From 12758616b2968bffc5673dd5a7d0165c71104dfc Mon Sep 17 00:00:00 2001 From: Steve Linton Date: Tue, 13 Nov 2018 23:11:59 +0000 Subject: [PATCH] Adjust test files. Hopefully these versions are safe on 32 and 64 bit --- hpcgap/tst/testinstall/comprvec.tst | 10 +- tst/testbugfix/00016.tst | 4 +- tst/testbugfix/2007-01-22-t00169.tst | 4 +- tst/testbugfix/2007-02-14-t00170.tst | 6 +- tst/testbugfix/2007-02-23-t00172.tst | 4 +- tst/testbugfix/2007-03-12-t00173.tst | 2 +- tst/testbugfix/2007-03-20-t00175.tst | 6 +- tst/testbugfix/2008-03-26-t00206.tst | 4 +- tst/testbugfix/2008-08-13-t00200.tst | 6 +- tst/testinstall/ffeconway.tst | 356 +++++++++++++-------------- tst/testinstall/hpc/tasks.tst | 2 +- tst/testinstall/zmodnz.tst | 68 ++--- 12 files changed, 235 insertions(+), 237 deletions(-) diff --git a/hpcgap/tst/testinstall/comprvec.tst b/hpcgap/tst/testinstall/comprvec.tst index 3543e1bbfa9..bcce999f901 100644 --- a/hpcgap/tst/testinstall/comprvec.tst +++ b/hpcgap/tst/testinstall/comprvec.tst @@ -63,8 +63,9 @@ gap> t:=CopyToVectorRep(v,4); [ Z(2)^0, Z(2)^0, Z(2)^0, 0*Z(2) ] gap> RepresentationsOfObject(t); [ "IsDataObjectRep", "Is8BitVectorRep" ] -gap> F:=GF(2^17);; -gap> v:=Filtered(F,x -> x in GF(256)); +gap> F:=GF(2^25);; +gap> p:=PrimitiveElement(F);; +gap> v:=[0*p, p^0]; [ 0z, z0 ] gap> IS_VECFFE(v); false @@ -82,8 +83,9 @@ gap> z1=z2; true gap> List([z,z1,z2],x -> IsIdenticalObj(v,x)); [ false, false, false ] -gap> F:=GF(41^3);; -gap> v:=Filtered(F,x -> x in GF(41));; +gap> F:=GF(41^5);; +gap> p:=PrimitiveElement(F)^((41^5-1)/(41-1));; +gap> v:=Concatenation([0*p],List([0..39],x->p^x));; gap> IS_VECFFE(v); false gap> IsFFECollection(v); diff --git a/tst/testbugfix/00016.tst b/tst/testbugfix/00016.tst index 68872886668..c24ef7ea724 100644 --- a/tst/testbugfix/00016.tst +++ b/tst/testbugfix/00016.tst @@ -1,6 +1,6 @@ ## bug 2 for fix 4. -gap> 1 * One( Integers mod NextPrimeInt( 2^16 ) ); -ZmodpZObj( 1, 65537 ) +gap> 1 * One( Integers mod NextPrimeInt( 2^24 ) ); +ZmodpZObj( 1, 16777259 ) gap> f:=FreeGroup("a","b");;g:=f/[Comm(f.1,f.2),f.1^5,f.2^7];;Pcgs(g);; gap> n:=Subgroup(g,[g.2]);; m:=ModuloPcgs(g,n);; gap> ExponentsOfPcElement(m,m[1]); diff --git a/tst/testbugfix/2007-01-22-t00169.tst b/tst/testbugfix/2007-01-22-t00169.tst index d1ab12fc47a..a320a30fe6d 100644 --- a/tst/testbugfix/2007-01-22-t00169.tst +++ b/tst/testbugfix/2007-01-22-t00169.tst @@ -1,7 +1,7 @@ # 2007/01/22 (SL) gap> F := GF(7,3);; -gap> F1 := GF(F,2);; +gap> F1 := GF(F,4);; gap> a := PrimitiveRoot(F1);; gap> B := Basis(F1);; gap> Coefficients(B,a^0); -[ z0, 0z ] +[ z0, 0z, 0z, 0z ] diff --git a/tst/testbugfix/2007-02-14-t00170.tst b/tst/testbugfix/2007-02-14-t00170.tst index 0e4cb708419..752b23020b5 100644 --- a/tst/testbugfix/2007-02-14-t00170.tst +++ b/tst/testbugfix/2007-02-14-t00170.tst @@ -1,6 +1,6 @@ # 2007/02/14 (SL) -gap> m:= [ [ Z(2,18)^0, 0*Z(2,18) ], -> [ Z(2)^0+Z(2,18)+Z(2,18)^2+Z(2,18)^7+Z(2,18)^8+Z(2,18)^10+Z(2,18)^12 -> +Z(2,18)^14+Z(2,18)^15, Z(2,18)^0 ] ];; +gap> m:= [ [ Z(2,28)^0, 0*Z(2,28) ], +> [ Z(2)^0+Z(2,28)+Z(2,28)^2+Z(2,28)^7+Z(2,28)^8+Z(2,28)^10+Z(2,28)^12 +> +Z(2,28)^14+Z(2,28)^15, Z(2,28)^0 ] ];; gap> KroneckerProduct( [[Z(2)]], m ); [ , [ 1+z+z2+z7+z8+z10+z12+z14+z15, z0 ] ] diff --git a/tst/testbugfix/2007-02-23-t00172.tst b/tst/testbugfix/2007-02-23-t00172.tst index de74e5f28ee..114b191b891 100644 --- a/tst/testbugfix/2007-02-23-t00172.tst +++ b/tst/testbugfix/2007-02-23-t00172.tst @@ -1,3 +1,3 @@ # 2007/02/23 (Max) -gap> Enumerator(GF(74761)); - +gap> Enumerator(GF(33554467)); + diff --git a/tst/testbugfix/2007-03-12-t00173.tst b/tst/testbugfix/2007-03-12-t00173.tst index e28078f81cc..d96c9c43b27 100644 --- a/tst/testbugfix/2007-03-12-t00173.tst +++ b/tst/testbugfix/2007-03-12-t00173.tst @@ -1,5 +1,5 @@ # 2007/03/12 (SL) -gap> z := Z(3,12)-Z(3,12); +gap> z := Z(3,20)-Z(3,20); 0z gap> DegreeFFE(z); 1 diff --git a/tst/testbugfix/2007-03-20-t00175.tst b/tst/testbugfix/2007-03-20-t00175.tst index 9bf015725a5..7af2da8f0c2 100644 --- a/tst/testbugfix/2007-03-20-t00175.tst +++ b/tst/testbugfix/2007-03-20-t00175.tst @@ -1,5 +1,5 @@ # 2007/03/20 (SL) -gap> x := Z(2,18)^((2^18-1)/511);; -gap> b := Basis(GF(512));; +gap> x := Z(2,28)^((2^28-1)/16383);; +gap> b := Basis(GF(2^14));; gap> Coefficients(b,x); -[ 0z, z0, 0z, 0z, 0z, 0z, 0z, 0z, 0z ] +[ 0z, z0, 0z, 0z, 0z, 0z, 0z, 0z, 0z, 0z, 0z, 0z, 0z, 0z ] diff --git a/tst/testbugfix/2008-03-26-t00206.tst b/tst/testbugfix/2008-03-26-t00206.tst index caf42e01aa5..b81da6846ea 100644 --- a/tst/testbugfix/2008-03-26-t00206.tst +++ b/tst/testbugfix/2008-03-26-t00206.tst @@ -1,3 +1,3 @@ # 2008/03/26 (TB) -gap> FrobeniusCharacterValue( E(55), 2 ); -z+z2+z3+z4+z5+z6+z8+z10+z12+z13+z14+z16+z17+z19 +gap> FrobeniusCharacterValue( E(55), 2 ) = Z(2,20)^19065; +true diff --git a/tst/testbugfix/2008-08-13-t00200.tst b/tst/testbugfix/2008-08-13-t00200.tst index bd6367d48f5..0ae1a32a41d 100644 --- a/tst/testbugfix/2008-08-13-t00200.tst +++ b/tst/testbugfix/2008-08-13-t00200.tst @@ -3,13 +3,11 @@ gap> Z(3,20) + Z(3,20)^0; 1+z gap> AA := Z(3^10)^30683; Z(3^10)^30683 -gap> BB := Z(3)^0+Z(3^15)^3+Z(3^15)^4+2*Z(3^15)^5+2*Z(3^15)^8+2*Z(3^15)^10+2*Z(3^15)^11+Z(3^15)^13; -1+z3+z4+2z5+2z8+2z10+2z11+z13 +gap> BB := Z(3)^0+Z(3^15)^3+Z(3^15)^4+2*Z(3^15)^5+2*Z(3^15)^8+2*Z(3^15)^10+2*Z(3^15)^11+Z(3^15)^13;; gap> AA=BB; false gap> RT := Z(3^6); Z(3^6) -gap> DD := Z(3^12)+Z(3^12)^2+2*Z(3^12)^3+2*Z(3^12)^4+Z(3^12)^5+Z(3^12)^6+Z(3^12)^7+Z(3^12)^8+2*Z(3^12)^9; -z+z2+2z3+2z4+z5+z6+z7+z8+2z9 +gap> DD := Z(3^12)+Z(3^12)^2+2*Z(3^12)^3+2*Z(3^12)^4+Z(3^12)^5+Z(3^12)^6+Z(3^12)^7+Z(3^12)^8+2*Z(3^12)^9;; gap> LogFFE(DD,RT); 340 diff --git a/tst/testinstall/ffeconway.tst b/tst/testinstall/ffeconway.tst index a75a8185dd2..d082dd9b517 100644 --- a/tst/testinstall/ffeconway.tst +++ b/tst/testinstall/ffeconway.tst @@ -27,8 +27,8 @@ gap> SetInfoLevel(InfoWarning,0); # A range of field sizes to hit various cases for the underlying vector # arithmetic. # -gap> fieldsizes := [ [2,17], [2,32], [2,60], [2,76], [2,87], [3,11], -> [3,20], [3,60], [17,4], [257,2], [257,11], [65521,2], [65537,2], +gap> fieldsizes := [ [2,25], [2,32], [2,60], [2,76], [2,87], [3,16], +> [3,20], [3,60], [17,6], [257,3], [257,11], [65521,2], > [268435399,2], [4294967291,2], [1152921504606846883,3] ];; gap> Add( fieldsizes, [NextPrimeInt(2^64),2] ); @@ -40,29 +40,29 @@ gap> Add( fieldsizes, [NextPrimeInt(2^64),2] ); gap> fieldpairs := Concatenation(List(fieldsizes, pd -> List(Filtered([1..pd[2]-1], > d2 -> IsCheapConwayPolynomial(pd[1],Lcm(pd[2],d2))), d2 -> > [pd[1],pd[2],d2]))); -[ [ 2, 17, 1 ], [ 2, 17, 2 ], [ 2, 17, 3 ], [ 2, 17, 4 ], [ 2, 17, 5 ], - [ 2, 17, 6 ], [ 2, 17, 7 ], [ 2, 32, 1 ], [ 2, 32, 2 ], [ 2, 32, 3 ], - [ 2, 32, 4 ], [ 2, 32, 6 ], [ 2, 32, 8 ], [ 2, 32, 12 ], [ 2, 32, 16 ], - [ 2, 32, 24 ], [ 2, 60, 1 ], [ 2, 60, 2 ], [ 2, 60, 3 ], [ 2, 60, 4 ], - [ 2, 60, 5 ], [ 2, 60, 6 ], [ 2, 60, 8 ], [ 2, 60, 10 ], [ 2, 60, 12 ], - [ 2, 60, 15 ], [ 2, 60, 20 ], [ 2, 60, 24 ], [ 2, 60, 30 ], [ 2, 60, 40 ], - [ 2, 76, 1 ], [ 