1############################################################################# 2## 3## This file tests the large finite fields. 4## 5#@local fieldpairs,fieldsizes,iF,iPI,iW,izs,zs,iFI,x 6gap> START_TEST("ffeconway.tst"); 7 8# 9# Disable various warnings which depend on state of prime number and 10# Conway Polynomial databases and on whether FactInt is loaded 11# 12gap> iPI := InfoLevel(InfoPrimeInt);; 13gap> iF := InfoLevel(InfoFactor);; 14gap> if IsBound(InfoFactInt) then iFI := InfoLevel(InfoFactInt); fi; 15gap> iW := InfoLevel(InfoWarning);; 16gap> SetInfoLevel(InfoPrimeInt,0); 17gap> SetInfoLevel(InfoFactor,0); 18gap> if IsBound(InfoFactInt) then SetInfoLevel(InfoFactInt,0); fi; 19gap> SetInfoLevel(InfoWarning,0); 20 21# 22# A range of field sizes to hit various cases for the underlying vector 23# arithmetic. 24# 25gap> fieldsizes := [ [2,17], [2,32], [2,60], [2,76], [2,87], [3,11], 26> [3,20], [3,60], [17,4], [257,2], [257,11], [65521,2], [65537,2], 27> [268435399,2], [4294967291,2], [1152921504606846883,3] ];; 28gap> Add( fieldsizes, [NextPrimeInt(2^64),2] ); 29 30# 31# When we come to test cross-field, we need to make sure we don't try and 32# create overlarge fields 33# leave the output here so we trip here if the Conway polynomial database changes 34# 35gap> fieldpairs := Concatenation(List(fieldsizes, pd -> List(Filtered([1..pd[2]-1], 36> d2 -> IsCheapConwayPolynomial(pd[1],Lcm(pd[2],d2))), d2 -> 37> [pd[1],pd[2],d2]))); 38[ [ 2, 17, 1 ], [ 2, 17, 2 ], [ 2, 17, 3 ], [ 2, 17, 4 ], [ 2, 17, 5 ], 39 [ 2, 17, 6 ], [ 2, 17, 7 ], [ 2, 32, 1 ], [ 2, 32, 2 ], [ 2, 32, 3 ], 40 [ 2, 32, 4 ], [ 2, 32, 6 ], [ 2, 32, 8 ], [ 2, 32, 12 ], [ 2, 32, 16 ], 41 [ 2, 32, 24 ], [ 2, 60, 1 ], [ 2, 60, 2 ], [ 2, 60, 3 ], [ 2, 60, 4 ], 42 [ 2, 60, 5 ], [ 2, 60, 6 ], [ 2, 60, 8 ], [ 2, 60, 10 ], [ 2, 60, 12 ], 43 [ 2, 60, 15 ], [ 2, 60, 20 ], [ 2, 60, 24 ], [ 2, 60, 30 ], [ 2, 60, 40 ], 44 [ 2, 76, 1 ], [ 2, 76, 2 ], [ 2, 76, 4 ], [ 2, 76, 19 ], [ 2, 76, 38 ], 45 [ 2, 87, 1 ], [ 2, 87, 3 ], [ 2, 87, 29 ], [ 3, 11, 1 ], [ 3, 11, 2 ], 46 [ 3, 11, 3 ], [ 3, 11, 4 ], [ 3, 11, 5 ], [ 3, 11, 6 ], [ 3, 11, 7 ], 47 [ 3, 20, 1 ], [ 3, 20, 2 ], [ 3, 20, 3 ], [ 3, 20, 4 ], [ 3, 20, 5 ], 48 [ 3, 20, 6 ], [ 3, 20, 8 ], [ 3, 20, 10 ], [ 3, 20, 12 ], [ 3, 20, 15 ], 49 [ 3, 60, 1 ], [ 3, 60, 2 ], [ 3, 60, 3 ], [ 3, 60, 4 ], [ 3, 60, 5 ], 50 [ 3, 60, 6 ], [ 3, 60, 10 ], [ 3, 60, 12 ], [ 3, 60, 15 ], [ 3, 60, 20 ], 51 [ 3, 60, 30 ], [ 17, 4, 1 ], [ 17, 4, 2 ], [ 17, 4, 3 ], [ 257, 2, 1 ], 52 [ 257, 11, 1 ], [ 65521, 2, 1 ], [ 65537, 2, 1 ], [ 268435399, 2, 1 ], 53 [ 4294967291, 2, 1 ], [ 1152921504606846883, 3, 1 ], 54 [ 18446744073709551629, 2, 1 ] ] 55 56# 57# construct generating elements 58# 59gap> zs := List(fieldsizes, pd -> Z(pd[1],pd[2])); 60[ z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z ] 61 62# 63# and another way 64# 65gap> zs = List(fieldsizes, pd -> Z(pd[1]^pd[2])); 66true 67 68# 69# Construct some more interesting elements and test View, Print and Display 70# 71gap> izs := List(zs, Inverse); 72[ z2+z16, z2+z3+z6+z8+z14+z31, 73 z+z2+z3+z4+z7+z11+z16+z18+z21+z24+z25+z29+z31+z32+z33+z35+z38+z40+z41+z43+z4\ 744+z59, 75 1+z+z4+z13+z14+z18+z19+z22+z23+z24+z26+z28+z30+z32+z33+z34+z35+z36+z37+z75, 76 1+z2+z4+z6+z7+z9+z10+z11+z12+z13+z15+z19+z25+z27+z29+z86, z+2z10, 77 1+2z2+2z3+2z4+z7+z8+z9+z10+2z12+z19, 78 2z+2z2+2z3+z4+2z5+2z7+z9+2z10+z13+2z14+2z15+z19+z20+2z21+2z23+2z25+2z26+2z27\ 79+z29+z31+2z32+z33+z34+2z35+2z37+2z38+z39+2z40+z43+z59, 8+9z+11z3, 2+171z, 80 99+86z10, 61667+23125z, 21846+43691z, 89478467+89478466z, 81 2147483646+2147483645z, 1+576460752303423442z2, 2+9223372036854775814z ] 82gap> Print(izs,"\n"); 83[ Z(2,17)^2+Z(2,17)^16, 84 Z(2,32)^2+Z(2,32)^3+Z(2,32)^6+Z(2,32)^8+Z(2,32)^14+Z(2,32)^31, 85 Z(2,60)+Z(2,60)^2+Z(2,60)^3+Z(2,60)^4+Z(2,60)^7+Z(2,60)^11+Z(2,60)^16+Z(2,60\ 86)^18+Z(2,60)^21+Z(2,60)^24+Z(2,60)^25+Z(2,60)^29+Z(2,60)^31+Z(2,60)^32+Z(2,60)\ 87^33+Z(2,60)^35+Z(2,60)^38+Z(2,60)^40+Z(2,60)^41+Z(2,60)^43+Z(2,60)^44+Z(2,60)^\ 8859, 89 Z(2)^0+Z(2,76)+Z(2,76)^4+Z(2,76)^13+Z(2,76)^14+Z(2,76)^18+Z(2,76)^19+Z(2,76)\ 90^22+Z(2,76)^23+Z(2,76)^24+Z(2,76)^26+Z(2,76)^28+Z(2,76)^30+Z(2,76)^32+Z(2,76)^\ 9133+Z(2,76)^34+Z(2,76)^35+Z(2,76)^36+Z(2,76)^37+Z(2,76)^75, 92 Z(2)^0+Z(2,87)^2+Z(2,87)^4+Z(2,87)^6+Z(2,87)^7+Z(2,87)^9+Z(2,87)^10+Z(2,87)^\ 9311+Z(2,87)^12+Z(2,87)^13+Z(2,87)^15+Z(2,87)^19+Z(2,87)^25+Z(2,87)^27+Z(2,87)^2\ 949+Z(2,87)^86, Z(3,11)+2*Z(3,11)^10, 95 Z(3)^0+2*Z(3,20)^2+2*Z(3,20)^3+2*Z(3,20)^4+Z(3,20)^7+Z(3,20)^8+Z(3,20)^9+Z(3\ 96,20)^10+2*Z(3,20)^12+Z(3,20)^19, 97 2*Z(3,60)+2*Z(3,60)^2+2*Z(3,60)^3+Z(3,60)^4+2*Z(3,60)^5+2*Z(3,60)^7+Z(3,60)^\ 989+2*Z(3,60)^10+Z(3,60)^13+2*Z(3,60)^14+2*Z(3,60)^15+Z(3,60)^19+Z(3,60)^20+2*Z(\ 993,60)^21+2*Z(3,60)^23+2*Z(3,60)^25+2*Z(3,60)^26+2*Z(3,60)^27+Z(3,60)^29+Z(3,60\ 100)^31+2*Z(3,60)^32+Z(3,60)^33+Z(3,60)^34+2*Z(3,60)^35+2*Z(3,60)^37+2*Z(3,60)^38\ 101+Z(3,60)^39+2*Z(3,60)^40+Z(3,60)^43+Z(3,60)^59, 102 Z(17)^10+9*Z(17,4)+11*Z(17,4)^3, Z(257)^48+171*Z(257,2), 103 Z(257)^198+86*Z(257,11)^10, Z(65521)^1451+23125*Z(65521,2), 