parameters [ x ]> 117gap> LiePValues(K); 118[ [ p, w ], [ 5, 2 ] ] 119gap> L := LiePRingsByLibrary(6)[100]; 120<LiePRing of dimension 6 over prime p> 121gap> l := BasisOfLiePRing(L); 122[ l1, l2, l3, l4, l5, l6 ] 123gap> U := LiePSubring(L, [5*l[1]]); 124WARNING: Dividing by 1/5 in 6.464 125<LiePRing of dimension 3 over prime p> 126gap> BasisOfLiePRing(U); 127[ l1, l4, l6 ] 128gap> 129gap> K := SpecialisePrimeOfLiePRing(L, 5); 130<LiePRing of dimension 6 over prime 5> 131gap> b := BasisOfLiePRing(K); 132[ l1, l2, l3, l4, l5, l6 ] 133gap> LiePSubring(K, [5*b[1]]); 134<LiePRing of dimension 2 over prime 5> 135gap> BasisOfLiePRing(last); 136[ l4, l6 ] 137gap> 138gap> K := SpecialisePrimeOfLiePRing(L, 7); 139<LiePRing of dimension 6 over prime 7> 140gap> b := BasisOfLiePRing(K); 141[ l1, l2, l3, l4, l5, l6 ] 142gap> U := LiePSubring(L, [5*b[1]]); 143<LiePRing of dimension 1 over prime p> 144gap> BasisOfLiePRing(U); 145[ l1 + 2*l4 ] 146gap> LiePIdeal(L, [l[1]]); 147<LiePRing of dimension 5 over prime p> 148gap> BasisOfLiePRing(last); 149[ l1, l3, l4, l5, l6 ] 150gap> LiePIdeal(K, [b[1]]); 151<LiePRing of dimension 5 over prime 7> 152gap> LiePIdeal(K, [b[2]]); 153<LiePRing of dimension 4 over prime 7> 154gap> LiePQuotient(K,last); 155<LiePRing of dimension 2 over prime 7> 156 157# 158gap> STOP_TEST( "", 1); 159