2, 76, 2 ], [ 2, 76, 4 ], [ 2, 76, 19 ], [ 2, 76, 38 ], - [ 2, 87, 1 ], [ 2, 87, 3 ], [ 2, 87, 29 ], [ 3, 11, 1 ], [ 3, 11, 2 ], - [ 3, 11, 3 ], [ 3, 11, 4 ], [ 3, 11, 5 ], [ 3, 11, 6 ], [ 3, 11, 7 ], - [ 3, 20, 1 ], [ 3, 20, 2 ], [ 3, 20, 3 ], [ 3, 20, 4 ], [ 3, 20, 5 ], - [ 3, 20, 6 ], [ 3, 20, 8 ], [ 3, 20, 10 ], [ 3, 20, 12 ], [ 3, 20, 15 ], - [ 3, 60, 1 ], [ 3, 60, 2 ], [ 3, 60, 3 ], [ 3, 60, 4 ], [ 3, 60, 5 ], - [ 3, 60, 6 ], [ 3, 60, 10 ], [ 3, 60, 12 ], [ 3, 60, 15 ], [ 3, 60, 20 ], - [ 3, 60, 30 ], [ 17, 4, 1 ], [ 17, 4, 2 ], [ 17, 4, 3 ], [ 257, 2, 1 ], - [ 257, 11, 1 ], [ 65521, 2, 1 ], [ 65537, 2, 1 ], [ 268435399, 2, 1 ], - [ 4294967291, 2, 1 ], [ 1152921504606846883, 3, 1 ], - [ 18446744073709551629, 2, 1 ] ] +[ [ 2, 25, 1 ], [ 2, 25, 2 ], [ 2, 25, 3 ], [ 2, 25, 4 ], [ 2, 25, 5 ], + [ 2, 25, 6 ], [ 2, 25, 10 ], [ 2, 25, 15 ], [ 2, 25, 20 ], [ 2, 32, 1 ], + [ 2, 32, 2 ], [ 2, 32, 3 ], [ 2, 32, 4 ], [ 2, 32, 6 ], [ 2, 32, 8 ], + [ 2, 32, 12 ], [ 2, 32, 16 ], [ 2, 32, 24 ], [ 2, 60, 1 ], [ 2, 60, 2 ], + [ 2, 60, 3 ], [ 2, 60, 4 ], [ 2, 60, 5 ], [ 2, 60, 6 ], [ 2, 60, 8 ], + [ 2, 60, 10 ], [ 2, 60, 12 ], [ 2, 60, 15 ], [ 2, 60, 20 ], [ 2, 60, 24 ], + [ 2, 60, 30 ], [ 2, 60, 40 ], [ 2, 76, 1 ], [ 2, 76, 2 ], [ 2, 76, 4 ], + [ 2, 76, 19 ], [ 2, 76, 38 ], [ 2, 87, 1 ], [ 2, 87, 3 ], [ 2, 87, 29 ], + [ 3, 16, 1 ], [ 3, 16, 2 ], [ 3, 16, 3 ], [ 3, 16, 4 ], [ 3, 16, 6 ], + [ 3, 16, 8 ], [ 3, 16, 12 ], [ 3, 20, 1 ], [ 3, 20, 2 ], [ 3, 20, 3 ], + [ 3, 20, 4 ], [ 3, 20, 5 ], [ 3, 20, 6 ], [ 3, 20, 8 ], [ 3, 20, 10 ], + [ 3, 20, 12 ], [ 3, 20, 15 ], [ 3, 60, 1 ], [ 3, 60, 2 ], [ 3, 60, 3 ], + [ 3, 60, 4 ], [ 3, 60, 5 ], [ 3, 60, 6 ], [ 3, 60, 10 ], [ 3, 60, 12 ], + [ 3, 60, 15 ], [ 3, 60, 20 ], [ 3, 60, 30 ], [ 17, 6, 1 ], [ 17, 6, 2 ], + [ 17, 6, 3 ], [ 17, 6, 4 ], [ 17, 6, 5 ], [ 257, 3, 1 ], [ 257, 3, 2 ], + [ 257, 11, 1 ], [ 65521, 2, 1 ], [ 268435399, 2, 1 ], [ 4294967291, 2, 1 ], + [ 1152921504606846883, 3, 1 ], [ 18446744073709551629, 2, 1 ] ] # # construct generating elements # gap> zs := List(fieldsizes, pd -> Z(pd[1],pd[2])); -[ z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z ] +[ z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z ] # # and another way @@ -74,18 +74,18 @@ true # Construct some more interesting elements and test View, Print and Display # gap> izs := List(zs, Inverse); -[ z2+z16, z2+z3+z6+z8+z14+z31, +[ z+z5+z7+z24, z2+z3+z6+z8+z14+z31, z+z2+z3+z4+z7+z11+z16+z18+z21+z24+z25+z29+z31+z32+z33+z35+z38+z40+z41+z43+z4\ 4+z59, 1+z+z4+z13+z14+z18+z19+z22+z23+z24+z26+z28+z30+z32+z33+z34+z35+z36+z37+z75, - 1+z2+z4+z6+z7+z9+z10+z11+z12+z13+z15+z19+z25+z27+z29+z86, z+2z10, - 1+2z2+2z3+2z4+z7+z8+z9+z10+2z12+z19, + 1+z2+z4+z6+z7+z9+z10+z11+z12+z13+z15+z19+z25+z27+z29+z86, + 1+2z+2z2+2z3+2z5+2z6+z15, 1+2z2+2z3+2z4+z7+z8+z9+z10+2z12+z19, 2z+2z2+2z3+z4+2z5+2z7+z9+2z10+z13+2z14+2z15+z19+z20+2z21+2z23+2z25+2z26+2z27\ -+z29+z31+2z32+z33+z34+2z35+2z37+2z38+z39+2z40+z43+z59, 8+9z+11z3, 2+171z, - 99+86z10, 61667+23125z, 21846+43691z, 89478467+89478466z, - 2147483646+2147483645z, 1+576460752303423442z2, 2+9223372036854775814z ] ++z29+z31+2z32+z33+z34+2z35+2z37+2z38+z39+2z40+z43+z59, 16+8z+5z3+11z5, + 2+86z2, 99+86z10, 61667+23125z, 89478467+89478466z, 2147483646+2147483645z, + 1+576460752303423442z2, 2+9223372036854775814z ] gap> Print(izs,"\n"); -[ Z(2,17)^2+Z(2,17)^16, +[ Z(2,25)+Z(2,25)^5+Z(2,25)^7+Z(2,25)^24, Z(2,32)^2+Z(2,32)^3+Z(2,32)^6+Z(2,32)^8+Z(2,32)^14+Z(2,32)^31, 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\ )^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)\ @@ -96,7 +96,8 @@ gap> Print(izs,"\n"); 33+Z(2,76)^34+Z(2,76)^35+Z(2,76)^36+Z(2,76)^37+Z(2,76)^75, 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)^\ 11+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\ -9+Z(2,87)^86, Z(3,11)+2*Z(3,11)^10, +9+Z(2,87)^86, + Z(3)^0+2*Z(3,16)+2*Z(3,16)^2+2*Z(3,16)^3+2*Z(3,16)^5+2*Z(3,16)^6+Z(3,16)^15, 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\ ,20)^10+2*Z(3,20)^12+Z(3,20)^19, 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)^\ @@ -104,9 +105,8 @@ gap> Print(izs,"\n"); 3,60)^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\ )^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\ +Z(3,60)^39+2*Z(3,60)^40+Z(3,60)^43+Z(3,60)^59, - Z(17)^10+9*Z(17,4)+11*Z(17,4)^3, Z(257)^48+171*Z(257,2), + Z(17)^8+8*Z(17,6)+5*Z(17,6)^3+11*Z(17,6)^5, Z(257)^48+86*Z(257,3)^2, Z(257)^198+86*Z(257,11)^10, Z(65521)^1451+23125*Z(65521,2), - ZmodpZObj(21846,65537)+43691*Z(65537,2), ZmodpZObj(89478467,268435399)+89478466*Z(268435399,2), ZmodpZObj(2147483646,4294967291)+2147483645*Z(4294967291,2), ZmodpZObj(1,1152921504606846883)+576460752303423442*Z(1152921504606846883,3)\ @@ -116,21 +116,20 @@ gap> Print(izs,"\n"); gap> for x in izs do > Display(x); > od; -z2+z16 +z+z5+z7+z24 z2+z3+z6+z8+z14+z31 z+z2+z3+z4+z7+z11+z16+z18+z21+z24+z25+z29+z31+z32+z33+z35+z38+z40+z41+z43+z44+\ z59 1+z+z4+z13+z14+z18+z19+z22+z23+z24+z26+z28+z30+z32+z33+z34+z35+z36+z37+z75 1+z2+z4+z6+z7+z9+z10+z11+z12+z13+z15+z19+z25+z27+z29+z86 -z+2z10 +1+2z+2z2+2z3+2z5+2z6+z15 1+2z2+2z3+2z4+z7+z8+z9+z10+2z12+z19 2z+2z2+2z3+z4+2z5+2z7+z9+2z10+z13+2z14+2z15+z19+z20+2z21+2z23+2z25+2z26+2z27+z\ 29+z31+2z32+z33+z34+2z35+2z37+2z38+z39+2z40+z43+z59 -8+9z+11z3 -2+171z +16+8z+5z3+11z5 +2+86z2 99+86z10 61667+23125z -21846+43691z 89478467+89478466z 2147483646+2147483645z 1+576460752303423442z2 @@ -140,68 +139,71 @@ z+2z10 # Test arithmetic within the field # gap> zs + izs; -[ z+z2+z16, z+z2+z3+z6+z8+z14+z31, +[ z5+z7+z24, z+z2+z3+z6+z8+z14+z31, z2+z3+z4+z7+z11+z16+z18+z21+z24+z25+z29+z31+z32+z33+z35+z38+z40+z41+z43+z44+\ z59, 1+z4+z13+z14+z18+z19+z22+z23+z24+z26+z28+z30+z32+z33+z34+z35+z36+z37+z75, - 1+z+z2+z4+z6+z7+z9+z10+z11+z12+z13+z15+z19+z25+z27+z29+z86, 2z+2z10, - 1+z+2z2+2z3+2z4+z7+z8+z9+z10+2z12+z19, + 1+z+z2+z4+z6+z7+z9+z10+z11+z12+z13+z15+z19+z25+z27+z29+z86, + 1+2z2+2z3+2z5+2z6+z15, 1+z+2z2+2z3+2z4+z7+z8+z9+z10+2z12+z19, 2z2+2z3+z4+2z5+2z7+z9+2z10+z13+2z14+2z15+z19+z20+2z21+2z23+2z25+2z26+2z27+z2\ -9+z31+2z32+z33+z34+2z35+2z37+2z38+z39+2z40+z43+z59, 8+10z+11z3, 2+172z, - 99+z+86z10, 61667+23126z, 21846+43692z, 89478467+89478467z, - 2147483646+2147483646z, 1+z+576460752303423442z2, 2+9223372036854775815z ] +9+z31+2z32+z33+z34+2z35+2z37+2z38+z39+2z40+z43+z59, 16+9z+5z3+11z5, 2+z+86z2, + 99+z+86z10, 61667+23126z, 89478467+89478467z, 2147483646+2147483646z, + 1+z+576460752303423442z2, 2+9223372036854775815z ] gap> zs - izs; -[ z+z2+z16, z+z2+z3+z6+z8+z14+z31, +[ z5+z7+z24, z+z2+z3+z6+z8+z14+z31, z2+z3+z4+z7+z11+z16+z18+z21+z24+z25+z29+z31+z32+z33+z35+z38+z40+z41+z43+z44+\ z59, 1+z4+z13+z14+z18+z19+z22+z23+z24+z26+z28+z30+z32+z33+z34+z35+z36+z37+z75, - 1+z+z2+z4+z6+z7+z9+z10+z11+z12+z13+z15+z19+z25+z27+z29+z86, z10, - 2+z+z2+z3+z4+2z7+2z8+2z9+2z10+z12+2z19, + 1+z+z2+z4+z6+z7+z9+z10+z11+z12+z13+z15+z19+z25+z27+z29+z86, + 2+2z+z2+z3+z5+z6+2z15, 2+z+z2+z3+z4+2z7+2z8+2z9+2z10+z12+2z19, 2z+z2+z3+2z4+z5+z7+2z9+z10+2z13+z14+z15+2z19+2z20+z21+z23+z25+z26+z27+2z29+2\ -z31+z32+2z33+2z34+z35+z37+z38+2z39+z40+2z43+2z59, 