104 ZmodpZObj(21846,65537)+43691*Z(65537,2), 105 ZmodpZObj(89478467,268435399)+89478466*Z(268435399,2), 106 ZmodpZObj(2147483646,4294967291)+2147483645*Z(4294967291,2), 107 ZmodpZObj(1,1152921504606846883)+576460752303423442*Z(1152921504606846883,3)\ 108^2, 109 ZmodpZObj(2,18446744073709551629)+9223372036854775814*Z(18446744073709551629\ 110,2) ] 111gap> for x in izs do 112> Display(x); 113> od; 114z2+z16 115z2+z3+z6+z8+z14+z31 116z+z2+z3+z4+z7+z11+z16+z18+z21+z24+z25+z29+z31+z32+z33+z35+z38+z40+z41+z43+z44+\ 117z59 1181+z+z4+z13+z14+z18+z19+z22+z23+z24+z26+z28+z30+z32+z33+z34+z35+z36+z37+z75 1191+z2+z4+z6+z7+z9+z10+z11+z12+z13+z15+z19+z25+z27+z29+z86 120z+2z10 1211+2z2+2z3+2z4+z7+z8+z9+z10+2z12+z19 1222z+2z2+2z3+z4+2z5+2z7+z9+2z10+z13+2z14+2z15+z19+z20+2z21+2z23+2z25+2z26+2z27+z\ 12329+z31+2z32+z33+z34+2z35+2z37+2z38+z39+2z40+z43+z59 1248+9z+11z3 1252+171z 12699+86z10 12761667+23125z 12821846+43691z 12989478467+89478466z 1302147483646+2147483645z 1311+576460752303423442z2 1322+9223372036854775814z 133 134# 135# Test arithmetic within the field 136# 137gap> zs + izs; 138[ z+z2+z16, z+z2+z3+z6+z8+z14+z31, 139 z2+z3+z4+z7+z11+z16+z18+z21+z24+z25+z29+z31+z32+z33+z35+z38+z40+z41+z43+z44+\ 140z59, 1+z4+z13+z14+z18+z19+z22+z23+z24+z26+z28+z30+z32+z33+z34+z35+z36+z37+z75, 141 1+z+z2+z4+z6+z7+z9+z10+z11+z12+z13+z15+z19+z25+z27+z29+z86, 2z+2z10, 142 1+z+2z2+2z3+2z4+z7+z8+z9+z10+2z12+z19, 143 2z2+2z3+z4+2z5+2z7+z9+2z10+z13+2z14+2z15+z19+z20+2z21+2z23+2z25+2z26+2z27+z2\ 1449+z31+2z32+z33+z34+2z35+2z37+2z38+z39+2z40+z43+z59, 8+10z+11z3, 2+172z, 145 99+z+86z10, 61667+23126z, 21846+43692z, 89478467+89478467z, 146 2147483646+2147483646z, 1+z+576460752303423442z2, 2+9223372036854775815z ] 147gap> zs - izs; 148[ z+z2+z16, z+z2+z3+z6+z8+z14+z31, 149 z2+z3+z4+z7+z11+z16+z18+z21+z24+z25+z29+z31+z32+z33+z35+z38+z40+z41+z43+z44+\ 150z59, 1+z4+z13+z14+z18+z19+z22+z23+z24+z26+z28+z30+z32+z33+z34+z35+z36+z37+z75, 151 1+z+z2+z4+z6+z7+z9+z10+z11+z12+z13+z15+z19+z25+z27+z29+z86, z10, 152 2+z+z2+z3+z4+2z7+2z8+2z9+2z10+z12+2z19, 153 2z+z2+z3+2z4+z5+z7+2z9+z10+2z13+z14+z15+2z19+2z20+z21+z23+z25+z26+z27+2z29+2\ 154z31+z32+2z33+2z34+z35+z37+z38+2z39+z40+2z43+2z59, 9+9z+6z3, 255+87z, 155 158+z+171z10, 3854+42397z, 43691+21847z, 178956932+178956934z, 156 2147483645+2147483647z, 1152921504606846882+z+576460752303423441z2, 157 18446744073709551627+9223372036854775816z ] 158gap> List(izs, x->x^2); 159[ z+z15, z+z2+z5+z7+z13+z30, 160 1+z+z2+z3+z6+z10+z15+z17+z20+z23+z24+z28+z30+z31+z32+z34+z37+z39+z40+z42+z43\ 161+z58, z+z3+z4+z12+z14+z17+z19+z21+z24+z25+z26+z27+z28+z29+z30+z31+z37+z74+z75, 162 1+z+z2+z3+z4+z5+z7+z8+z13+z14+z15+z18+z19+z24+z25+z26+z27+z28+z29+z85+z86, 163 1+2z9, 1+2z+z2+z3+2z4+z6+2z7+2z8+2z9+z10+2z11+2z12+z18+z19, 164 2+2z+2z2+z3+2z4+2z6+z8+2z9+z12+2z13+2z14+z18+z19+2z20+2z22+2z24+2z25+2z26+z2\ 1658+z30+2z31+z32+z33+2z34+2z36+2z37+z38+2z39+z42+z58, 5+4z+11z2+3z3, 175+85z, 166 35+86z9+33z10, 3174+50331z, 50973+58255z, 59652311+149130777z, 167 3221225468+3221225468z, 1+576460752303423442z+576460752303423442z2, 168 9223372036854775818+18446744073709551628z ] 169gap> List([1..Length(zs)] , i-> zs[i]/izs[i]); 170[ z2, z2, z2, z2, z2, z2, z2, z2, z2, 254+6z, z2, 65504+3z, 65534+z, 171 268435396+2z, 4294967289+z, z2, 18446744073709551627+4z ] 172gap> List(izs, AdditiveInverse); 173[ z2+z16, z2+z3+z6+z8+z14+z31, 174 z+z2+z3+z4+z7+z11+z16+z18+z21+z24+z25+z29+z31+z32+z33+z35+z38+z40+z41+z43+z4\ 1754+z59, 176 1+z+z4+z13+z14+z18+z19+z22+z23+z24+z26+z28+z30+z32+z33+z34+z35+z36+z37+z75, 177 1+z2+z4+z6+z7+z9+z10+z11+z12+z13+z15+z19+z25+z27+z29+z86, 2z+z10, 178 2+z2+z3+z4+2z7+2z8+2z9+2z10+z12+2z19, 179 z+z2+z3+2z4+z5+z7+2z9+z10+2z13+z14+z15+2z19+2z20+z21+z23+z25+z26+z27+2z29+2z\ 18031+z32+2z33+2z34+z35+z37+z38+2z39+z40+2z43+2z59, 9+8z+6z3, 255+86z, 181 158+171z10, 3854+42396z, 43691+21846z, 178956932+178956933z, 182 2147483645+2147483646z, 1152921504606846882+576460752303423441z2, 183 18446744073709551627+9223372036854775815z ] 184 185# 186# and across fields 187# 188gap> List(fieldpairs, pdd -> Z(pdd[1],pdd[2])+Z(pdd[1],pdd[3])); 189[ 1+z, z+z4+z9+z10+z15+z17+z19+z21+z23+z25+z26+z27+z29+z30+z33, 190 z2+z3+z6+z10+z13+z15+z16+z18+z19+z20+z24+z25+z35+z38+z39+z40+z41+z44+z46+z48\ 191+z49, 192 1+z2+z3+z4+z5+z7+z10+z11+z12+z13+z14+z16+z17+z18+z19+z21+z22+z23+z24+z25+z26\ 193+z30+z31+z32+z35+z37+z38+z40+z47+z48+z50+z51+z56+z58+z62+z63+z67, 194 z+z3+z7+z8+z9+z10+z13+z14+z17+z19+z20+z21+z22+z24+z25+z27+z28+z30+z32+z33+z3\ 1956+z38+z41+z42+z45+z46+z47+z48+z50+z51+z52+z54+z58+z59+z60+z61+z63+z65+z68+z69+\ 196z71+z73+z75+z76+z77+z82, 197 z2+z3+z5+z7+z10+z11+z13+z16+z18+z19+z20+z21+z22+z25+z26+z27+z28+z30+z31+z32+\ 198z34+z35+z37+z38+z39+z40+z44+z45+z47+z54+z55+z56+z58+z60+z61+z63+z65+z67+z69+z7\ 1993+z74+z79+z83+z87+z89+z96+z97+z99+z100, <<an element of GF(2, 119)>>, 1+z, 200 1+z3+z4+z5+z6+z8+z9+z14+z17+z18+z19+z20+z21+z24+z29+z30, 201 z+z5+z7+z9+z12+z14+z15+z16+z17+z20+z22+z23+z24+z25+z28+z31+z33+z36+z37+z38+z\ 20239+z42+z43+z44+z52+z56+z61+z62+z65+z67+z68+z69+z70+z71+z72+z73+z76+z77+z79+z80\ 203+z81+z82+z83+z85+z86+z89+z94, 204 z4+z5+z6+z8+z10+z12+z14+z15+z17+z18+z19+z20+z21+z22+z23+z24+z25+z29+z30, 205 1+z6+z11+z12+z13+z15+z18+z22+z23+z30+z31+z36+z37+z38+z39+z41+z44+z45+z47+z48\ 206+z50+z51+z52+z55+z56+z57+z58+z59+z60+z63+z64+z66+z68+z69+z74+z76+z81+z83+z84+z\ 20785+z86+z88+z89+z90+z91+z92+z93, 208 z+z2+z3+z6+z7+z10+z12+z14+z17+z19+z20+z21+z22+z29+z31, 209 z2+z9+z10+z11+z15+z16+z17+z18+z20+z23+z25+z27+z29+z33+z35+z36+z39+z40+z42+z4\ 2105+z47+z48+z52+z54+z55+z56+z57+z59+z62+z67+z68+z71+z74+z75+z76+z80+z81+z83+z85+\ 211z86+z89+z90+z92+z93, 212 z+z2+z4+z5+z6+z7+z10+z11+z14+z15+z16+z20+z23+z26+z28+z29+z30+z31, 213 1+z+z4+z6+z7+z9+z12+z14+z17+z19+z21+z22+z28+z30+z33+z34+z36+z38+z40+z41+z45+\ 214z48+z49+z51+z52+z53+z59+z61+z63+z67+z69+z70+z75+z78+z81+z83+z85+z86+z87+z90+z9\ 2153+z94, 1+z, 216 z2+z4+z5+z7+z9+z11+z14+z17+z19+z20+z21+z23+z24+z25+z27+z30+z35+z36+z38+z39+z\ 21741+z43+z50+z51+z53+z54+z55+z57+z59, 218 1+z+z5+z7+z8+z11+z12+z15+z17+z22+z23+z24+z27+z28+z29+z31+z34+z35+z37+z38+z39\ 219+z42+z47+z48+z51+z52+z53, 220 1+z2+z3+z4+z7+z8+z9+z10+z11+z16+z18+z19+z20+z21+z23+z26+z27+z31+z32+z34+z36+\ 221z37+z39+z40+z41+z42+z45+z46+z47+z49+z50+z51+z53+z54+z56+z57+z58, 222 z+z2+z3+z6+z7+z9+z11+z13+z17+z19+z21+z22+z23+z25+z27+z29+z30+z31+z36+z38+z39\ 223+z41+z45+z46+z48+z51+z53+z54+z55+z56+z59, 224 z2+z4+z6+z7+z9+z11+z12+z14+z16+z17+z19+z20+z21+z22+z25+z26+z31+z34+z35+z36+z\ 22537+z38+z44+z46+z48+z49+z51+z52+z57+z58+z59, <<an element of GF(2, 120)>>, 226 z+z3+z4+z6+z8+z10+z11+z15+z18+z19+z22+z24+z26+z28+z30+z31+z32+z33+z34+z36+z3\ 2277+z39+z40+z41+z42+z47+z48+z50+z53+z54+z56+z57+z59, 228 z4+z6+z7+z13+z14+z16+z17+z18+z19+z20+z21+z22+z24+z26+z28+z31+z33+z34+z35+z37\ 229+z39+z43+z47+z48+z51+z52+z54+z58, 230 1+z4+z6+z8+z9+z14+z16+z24+z28+z29+z32+z34+z38+z39+z40+z42+z47+z48+z50+z51+z5\ 2312+z54+z56+z57+z59, 232 1+z+z2+z3+z4+z7+z11+z14+z15+z16+z17+z18+z22+z25+z26+z29+z34+z35+z36+z37+z38+\ 233z40+z44+z45+z46+z47+z48+z50+z52+z55+z56+z57+z58, <<an element of GF(2, 120)>>, 234 z2+z4+z7+z10+z13+z15+z18+z20+z23+z25+z26+z38+z39+z41+z43+z44+z46+z48+z50+z51\ 235+z55+z56+z57+z59, <<an element of GF(2, 120)>>, 1+z, 236 z3+z6+z7+z8+z10+z14+z15+z18+z20+z22+z23+z25+z26+z27+z30+z31+z32+z33+z35+z36+\ 237z38+z42+z45+z46+z47+z50+z51+z54+z55+z57+z58+z60+z62+z63+z64+z65+z66+z67+z69+z7\ 2381+z73+z75, 239 1+z2+z3+z4+z7+z8+z9+z17+z18+z19+z21+z26+z29+z30+z31+z32+z34+z35+z36+z39+z43+\ 240z44+z45+z46+z48+z49+z52+z53+z56+z57+z60+z63+z64+z65+z69+z70+z71+z73+z74+z75, 241 1+z2+z5+z6+z7+z8+z10+z12+z13+z15+z16+z18+z19+z20+z26+z28+z33+z35+z37+z40+z41\ 242+z43+z44+z45+z46+z48+z49+z52+z53+z54+z55+z57+z60+z62+z65+z67+z72+z73+z74, 243 z2+z3+z5+z6+z8+z9+z11+z19+z23+z27+z31+z32+z34+z35+z36+z38+z42+z46+z48+z49+z5\ 2440+z53+z58+z59+z60+z62+z63+z65+z66+z67+z68+z69+z70+z74, 1+z, 245 1+z2+z3+z5+z9+z15+z22+z25+z26+z27+z28+z29+z30+z31+z32+z34+z36+z40+z42+z43+z4\ 2464+z48+z51+z52+z55+z56+z57+z60+z61+z62+z63+z64+z65+z67+z68+z69+z70+z71+z72+z75+\ 247z77+z79+z81+z83+z84+z86, 248 z+z2+z6+z8+z9+z10+z14+z15+z16+z19+z20+z22+z23+z26+z28+z30+z31+z33+z34+z37+z4\ 2491+z46+z50+z51+z54+z55+z56+z57+z58+z59+z60+z61+z63+z64+z66+z68+z71+z72+z76+z78+\ 250z81+z82+z83+z84+z85, 2+z, 251 2+z+z2+2z3+z4+2z5+2z6+z7+2z9+2z11+z12+2z14+z16+z17+2z18+2z19+2z20+2z21, 252 1+2z+2z3+2z4+2z6+2z8+2z9+z11+z12+z14+2z15+2z17+z18+z19+2z21+2z23+z25+2z26+2z\ 25327+2z28+2z29+2z30+z32, 254 2z+2z3+z8+z9+z12+z15+2z17+2z19+z21+z22+z23+z24+z25+z30+z34+z35+z37+2z38+2z40\ 255+z41+2z42+z43, 256 2+z+z4+2z6+z7+2z9+z10+2z14+z16+2z19+z20+2z21+2z22+z23+2z25+z26+2z27+z28+2z29\ 257+z30+z31+2z34+2z35+z36+z38+z40+z41+z42+z44+2z45+2z47+z51+z52, 258 1+z+z4+z6+2z8+z9+z11+2z13+z14+z17+z19+z20+2z21+z23+z25+2z26+z27+z28+z29+z31+\ 259z32+z33+z34+z35+2z38+z40+z41+2z42+2z45+z46+2z47+z50+2z51+z52+2z57+z58+2z59+z60\ 260+z61+2z62+2z63+2z64+z65, 261 1+z2+2z4+z5+2z6+2z7+z8+2z9+2z10+z11+2z12+2z13+z14+z16+2z17+2z18+z21+z22+z24+\ 2622z27+2z28+2z29+2z32+z33+z35+z36+z40+2z41+2z42+z45+2z46+2z48+2z49+z51+z52+z53+2\ 263z54+z55+z56+z57+2z58+z59+z60+z61+z63+z64+2z65+2z66+2z67+z68+2z73+2z76, 2+z, 264 z+z2+2z3+2z4+z7+2z8+z9+z10+2z12+2z13+2z14+z15+2z17+2z18+z19, 265 2+z2+z3+2z5+z7+2z11+z12+z14+z15+z16+z18+z19+2z20+2z22+z25+z27+z29+2z30+z32+z\ 26633+2z34+z35+2z36+2z39+z40+z41+2z43+2z45+z46+2z48+2z49+2z50+z53+2z54+2z55+z56+2\ 267z57, 1+2z+z2+2z3+2z4+2z5+z6+z7+2z11+2z12+z13+z14+z15+2z16+z17+z18+z19, 268 2z+2z2+z4+z5+z6+2z8+z11+2z12+z16+z19, 269 2z+z2+z3+2z4+z6+2z7+2z8+2z9+2z10+2z12+2z13+z15+z16+z17+2z18+z19+z20+2z21+z24\ 270+z25+2z26+2z27+z28+2z29+z30+2z31+z32+z33+z35+z36+2z37+z39+2z40+2z42+z45+z46+z4\ 2717+2z48+2z50+z51+2z52+z53+z54+z55+2z57+2z58+2z59, 272 2+z+2z3+2z4+2z5+z6+2z7+2z8+z9+2z11+2z12+z13+2z15+z16+z19+z23+2z24+2z25+2z26+\ 273z27+2z28+z29+2z30+2z33+2z35+z39, 274 z+z3+2z4+2z7+z8+2z10+z11+2z12+z13+z14+z15+z17+z18+2z19, 275 2+z+2z2+2z5+2z6+z8+2z9+z10+z12+2z15+z18+z19+z20+z23+2z25+2z26+z27+2z28+2z29+\ 2762z30+z31+2z32+2z33+2z34+2z38+2z39+2z40+z42+z44+z45+2z46+z48+z49+2z50+2z52+z53+\ 277z54+2z55+2z56+z57+z58, 278 