9+9z+6z3, 255+87z, - 158+z+171z10, 3854+42397z, 43691+21847z, 178956932+178956934z, +z31+z32+2z33+2z34+z35+z37+z38+2z39+z40+2z43+2z59, 1+10z+12z3+6z5, + 255+z+171z2, 158+z+171z10, 3854+42397z, 178956932+178956934z, 2147483645+2147483647z, 1152921504606846882+z+576460752303423441z2, 18446744073709551627+9223372036854775816z ] gap> List(izs, x->x^2); -[ z+z15, z+z2+z5+z7+z13+z30, +[ 1+z4+z6+z23, z+z2+z5+z7+z13+z30, 1+z+z2+z3+z6+z10+z15+z17+z20+z23+z24+z28+z30+z31+z32+z34+z37+z39+z40+z42+z43\ +z58, z+z3+z4+z12+z14+z17+z19+z21+z24+z25+z26+z27+z28+z29+z30+z31+z37+z74+z75, 1+z+z2+z3+z4+z5+z7+z8+z13+z14+z15+z18+z19+z24+z25+z26+z27+z28+z29+z85+z86, - 1+2z9, 1+2z+z2+z3+2z4+z6+2z7+2z8+2z9+z10+2z11+2z12+z18+z19, + z+z2+2z3+2z4+z5+2z6+z14+z15, + 1+2z+z2+z3+2z4+z6+2z7+2z8+2z9+z10+2z11+2z12+z18+z19, 2+2z+2z2+z3+2z4+2z6+z8+2z9+z12+2z13+2z14+z18+z19+2z20+2z22+2z24+2z25+2z26+z2\ -8+z30+2z31+z32+z33+2z34+2z36+2z37+z38+2z39+z42+z58, 5+4z+11z2+3z3, 175+85z, - 35+86z9+33z10, 3174+50331z, 50973+58255z, 59652311+149130777z, +8+z30+2z31+z32+z33+2z34+2z36+2z37+z38+2z39+z42+z58, 9+9z+5z2+12z3+11z4+6z5, + 4+86z+172z2, 35+86z9+33z10, 3174+50331z, 59652311+149130777z, 3221225468+3221225468z, 1+576460752303423442z+576460752303423442z2, 9223372036854775818+18446744073709551628z ] gap> List([1..Length(zs)] , i-> zs[i]/izs[i]); -[ z2, z2, z2, z2, z2, z2, z2, z2, z2, 254+6z, z2, 65504+3z, 65534+z, - 268435396+2z, 4294967289+z, z2, 18446744073709551627+4z ] +[ z2, z2, z2, z2, z2, z2, z2, z2, z2, z2, z2, 65504+3z, 268435396+2z, + 4294967289+z, z2, 18446744073709551627+4z ] gap> List(izs, AdditiveInverse); -[ z2+z16, z2+z3+z6+z8+z14+z31, +[ z+z5+z7+z24, z2+z3+z6+z8+z14+z31, z+z2+z3+z4+z7+z11+z16+z18+z21+z24+z25+z29+z31+z32+z33+z35+z38+z40+z41+z43+z4\ 4+z59, 1+z+z4+z13+z14+z18+z19+z22+z23+z24+z26+z28+z30+z32+z33+z34+z35+z36+z37+z75, - 1+z2+z4+z6+z7+z9+z10+z11+z12+z13+z15+z19+z25+z27+z29+z86, 2z+z10, - 2+z2+z3+z4+2z7+2z8+2z9+2z10+z12+2z19, + 1+z2+z4+z6+z7+z9+z10+z11+z12+z13+z15+z19+z25+z27+z29+z86, + 2+z+z2+z3+z5+z6+2z15, 2+z2+z3+z4+2z7+2z8+2z9+2z10+z12+2z19, z+z2+z3+2z4+z5+z7+2z9+z10+2z13+z14+z15+2z19+2z20+z21+z23+z25+z26+z27+2z29+2z\ -31+z32+2z33+2z34+z35+z37+z38+2z39+z40+2z43+2z59, 9+8z+6z3, 255+86z, - 158+171z10, 3854+42396z, 43691+21846z, 178956932+178956933z, - 2147483645+2147483646z, 