2+z+2z2+2z3+z4+z7+2z8+2z9+2z10+z11+z13+z14+z15+2z19+2z21+2z23+2z24+z25+2z29+\ 2792z31+z32+z34+z35+z36+z37+z38+z39+2z40+2z42+2z44+z45+2z46+z49+z50+z51+2z53+z54+\ 2802z55+2z57+2z58+2z59, 2+z, 281 2+2z+2z2+2z4+2z5+z6+2z7+z8+2z9+2z11+z13+2z14+2z15+z16+2z17+2z18+z19+2z20+z21\ 282+z22+2z23+2z25+2z27+z28+2z29+2z31+z35+2z36+z37+2z38+2z39+z40+2z42+z43+2z45+2z4\ 2836+z47+z49+z51+2z52+2z53+z55+2z58+z59, 284 1+z+2z2+2z3+z4+2z5+2z6+z7+z9+z10+z11+z12+2z16+z17+z18+z19+z21+z25+z26+2z27+z\ 28528+2z29+2z30+z31+z34+z35+z36+2z37+z38+2z39+z40+2z42+2z43+2z46+z47+2z48+2z49+z5\ 2862+2z53+2z55+z57+2z58+2z59, 287 1+z+z3+2z5+2z7+2z8+2z9+z10+z12+z13+2z14+2z19+z20+z22+2z23+z26+2z27+z28+2z29+\ 288z30+z32+2z33+z34+2z35+z37+2z38+2z40+z41+2z42+z43+2z44+2z45+z46+2z47+z48+z49+2z\ 28951+z53+2z56+z57+2z58+z59, 290 2+2z+2z3+z4+2z5+z7+z8+z9+z10+2z11+2z12+2z13+z14+z18+2z20+z24+z25+z28+2z29+2z\ 29130+2z31+z32+z33+z34+2z35+z36+2z37+z38+z40+z44+z46+z47+z49+z50+2z52+2z53+2z57+2\ 292z58+2z59, 293 2+2z2+2z3+2z7+2z8+2z11+2z12+2z13+2z14+2z16+2z17+2z18+z19+2z20+z22+z24+z25+2z\ 29428+z30+2z34+z35+z37+z38+z39+2z40+2z41+z42+2z45+2z46+2z47+2z48+z51+2z53+2z54+z5\ 2955+2z56+z57+z58+z59, 296 z+2z3+2z4+z5+z6+2z8+z10+z11+2z12+2z15+2z16+z19+z21+2z22+z25+2z29+2z30+2z31+2\ 297z32+z33+2z34+z38+2z39+z41+z43+2z48+2z49+z50+z53+2z54+2z55+2z56+2z57+z58+z59, 298 1+2z+z3+z4+2z5+z6+z8+2z10+2z11+z12+2z14+z15+z16+z17+z18+z19+2z20+z21+z22+z23\ 299+2z25+2z27+2z30+2z31+z32+z33+z34+2z36+2z37+2z39+2z40+2z41+z44+2z45+z47+z48+z49\ 300+2z53+2z54+2z55+z56+2z59, 301 1+2z+2z4+2z6+z7+2z8+z13+z16+z17+2z19+z20+z22+2z23+2z24+z25+z26+z27+z28+2z33+\ 302z35+2z38+z39+2z40+2z41+z42+2z44+2z45+z47+z49+2z50+z51+z52+2z54+2z55+2z56+z57+z\ 30358+z59, 304 1+z+2z2+2z3+2z4+z6+2z9+2z10+z11+z14+z15+2z16+2z17+2z20+2z21+2z22+2z26+2z27+2\ 305z28+2z29+2z31+z32+z33+z34+z36+z37+2z38+z41+z42+2z45+2z46+2z47+2z50+2z52+2z53+2\ 306z54+z56+z57+z58+z59, 307 1+z+2z2+z3+z4+2z6+2z7+2z9+z10+z11+2z12+z14+2z15+z16+z19+2z21+2z24+z26+2z28+2\ 308z29+2z30+z32+z33+z34+z35+2z37+2z40+z41+2z42+2z46+2z48+z49+2z50+2z53+z54+z55+z5\ 3096+z58+2z59, 3+z, 12+z2+9z3, 10+9z+13z3+11z4+5z5+10z6+15z7+5z8+13z9+6z10+9z11, 310 3+z, 3+z, 17+z, 3+z, 3+z, 2+z, 2+z, 2+z ] 311gap> List(fieldpairs, pdd -> Z(pdd[1],pdd[2])-Z(pdd[1],pdd[3])); 312[ 1+z, z+z4+z9+z10+z15+z17+z19+z21+z23+z25+z26+z27+z29+z30+z33, 313 z2+z3+z6+z10+z13+z15+z16+z18+z19+z20+z24+z25+z35+z38+z39+z40+z41+z44+z46+z48\ 314+z49, 315 1+z2+z3+z4+z5+z7+z10+z11+z12+z13+z14+z16+z17+z18+z19+z21+z22+z23+z24+z25+z26\ 316+z30+z31+z32+z35+z37+z38+z40+z47+z48+z50+z51+z56+z58+z62+z63+z67, 317 z+z3+z7+z8+z9+z10+z13+z14+z17+z19+z20+z21+z22+z24+z25+z27+z28+z30+z32+z33+z3\ 3186+z38+z41+z42+z45+z46+z47+z48+z50+z51+z52+z54+z58+z59+z60+z61+z63+z65+z68+z69+\ 319z71+z73+z75+z76+z77+z82, 320 z2+z3+z5+z7+z10+z11+z13+z16+z18+z19+z20+z21+z22+z25+z26+z27+z28+z30+z31+z32+\ 321z34+z35+z37+z38+z39+z40+z44+z45+z47+z54+z55+z56+z58+z60+z61+z63+z65+z67+z69+z7\ 3223+z74+z79+z83+z87+z89+z96+z97+z99+z100, <<an element of GF(2, 119)>>, 1+z, 323 1+z3+z4+z5+z6+z8+z9+z14+z17+z18+z19+z20+z21+z24+z29+z30, 324 z+z5+z7+z9+z12+z14+z15+z16+z17+z20+z22+z23+z24+z25+z28+z31+z33+z36+z37+z38+z\ 32539+z42+z43+z44+z52+z56+z61+z62+z65+z67+z68+z69+z70+z71+z72+z73+z76+z77+z79+z80\ 326+z81+z82+z83+z85+z86+z89+z94, 327 z4+z5+z6+z8+z10+z12+z14+z15+z17+z18+z19+z20+z21+z22+z23+z24+z25+z29+z30, 328 1+z6+z11+z12+z13+z15+z18+z22+z23+z30+z31+z36+z37+z38+z39+z41+z44+z45+z47+z48\ 329+z50+z51+z52+z55+z56+z57+z58+z59+z60+z63+z64+z66+z68+z69+z74+z76+z81+z83+z84+z\ 33085+z86+z88+z89+z90+z91+z92+z93, 331 z+z2+z3+z6+z7+z10+z12+z14+z17+z19+z20+z21+z22+z29+z31, 332 z2+z9+z10+z11+z15+z16+z17+z18+z20+z23+z25+z27+z29+z33+z35+z36+z39+z40+z42+z4\ 3335+z47+z48+z52+z54+z55+z56+z57+z59+z62+z67+z68+z71+z74+z75+z76+z80+z81+z83+z85+\ 334z86+z89+z90+z92+z93, 335 z+z2+z4+z5+z6+z7+z10+z11+z14+z15+z16+z20+z23+z26+z28+z29+z30+z31, 336 1+z+z4+z6+z7+z9+z12+z14+z17+z19+z21+z22+z28+z30+z33+z34+z36+z38+z40+z41+z45+\ 337z48+z49+z51+z52+z53+z59+z61+z63+z67+z69+z70+z75+z78+z81+z83+z85+z86+z87+z90+z9\ 3383+z94, 1+z, 339 z2+z4+z5+z7+z9+z11+z14+z17+z19+z20+z21+z23+z24+z25+z27+z30+z35+z36+z38+z39+z\ 34041+z43+z50+z51+z53+z54+z55+z57+z59, 341 1+z+z5+z7+z8+z11+z12+z15+z17+z22+z23+z24+z27+z28+z29+z31+z34+z35+z37+z38+z39\ 342+z42+z47+z48+z51+z52+z53, 343 1+z2+z3+z4+z7+z8+z9+z10+z11+z16+z18+z19+z20+z21+z23+z26+z27+z31+z32+z34+z36+\ 344z37+z39+z40+z41+z42+z45+z46+z47+z49+z50+z51+z53+z54+z56+z57+z58, 345 z+z2+z3+z6+z7+z9+z11+z13+z17+z19+z21+z22+z23+z25+z27+z29+z30+z31+z36+z38+z39\ 346+z41+z45+z46+z48+z51+z53+z54+z55+z56+z59, 347 z2+z4+z6+z7+z9+z11+z12+z14+z16+z17+z19+z20+z21+z22+z25+z26+z31+z34+z35+z36+z\ 34837+z38+z44+z46+z48+z49+z51+z52+z57+z58+z59, <<an element of GF(2, 120)>>, 349 z+z3+z4+z6+z8+z10+z11+z15+z18+z19+z22+z24+z26+z28+z30+z31+z32+z33+z34+z36+z3\ 3507+z39+z40+z41+z42+z47+z48+z50+z53+z54+z56+z57+z59, 351 z4+z6+z7+z13+z14+z16+z17+z18+z19+z20+z21+z22+z24+z26+z28+z31+z33+z34+z35+z37\ 352+z39+z43+z47+z48+z51+z52+z54+z58, 353 1+z4+z6+z8+z9+z14+z16+z24+z28+z29+z32+z34+z38+z39+z40+z42+z47+z48+z50+z51+z5\ 3542+z54+z56+z57+z59, 355 1+z+z2+z3+z4+z7+z11+z14+z15+z16+z17+z18+z22+z25+z26+z29+z34+z35+z36+z37+z38+\ 356z40+z44+z45+z46+z47+z48+z50+z52+z55+z56+z57+z58, <<an element of GF(2, 120)>>, 357 z2+z4+z7+z10+z13+z15+z18+z20+z23+z25+z26+z38+z39+z41+z43+z44+z46+z48+z50+z51\ 358+z55+z56+z57+z59, <<an element of GF(2, 120)>>, 1+z, 359 z3+z6+z7+z8+z10+z14+z15+z18+z20+z22+z23+z25+z26+z27+z30+z31+z32+z33+z35+z36+\ 360z38+z42+z45+z46+z47+z50+z51+z54+z55+z57+z58+z60+z62+z63+z64+z65+z66+z67+z69+z7\ 3611+z73+z75, 362 1+z2+z3+z4+z7+z8+z9+z17+z18+z19+z21+z26+z29+z30+z31+z32+z34+z35+z36+z39+z43+\ 363z44+z45+z46+z48+z49+z52+z53+z56+z57+z60+z63+z64+z65+z69+z70+z71+z73+z74+z75, 364 1+z2+z5+z6+z7+z8+z10+z12+z13+z15+z16+z18+z19+z20+z26+z28+z33+z35+z37+z40+z41\ 365+z43+z44+z45+z46+z48+z49+z52+z53+z54+z55+z57+z60+z62+z65+z67+z72+z73+z74, 366 z2+z3+z5+z6+z8+z9+z11+z19+z23+z27+z31+z32+z34+z35+z36+z38+z42+z46+z48+z49+z5\ 3670+z53+z58+z59+z60+z62+z63+z65+z66+z67+z68+z69+z70+z74, 1+z, 368 1+z2+z3+z5+z9+z15+z22+z25+z26+z27+z28+z29+z30+z31+z32+z34+z36+z40+z42+z43+z4\ 3694+z48+z51+z52+z55+z56+z57+z60+z61+z62+z63+z64+z65+z67+z68+z69+z70+z71+z72+z75+\ 370z77+z79+z81+z83+z84+z86, 371 z+z2+z6+z8+z9+z10+z14+z15+z16+z19+z20+z22+z23+z26+z28+z30+z31+z33+z34+z37+z4\ 3721+z46+z50+z51+z54+z55+z56+z57+z58+z59+z60+z61+z63+z64+z66+z68+z71+z72+z76+z78+\ 373z81+z82+z83+z84+z85, 1+z, 374 2+2z+2z2+2z3+z4+2z5+z8+z9+2z10+z11+z12+z15+z16+2z18+2z19+2z20+z21, 375 1+2z+2z2+2z3+z4+z6+z8+2z11+z12+2z13+2z14+2z15+2z16+2z17+z18+z20+2z21+z22+z23\ 376+z24+2z25+z26+2z28+z30+2z31, 377 2z+z5+2z7+2z8+z9+z10+2z11+z12+z13+z14+z17+z18+2z19+2z20+2z23+2z26+2z28+2z31+\ 3782z33+2z35+z36+2z38+z39+z40+2z41+2z42+2z43, 379 1+z+z3+2z4+2z5+z6+2z9+z11+z12+z15+2z18+2z19+z20+2z21+z22+2z24+z25+2z27+z28+z\ 38029+2z34+z36+2z37+2z38+z40+2z41+2z43+2z45+z47+2z51+z52+2z54, 381 1+z+z3+z4+2z5+2z6+z9+z10+z11+z13+2z14+2z15+z16+2z17+2z18+z19+2z22+2z23+2z24+\ 382z26+z28+z30+z31+2z33+z34+z35+z37+2z38+z40+2z41+z42+z44+2z45+z46+2z47+z49+2z50+\ 383z51+2z52+z54+2z55+z56+z57+z58+z59+2z61+z62+z64, 384 2+z+z5+z6+2z9+2z11+2z13+z14+z16+2z20+z23+2z24+z27+z28+2z29+2z30+z31+2z32+2z3\ 3854+2z35+z36+2z37+z38+z39+2z40+2z41+z42+z45+2z46+z47+2z49+2z51+2z52+2z55+z56+2z5\ 3867+z58+z61+2z63+z64+2z65+2z67+2z69+2z70+z71+z72+z73+z75+2z76, 1+z, 387 z+2z2+z3+z4+2z7+z8+2z9+2z10+z12+z13+z14+2z15+z17+z18+2z19, 388 z4+z5+2z6+2z7+z9+z10+2z12+z14+z15+z17+2z18+2z19+2z20+z21+2z22+2z25+z26+z28+z\ 38930+z31+z32+z33+2z35+2z37+z38+z39+2z40+z41+2z42+z43+2z45+z47+z48+z49+2z50+z52+2\ 390z54+z55+z56+2z58+2z59, 391 2+2z2+z3+z4+z5+2z6+2z7+z11+z12+2z13+2z14+2z15+z16+2z17+2z18+2z19, 392 z2+2z4+2z5+2z6+z8+2z11+z12+2z16+2z19, 393 2+z+2z4+z6+z7+z8+2z9+2z10+2z11+z12+z13+2z14+z15+z18+2z19+2z21+z22+2z24+2z25+\ 3942z26+2z27+2z29+2z30+2z31+z32+z33+2z34+2z35+z36+z38+2z39+z40+2z41+z48+2z50+2z51\ 395+2z52+2z55+2z56, 396 2+z+2z7+2z8+2z9+2z10+2z11+2z12+z13+2z14+z15+2z16+2z17+z18+2z20+2z21+2z22+z24\ 397+2z25+2z26+2z28+z29+2z30+2z32+z33+z34+z36+2z38+z39, 398 z+2z3+z4+z7+2z8+z10+2z11+z12+2z13+2z14+2z15+2z17+2z18+z19, 399 2z+2z2+z3+z4+z5+2z8+2z9+2z11+2z12+2z14+z16+z17+2z18+2z19+z21+z22+2z23+z25+2z\ 40026+2z28+2z29+z30+2z36+2z37+2z38+z39+z40+2z41+z42+2z44+2z46+z47+2z48+2z49+2z50+\ 4012z52+z55+z57+z58+2z59, 402 2z+2z2+2z3+2z6+2z7+z8+2z9+2z10+z11+2z13+z14+z15+z16+z17+z19+z20+2z21+z22+z23\ 403+z24+2z25+z26+z27+z28+2z29+2z31+z32+2z33+z34+2z35+z36+z37+2z39+z40+2z41+z44+2z\ 40446+z47+2z49+2z51+z52+2z53+z55+2z56, 1+z, 405 1+z2+z4+z5+2z6+z7+2z8+z9+z11+2z13+z14+z15+2z16+z17+z18+2z19+z20+2z21+2z22+z2\ 4063+z25+z27+2z28+z29+z31+2z35+z36+2z37+z38+z39+2z40+z42+2z43+z45+z46+2z47+2z49+2\ 407z51+z52+z53+2z55+z58+2z59, 408 2+z+z2+z3+2z4+z5+z6+2z7+2z9+2z10+2z11+2z12+z16+2z17+2z18+2z19+2z21+2z25+2z26\ 409+z27+2z28+z29+z30+2z31+2z34+2z35+2z36+z37+2z38+z39+2z40+z42+z43+z46+2z47+z48+z\ 41049+2z52+z53+z55+2z57+z58+z59, 411 2+z+2z3+z5+z7+z8+z9+2z10+2z12+2z13+z14+z19+2z20+2z22+z23+2z26+z27+2z28+z29+2\ 412z30+2z32+z33+2z34+z35+2z37+z38+z40+2z41+z42+2z43+z44+z45+2z46+z47+2z48+2z49+z5\ 4131+2z53+z56+2z57+z58+2z59, 414 1+z3+2z4+z5+2z7+2z8+2z9+2z10+z11+z12+z13+2z14+2z18+z20+2z24+2z25+2z28+z29+z3\ 4150+z31+2z32+2z33+2z34+z35+2z36+z37+2z38+2z40+2z44+2z46+2z47+2z49+2z50+z52+z53+z\ 41657+z58+z59, 417 1+2z+z2+z3+z7+z8+z11+z12+z13+z14+z16+z17+z18+2z19+z20+2z22+2z24+2z25+z28+2z3\ 4180+z34+2z35+2z37+2z38+2z39+z40+z41+2z42+z45+z46+z47+z48+2z51+z53+z54+2z55+z56+2\ 419z57+2z58+2z59, 420 z+z3+z4+2z5+2z6+z8+2z10+2z11+z12+z15+z16+2z19+2z21+z22+2z25+z29+z30+z31+z32+\ 4212z33+z34+2z38+z39+2z41+2z43+z48+z49+2z50+2z53+z54+z55+z56+z57+2z58+2z59, 422 2+2z3+2z4+z5+2z6+2z8+z10+z11+2z12+z14+2z15+2z16+2z17+2z18+2z19+z20+2z21+2z22\ 423+2z23+z25+z27+z30+z31+2z32+2z33+2z34+z36+z37+z39+z40+z41+2z44+z45+2z47+2z48+2z\ 42449+z53+z54+z55+2z56+z59, 425 2+z4+z6+2z7+z8+2z13+2z16+2z17+z19+2z20+2z22+z23+z24+2z25+2z26+2z27+2z28+z33+\ 4262z35+z38+2z39+z40+z41+2z42+z44+z45+2z47+2z49+z50+2z51+2z52+z54+z55+z56+2z57+2z\ 42758+2z59, 428 2+z+z2+z3+z4+2z6+z9+z10+2z11+2z14+2z15+z16+z17+z20+z21+z22+z26+z27+z28+z29+z\ 42931+2z32+2z33+2z34+2z36+2z37+z38+2z41+2z42+z45+z46+z47+z50+z52+z53+z54+2z56+2z5\ 4307+2z58+2z59, 431 2+z+z2+2z3+2z4+z6+z7+z9+2z10+2z11+z12+2z14+z15+2z16+2z19+z21+z24+2z26+z28+z2\ 4329+z30+2z32+2z33+2z34+2z35+z37+z40+2z41+z42+z46+z48+2z49+z50+z53+2z54+2z55+2z56\ 433+2z58+z59, 14+z, 5+2z+16z2+8z3, 4z+13z2+8z3+4z4+8z6+16z7+9z8+14z9+16z10+11z11, 434 254+z, 254+z, 65504+z, 65534+z, 268435396+z, 4294967289+z, 435 1152921504606846881+z, 18446744073709551627+z ] 436gap> List(fieldpairs, pdd -> Z(pdd[1],pdd[2])*Z(pdd[1],pdd[3])); 437[ z, 1+z2+z4+z9+z10+z13+z14+z15+z16+z18+z20+z21+z24+z25+z29+z30+z31+z33, 438 1+z+z3+z9+z10+z11+z14+z19+z20+z21+z22+z23+z25+z26+z33+z35+z36+z37+z41+z43+z4\ 4396+z47+z49, 440 z+z3+z4+z5+z7+z10+z14+z15+z17+z19+z26+z28+z31+z32+z37+z40+z41+z44+z45+z47+z4\ 4418+z51+z53+z55+z57+z60+z62+z64+z65+z66+z67, 442 1+z3+z5+z6+z7+z9+z10+z11+z12+z13+z14+z16+z18+z19+z22+z26+z28+z29+z31+z34+z42\ 443+z44+z47+z51+z55+z56+z58+z60+z64+z68+z71+z72+z73+z74+z75+z76+z77+z80+z81+z82+z\ 44484, 445 1+z+z4+z6+z8+z10+z11+z13+z15+z16+z17+z19+z20+z23+z26+z31+z37+z38+z39+z42+z45\ 446+z46+z50+z51+z52+z56+z57+z62+z63+z65+z66+z69+z71+z72+z73+z76+z81+z83+z84+z85+z\ 44787+z88+z91+z93+z98+z100+z101, 448 1+z2+z4+z6+z8+z11+z13+z16+z17+z20+z21+z23+z24+z27+z28+z29+z32+z35+z36+z38+z4\ 4490+z48+z49+z51+z52+z54+z55+z56+z58+z59+z61+z68+z69+z70+z72+z75+z77+z78+z79+z80+\ 450z81+z87+z91+z92+z96+z101+z102+z107+z109+z111+z112+z113+z115+z118, z, 451 z+z2+z4+z5+z6+z7+z9+z10+z15+z18+z19+z20+z21+z22+z25+z30+z31, 452 z2+z3+z8+z13+z17+z19+z22+z23+z24+z27+z29+z31+z33+z37+z39+z40+z42+z45+z48+z51\ 453+z52+z54+z55+z58+z59+z60+z63+z64+z68+z69+z70+z76+z78+z79+z81+z82+z83+z86+z87+z\ 45488+z89+z93+z94+z95, 455 z2+z5+z6+z7+z9+z11+z13+z15+z16+z18+z19+z20+z21+z22+z23+z24+z25+z26+z30+z31, 456 z+z3+z6+z8+z10+z16+z18+z19+z25+z26+z28+z32+z35+z36+z40+z41+z42+z43+z44+z45+z\ 45747+z48+z49+z50+z51+z52+z53+z54+z55+z56+z57+z58+z60+z65+z67+z69+z71+z72+z74+z77\ 458+z83+z84+z88+z89+z91+z93+z94+z95, 1+z8+z9+z11+z13+z18+z20+z21+z22+z23+z30, 459 z+z2+z3+z4+z5+z6+z7+z8+z10+z11+z13+z15+z18+z20+z21+z24+z26+z27+z28+z29+z30+z\ 46032+z37+z38+z39+z40+z43+z46+z47+z48+z49+z52+z53+z54+z57+z62+z66+z67+z68+z70+z74\ 461+z77+z79+z80+z82+z83+z86+z87+z89+z90+z91+z93+z94+z95, 462 1+z4+z5+z6+z8+z9+z11+z12+z16+z17+z21+z24+z27+z29+z30+z31, 463 1+z+z3+z5+z6+z10+z11+z13+z14+z17+z18+z19+z20+z23+z25+z27+z29+z33+z34+z41+z42\ 464+z43+z45+z46+z47+z50+z51+z53+z54+z55+z56+z57+z60+z61+z62+z64+z67+z68+z70+z73+z\ 46575+z77+z81+z82+z84+z88+z89+z94, z, 466 1+z4+z6+z10+z15+z17+z18+z19+z20+z21+z24+z28+z30+z31+z32+z33+z34+z37+z40+z41+\ 467z45+z51+z52+z54+z55+z56+z58, 468 z+z6+z8+z9+z12+z13+z16+z18+z23+z24+z25+z28+z29+z30+z32+z35+z36+z38+z39+z40+z\ 46943+z48+z49+z52+z53+z54, 470 z+z2+z3+z4+z5+z8+z9+z10+z11+z12+z17+z19+z20+z21+z22+z24+z27+z28+z32+z33+z35+\ 471z37+z38+z40+z41+z42+z43+z46+z47+z48+z50+z51+z52+z54+z55+z57+z58+z59, 472 1+z2+z5+z7+z10+z14+z17+z18+z19+z20+z23+z24+z25+z28+z31+z33+z34+z36+z37+z40+z\ 47341+z44+z45+z46+z47+z49+z52+z54+z55+z56+z57, 474 1+z4+z7+z10+z13+z15+z18+z19+z20+z21+z23+z25+z27+z30+z33+z34+z35+z37+z38+z41+\ 475z42+z44+z47+z49+z50+z52+z53+z58+z59, 476 1+z2+z3+z4+z5+z6+z7+z12+z16+z17+z19+z20+z22+z26+z27+z28+z29+z30+z33+z36+z37+\ 477z38+z40+z41+z45+z46+z47+z48+z52+z53+z54+z56+z57+z59+z62+z64+z69+z73+z75+z85+z8\ 4787+z89+z92+z95+z100+z101+z104+z105+z106+z108+z110+z113+z115+z118, 479 1+z2+z3+z7+z8+z9+z11+z16+z17+z20+z22+z23+z26+z27+z29+z30+z31+z35+z36+z37+z38\ 480+z39+z40+z43+z44+z45+z48+z49+z51+z54+z55+z57+z58, 481 z2+z5+z7+z8+z14+z15+z17+z18+z19+z20+z21+z22+z23+z25+z27+z29+z32+z34+z35+z36+\ 482z38+z40+z44+z48+z49+z52+z53+z55+z59, 483 1+z+z3+z4+z7+z8+z9+z10+z12+z15+z19+z22+z26+z29+z32+z34+z35+z36+z40+z42+z43+z\ 48444+z45+z48+z49+z51+z52+z53+z55+z57+z58, 485 z+z3+z4+z5+z8+z12+z15+z16+z17+z18+z19+z23+z26+z27+z30+z35+z36+z37+z38+z39+z4\ 4861+z45+z46+z47+z48+z49+z51+z53+z56+z57+z58+z59, <<an element of GF(2, 120)>>, 487 1+z4+z11+z12+z14+z16+z17+z21+z22+z24+z25+z27+z30+z32+z33+z34+z36+z40+z41+z47\ 488+z49+z51+z52+z56+z57+z58, <<an element of GF(2, 120)>>, z, 489 1+z+z4+z5+z7+z8+z9+z11+z14+z16+z20+z21+z25+z26+z28+z29+z32+z35+z38+z39+z43+z\ 49046+z47+z48+z51+z52+z55+z56+z58+z59+z61+z63+z64+z65+z66+z67+z68+z70+z72+z74, 491 1+z3+z4+z8+z9+z10+z14+z15+z18+z22+z23+z24+z25+z29+z30+z32+z34+z38+z40+z44+z4\ 4925+z46+z47+z49+z50+z53+z54+z57+z58+z61+z64+z65+z66+z70+z71+z72+z74+z75, 493 z+z2+z3+z6+z7+z8+z9+z11+z13+z14+z16+z17+z19+z20+z21+z27+z29+z34+z36+z38+z41+\ 494z42+z44+z45+z46+z47+z49+z50+z53+z54+z55+z56+z58+z61+z63+z66+z68+z73+z74+z75, 495 z2+z3+z4+z6+z7+z9+z10+z12+z20+z24+z28+z32+z33+z35+z36+z37+z39+z43+z47+z49+z5\ 4960+z51+z54+z59+z60+z61+z63+z64+z66+z67+z68+z69+z70+z71+z75, z, 497 1+z2+z4+z5+z6+z7+z8+z11+z12+z13+z14+z20+z23+z27+z29+z31+z32+z33+z35+z37+z41+\ 498z43+z44+z45+z49+z52+z53+z56+z57+z58+z61+z62+z63+z64+z65+z66+z68+z69+z70+z71+z7\ 4992+z73+z76+z78+z80+z82+z84+z85, 500 z3+z7+z9+z10+z11+z15+z16+z17+z20+z21+z23+z24+z27+z29+z31+z32+z34+z35+z38+z42\ 501+z47+z51+z52+z55+z56+z57+z58+z59+z60+z61+z62+z64+z65+z67+z69+z72+z73+z77+z79+z\ 50282+z83+z84+z85+z86, 2z, 1+z+2z2+2z3+z4+z5+z9+2z12+2z14+z17+z18, 503 1+2z+2z2+z3+2z4+z6+z7+2z8+2z9+2z10+z11+2z13+2z14+2z16+z18+z20+z21+2z22+2z24+\ 5042z25+z26+z27+2z31, 505 2z+2z2+z3+z6+2z7+z8+2z11+2z12+2z13+z16+2z17+z18+2z22+2z24+2z26+z27+z28+z29+2\ 506z30+2z31+2z32+z33+z37+z38+2z41, 507 2z2+2z4+z5+z6+2z9+2z11+z12+z13+z16+z17+z18+2z19+z21+z23+z24+z27+z28+2z31+z32\ 508+2z33+2z34+2z36+2z39+2z41+2z44+z45+2z46+2z47+2z48+2z51+2z52+2z53+2z54, 509 1+z+z2+2z3+z5+z6+2z8+z9+2z13+2z16+2z17+2z18+2z19+z20+z21+z22+2z23+z24+2z25+z\ 51026+2z27+z28+z33+2z34+2z35+z36+2z38+2z39+z40+2z41+z42+z44+z45+z47+z48+z49+z50+2\ 511z51+2z52+z53+2z54+2z55+z56+2z57+2z59+2z60+2z61+2z62+2z63, 512 1+2z+z5+2z8+2z9+z12+z13+2z16+2z17+z19+z20+z24+z25+z27+z29+z30+z31+z32+2z33+2\ 513z34+z35+2z38+z39+2z42+z44+z45+2z46+z48+z49+z50+z52+2z54+2z55+2z57+z58+z59+2z62\ 514+z64+2z66+z68+z69+z71+2z72+z73+z75, 2z, 1+2z+2z3+z9+2z14+2z15+z16+2z18+2z19, 515 2+2z+2z2+z6+z7+2z10+z17+z19+2z20+2z21+z24+2z25+2z27+z28+z29+2z30+z31+2z32+2z\ 51635+z36+2z37+z38+2z40+2z41+2z42+z44+2z46+z47+z49+z51+z52+z54+z56+2z57+2z58+z59, 517 1+z2+2z3+2z6+z7+2z9+2z10+2z11+2z12+z14+z15+z16+2z17+z18+z19, 518 1+2z+z2+z4+2z5+z6+z7+2z8+z9+2z10+2z11+z12+z17, 519 1+z+2z2+2z3+z5+2z6+z7+2z10+2z11+2z12+2z13+z14+z15+z16+2z17+2z18+z20+2z21+2z2\ 5203+2z24+2z25+z28+2z30+z31+2z32+z34+2z36+z37+z41+2z42+2z43+2z44+z45+z47+z48+2z49\ 521+z53+z54+2z55+z56+2z59, 522 1+z+2z2+z3+2z6+z7+z10+2z11+z13+2z14+z15+z16+z17+2z18+z19+z21+z22+z23+z24+2z2\ 5235+z28+2z29+2z31+2z33+z35+z36+z38+2z39, 524 2+z+2z3+z5+2z9+z10+z12+z13+z14+z15+z16+z18+z19, 525 2+z+2z4+2z6+2z7+z8+2z10+z11+z12+z13+z16+z18+2z19+z20+2z22+z23+z25+2z26+2z28+\ 526z29+z30+2z31+2z32+2z33+z37+z38+z40+z41+z42+2z46+2z47+2z48+z50+z51+2z52+2z53+2z\ 52754+2z55+z56+z57, 528 2+z+2z2+2z4+2z6+2z7+2z9+2z11+2z12+2z13+z14+z15+2z16+2z17+2z18+2z20+2z21+z22+\ 529z23+2z24+2z25+z28+z29+z30+2z31+z32+2z33+2z34+2z35+z36+2z37+2z39+2z40+z41+2z42+\ 5302z43+2z44+2z45+z46+z47+2z48+z49+z50+z51+z52+z53+2z54+z57+2z58, 2z, 531 1+2z+2z2+z4+z5+z7+z9+z10+z11+2z12+z17+2z18+2z19+z21+2z22+z23+z27+z29+z30+z32\ 532+z33+2z34+2z35+2z36+2z37+2z38+z40+2z41+2z43+2z46+2z47+z48+z50+z52+2z53+2z54+z5\ 5336+2z59, 534 2+z+2z2+z3+z4+2z5+z6+2z7+2z10+z12+z13+z14+2z15+2z16+2z17+z18+z19+2z20+z21+2z\ 53524+z28+z29+2z31+2z32+2z33+z34+2z35+z37+z38+2z43+2z47+z48+2z49+2z50+z53+2z54+2z\ 53656+z58+2z59, 537 1+z+z2+z3+2z4+2z5+2z9+z10+2z11+z13+z16+z20+z22+z23+z26+2z27+z29+z30+z31+2z32\ 538+2z33+z34+2z38+2z40+z42+2z43+2z45+2z46+z47+2z48+z49+z50+2z52+z54+2z57+z58+2z59 539 , 540 2+2z+2z3+z4+2z5+z6+z9+2z10+2z12+2z13+2z16+z19+z20+2z22+2z24+z25+2z27+2z28+z2\ 5419+2z31+2z34+2z35+z36+z37+z38+z40+z44+z45+z47+z48+z50+z51+2z53+2z54+2z58+2z59, 542 1+2z+2z5+z6+2z9+2z10+z11+2z12+2z13+z14+z16+2z17+2z18+2z19+z21+z22+z23+z24+z2\ 5435+2z26+z27+z28+2z29+2z30+z31+2z32+z33+2z34+z35+2z36+2z38+2z39+2z42+z43+2z44+2z\ 54446+2z47+2z48+2z49+z52+2z54+2z55+z56+2z57+z58+z59, 545 1+z2+z3+z5+2z6+z7+z8+2z9+2z10+2z11+z12+2z13+2z14+z15+2z17+2z21+2z22+2z23+z24\ 546+2z26+z27+z28+z30+2z31+z32+z35+z36+z38+2z39+z40+z41+z42+2z49+2z50+z51+z54+2z55\ 547+2z56+2z57+2z58+z59, 548 2+z+2z3+2z5+z6+z7+2z8+z9+z10+z11+2z12+z13+z14+z15+z17+z18+z19+2z20+z23+z26+2\ 549z27+z28+z30+2z31+2z34+2z35+2z36+2z37+z38+2z39+z41+2z42+z44+z45+2z46+z48+z49+z5\ 5500+2z54+2z55+2z56+z57, 551 1+z+2z2+z3+z4+z5+z6+2z7+2z8+2z9+2z10+z11+z15+z16+z17+z18+z20+z22+z23+2z25+2z\ 55226+2z27+2z28+z29+2z30+2z32+z33+z34+2z35+2z36+z38+2z42+z43+2z44+2z45+2z46+z48+z\ 55350+2z51+z52+z53+2z55+2z56+2z57+z58+z59, 554 1+z+z2+z5+z6+z7+z8+z10+z12+2z14+2z15+2z16+2z17+2z18+2z20+z21+2z23+z24+z26+2z\ 55529+z30+z32+2z33+z36+z37+2z38+2z40+z41+z42+z43+2z44+2z46+2z47+2z48+2z51+2z53+2z\ 55654+2z55+z57+z58+z59, 557 2+z+2z2+z3+2z5+2z6+2z7+z8+z12+2z13+z14+z16+z17+2z20+z21+z22+2z24+2z25+2z26+2\ 558z28+2z29+2z31+z32+2z34+2z35+z38+2z39+z40+z41+z42+2z43+z44+2z47+2z49+z50+2z51+2\ 559z54+z55+z56+z57+z59, 3z, 7+7z+4z2+z3, 560 5+12z+z2+11z3+3z5+8z6+z7+11z8+10z9+16z10+7z11, 3z, 3z, 17z, 3z, 3z, 2z, 2z, 561 2z ] 562gap> List(fieldpairs, pdd -> Z(pdd[1],pdd[2])/Z(pdd[1],pdd[3])); 563[ z, z+z4+z7+z8+z9+z10+z13+z14+z17+z18+z19+z23+z24+z25+z26+z27+z28+z29+z32, 564 1+z+z9+z10+z12+z13+z20+z21+z26+z28+z30+z31+z32+z33+z34+z37+z39+z46+z48+z49+z\ 56550, 566 z+z5+z6+z10+z11+z12+z15+z16+z20+z24+z25+z28+z34+z36+z37+z38+z40+z43+z44+z45+\ 567z46+z47+z48+z49+z53+z55+z57+z58+z59+z63+z64, 568 z+z2+z5+z8+z9+z13+z14+z15+z16+z20+z21+z22+z24+z26+z27+z28+z29+z30+z31+z32+z3\ 5693+z38+z41+z42+z44+z46+z48+z49+z50+z53+z55+z59+z62+z63+z65+z66+z68+z70+z72+z75+\ 570z77+z78+z79+z80+z82+z83, 571 1+z2+z7+z8+z9+z10+z11+z12+z13+z16+z17+z19+z20+z22+z27+z28+z29+z30+z34+z36+z3\ 5727+z39+z40+z41+z45+z47+z51+z52+z54+z56+z58+z59+z60+z63+z65+z67+z68+z69+z72+z74+\ 573z81+z84+z88+z89+z90+z93+z95+z97+z101, 574 1+z2+z3+z4+z8+z10+z11+z12+z14+z15+z16+z21+z22+z24+z32+z33+z34+z36+z39+z40+z4\ 5754+z50+z51+z52+z54+z62+z63+z65+z68+z70+z71+z74+z77+z80+z88+z89+z92+z94+z101+z10\ 5762+z104+z107+z108+z109+z110+z111+z118, z, 577 z2+z4+z5+z6+z7+z9+z10+z15+z18+z19+z20+z21+z22+z25+z30+z31, 578 1+z3+z8+z9+z10+z12+z13+z16+z17+z18+z20+z23+z24+z28+z29+z31+z34+z36+z38+z40+z\ 57942+z43+z46+z47+z48+z51+z55+z56+z57+z59+z63+z64+z65+z66+z69+z71+z72+z73+z77+z79\ 580+z81+z82+z83+z85+z86+z87+z88+z90+z91+z92+z93+z94+z95, 581 z+z2+z4+z6+z8+z9+z12+z16+z17+z18+z20+z21+z23+z24+z26+z28+z29+z30, 582 1+z3+z6+z7+z8+z10+z11+z13+z15+z16+z17+z18+z19+z21+z22+z29+z31+z32+z36+z37+z3\ 5838+z39+z40+z41+z42+z45+z46+z47+z48+z49+z50+z51+z53+z55+z58+z61+z62+z65+z67+z68+\ 584z72+z73+z76+z78+z81+z84+z87+z88+z92+z93+z94+z95, 585 z2+z7+z8+z11+z14+z16+z17+z19+z21+z24+z25+z27+z28+z30+z31, 586 1+z2+z3+z5+z9+z11+z13+z15+z16+z17+z18+z19+z20+z23+z26+z27+z33+z39+z40+z41+z4\ 5875+z46+z48+z49+z50+z51+z53+z55+z56+z59+z60+z61+z62+z63+z64+z65+z67+z68+z69+z70+\ 588z73+z77+z82+z83+z84+z88+z89+z90+z91+z93+z94+z95, 589 1+z3+z4+z5+z7+z10+z11+z13+z14+z15+z16+z18+z19+z20+z22+z23+z24+z26+z29+z30+z3\ 5901, 591 z+z2+z7+z10+z11+z13+z14+z18+z20+z21+z24+z25+z27+z30+z33+z34+z37+z38+z39+z41+\ 592z43+z44+z46+z48+z50+z51+z52+z55+z56+z58+z59+z63+z65+z66+z67+z68+z69+z71+z76+z7\ 5938+z80+z81+z83+z88+z89+z90+z91+z92+z94, z, 594 1+z+z4+z6+z10+z15+z17+z18+z19+z20+z21+z24+z28+z30+z31+z32+z33+z34+z37+z40+z4\ 5951+z45+z51+z52+z54+z55+z56+z58, 596 z+z2+z5+z6+z7+z8+z10+z11+z12+z13+z15+z17+z19+z20+z22+z23+z24+z25+z26+z27+z29\ 597+z32+z34+z38+z39+z41+z43+z50+z52+z56+z57, 598 1+z2+z3+z5+z6+z7+z8+z11+z14+z16+z19+z20+z22+z23+z26+z27+z30+z31+z32+z36+z42+\ 599z43+z44+z45+z47+z48+z50+z52+z58+z59, 600 1+z4+z6+z7+z8+z9+z10+z13+z17+z20+z21+z25+z26+z35+z37+z38+z44+z45+z47+z48+z56\ 601+z57+z58+z59, 602 1+z2+z4+z5+z6+z7+z9+z11+z16+z21+z22+z24+z26+z27+z31+z32+z33+z35+z36+z37+z45+\ 603z48+z49+z50+z51+z52+z53+z55+z57+z58, 604 1+z3+z5+z8+z9+z11+z13+z16+z17+z20+z21+z22+z26+z27+z28+z29+z32+z33+z35+z42+z4\ 6056+z47+z49+z50+z51+z52+z55+z60+z61+z62+z63+z66+z67+z69+z70+z72+z73+z74+z78+z80+\ 606z81+z82+z83+z87+z88+z92+z93+z96+z99+z100+z102+z103+z105+z106+z107+z108+z115+z1\ 60716, 608 z+z2+z3+z4+z6+z8+z9+z10+z11+z12+z13+z14+z15+z17+z20+z24+z25+z28+z30+z37+z40+\ 609z41+z42+z45+z46+z48+z50+z51+z54+z57+z58, 610 z2+z3+z5+z6+z7+z10+z11+z13+z15+z16+z21+z22+z26+z29+z30+z32+z33+z35+z36+z37+z\ 61138+z43+z45+z46+z47+z49+z50+z51+z53+z54+z56+z58, 612 z2+z3+z4+z6+z9+z12+z13+z14+z16+z24+z25+z26+z30+z31+z32+z34+z37+z40+z42+z43+z\ 61344+z45+z46+z49+z50, 614 z3+z8+z9+z13+z14+z17+z19+z22+z23+z24+z25+z28+z29+z32+z33+z36+z38+z40+z41+z42\ 615+z43+z44+z46+z47+z51+z53+z54+z57, 616 z2+z3+z4+z7+z12+z17+z19+z20+z21+z22+z23+z28+z29+z30+z31+z32+z34+z36+z37+z38+\ 617z41+z50+z51+z57+z58+z60+z61+z63+z66+z67+z68+z69+z73+z74+z75+z76+z79+z81+z82+z8\ 6183+z85+z87+z89+z93+z94+z97+z98+z99+z100+z101+z102+z104+z106+z107+z110+z112+z116\ 619+z117, 620 z2+z4+z5+z6+z8+z10+z11+z12+z16+z17+z18+z20+z21+z23+z24+z25+z27+z30+z34+z36+z\ 62138+z39+z41+z43+z44+z45+z48+z49+z51+z53+z54+z56+z59, 622 1+z+z2+z6+z11+z13+z17+z18+z22+z23+z24+z26+z31+z32+z33+z35+z40+z44+z45+z47+z4\ 6238+z49+z51+z55+z57+z59+z62+z66+z67+z69+z71+z74+z76+z77+z79+z81+z82+z83+z88+z89+\ 624z90+z93+z94+z96+z97+z98+z99+z102+z104+z105+z106+z108+z111+z112+z114+z118+z119, 625 z, 626 1+z4+z5+z7+z8+z9+z11+z14+z16+z20+z21+z25+z26+z28+z29+z32+z35+z38+z39+z43+z46\ 627+z47+z48+z51+z52+z55+z56+z58+z59+z61+z63+z64+z65+z66+z67+z68+z70+z72+z74, 628 z2+z4+z7+z8+z9+z11+z12+z13+z15+z16+z17+z19+z22+z23+z25+z26+z31+z34+z35+z37+z\ 62938+z41+z42+z44+z45+z47+z50+z53+z54+z55+z56+z57+z58+z61+z62+z64+z67+z68+z69+z70\ 630+z71+z72+z73+z75, 631 1+z2+z3+z8+z9+z10+z11+z13+z17+z19+z21+z25+z26+z27+z28+z29+z31+z32+z35+z36+z4\ 6321+z43+z47+z51+z52+z59+z60+z61+z63+z64+z67+z69+z75, 633 z2+z3+z8+z9+z11+z14+z15+z16+z20+z21+z22+z24+z27+z28+z30+z33+z34+z39+z40+z41+\ 634z44+z46+z48+z50+z51+z53+z58+z61+z62+z63+z64+z65+z66+z67+z68+z69+z70+z71+z72+z7\ 6353+z74+z75, z, 636 1+z2+z4+z5+z6+z8+z11+z13+z15+z16+z18+z20+z24+z25+z27+z29+z30+z31+z33+z37+z40\ 637+z42+z44+z45+z48+z49+z50+z53+z54+z55+z58+z59+z62+z63+z65+z67+z68+z69+z70+z71+z\ 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69633+z35+2z37+2z38+z40+2z41+z44+z45+2z46+2z48+2z49+2z50+z52+z56+2z58+z59, 697 2z+2z2+2z4+z5+2z7+z8+2z9+2z10+2z12+z14+2z15+z16+z17+2z18+z19+z20+z21+2z22+z2\ 6985+2z26+z28+2z29+z30+z32+z33+2z34+z35+2z36+z39+z40+2z41+z42+z44+2z46+z47+2z48+z\ 69949+z51+2z52+z53+z54+z57+z58+2z59, 6z, 9+15z+10z2+11z3, 700 5+7z+14z2+13z3+10z4+10z5+4z6+13z7+5z8+12z9+3z10+7z11, 86z, 86z, 42396z, 701 21846z, 178956933z, 2147483646z, 576460752303423442z, 9223372036854775815z ] 702gap> ForAll(fieldsizes, pd -> ForAll(DivisorsInt(pd[2]), d2 -> 703> Z(pd[1],pd[2])^((pd[1]^pd[2]-1)/(pd[1]^d2-1)) = Z(pd[1],d2) )); 704true 705gap> AsInternalFFE(0*Z(2,10)); 7060*Z(2) 707gap> AsInternalFFE(Z(2,10)^0); 708Z(2)^0 709gap> AsInternalFFE(Z(2,10)); 710Z(2^10) 711gap> AsInternalFFE(0*Z(7,6)); 7120*Z(7) 713gap> AsInternalFFE(Z(7,6)^0); 714Z(7)^0 715gap> AsInternalFFE(Z(7,6)); 716fail 717gap> AsInternalFFE(0*Z(65537,2)); 718fail 719gap> AsInternalFFE(Z(65537,2)^0); 720fail 721gap> AsInternalFFE(Z(65537,2)); 722fail 723gap> SetInfoLevel(InfoPrimeInt,iPI); 724gap> SetInfoLevel(InfoFactor,iF); 725gap> if IsBound(InfoFactInt) then SetInfoLevel(InfoFactInt,iFI); fi; 726gap> SetInfoLevel(InfoWarning,iW); 727gap> STOP_TEST( "ffeconway.tst", 1); 728