1152921504606846882+576460752303423441z2, +31+z32+2z33+2z34+z35+z37+z38+2z39+z40+2z43+2z59, 1+9z+12z3+6z5, 255+171z2, + 158+171z10, 3854+42396z, 178956932+178956933z, 2147483645+2147483646z, + 1152921504606846882+576460752303423441z2, 18446744073709551627+9223372036854775815z ] # # and across fields # gap> List(fieldpairs, pdd -> Z(pdd[1],pdd[2])+Z(pdd[1],pdd[3])); -[ 1+z, z+z4+z9+z10+z15+z17+z19+z21+z23+z25+z26+z27+z29+z30+z33, - z2+z3+z6+z10+z13+z15+z16+z18+z19+z20+z24+z25+z35+z38+z39+z40+z41+z44+z46+z48\ -+z49, - 1+z2+z3+z4+z5+z7+z10+z11+z12+z13+z14+z16+z17+z18+z19+z21+z22+z23+z24+z25+z26\ -+z30+z31+z32+z35+z37+z38+z40+z47+z48+z50+z51+z56+z58+z62+z63+z67, - z+z3+z7+z8+z9+z10+z13+z14+z17+z19+z20+z21+z22+z24+z25+z27+z28+z30+z32+z33+z3\ -6+z38+z41+z42+z45+z46+z47+z48+z50+z51+z52+z54+z58+z59+z60+z61+z63+z65+z68+z69+\ -z71+z73+z75+z76+z77+z82, - z2+z3+z5+z7+z10+z11+z13+z16+z18+z19+z20+z21+z22+z25+z26+z27+z28+z30+z31+z32+\ -z34+z35+z37+z38+z39+z40+z44+z45+z47+z54+z55+z56+z58+z60+z61+z63+z65+z67+z69+z7\ -3+z74+z79+z83+z87+z89+z96+z97+z99+z100, <>, 1+z, +[ 1+z, + z2+z4+z6+z10+z11+z14+z15+z16+z17+z18+z19+z21+z26+z30+z34+z35+z37+z43+z47, + 1+z+z2+z3+z5+z8+z12+z14+z17+z18+z21+z22+z23+z24+z25+z27+z28+z30+z33+z41+z44+\ +z45+z46+z47+z49+z51+z54+z55+z57+z61+z62+z66+z68+z70+z72+z73, + z+z4+z6+z7+z8+z11+z12+z15+z16+z17+z18+z23+z24+z27+z28+z30+z31+z33+z34+z35+z3\ +7+z40+z41+z42+z43+z44+z45+z48+z52+z54+z55+z57+z59+z61+z63+z64+z69+z71+z72+z75+\ +z78+z79+z80+z81+z82+z85+z87+z89+z92+z95+z98+z99, + 1+z3+z5+z7+z12+z15+z16+z17+z18+z21+z22+z24, <>, + 1+z3+z4+z5+z7+z8+z9+z15+z18+z25+z26+z28+z29+z30+z33+z34+z38+z40+z42+z43+z45, + 1+z6+z7+z9+z17+z18+z19+z20+z23+z25+z27+z30+z32+z33+z34+z35+z37+z38+z42+z45+z\ +48+z54+z56+z57+z59+z61+z63+z66+z67+z68+z70+z71+z72+z74, + 1+z3+z5+z6+z7+z12+z15+z17+z24+z31+z33+z37+z39+z41+z44+z47+z48+z50+z55+z56+z5\ +9+z61+z67+z72+z73+z75+z76+z78+z82+z84+z87+z90+z92+z93+z99, 1+z, 1+z3+z4+z5+z6+z8+z9+z14+z17+z18+z19+z20+z21+z24+z29+z30, z+z5+z7+z9+z12+z14+z15+z16+z17+z20+z22+z23+z24+z25+z28+z31+z33+z36+z37+z38+z\ 39+z42+z43+z44+z52+z56+z61+z62+z65+z67+z68+z69+z70+z71+z72+z73+z76+z77+z79+z80\ @@ -252,20 +254,15 @@ z44+z45+z46+z48+z49+z52+z53+z56+z57+z60+z63+z64+z65+z69+z70+z71+z73+z74+z75, z77+z79+z81+z83+z84+z86, z+z2+z6+z8+z9+z10+z14+z15+z16+z19+z20+z22+z23+z26+z28+z30+z31+z33+z34+z37+z4\ 1+z46+z50+z51+z54+z55+z56+z57+z58+z59+z60+z61+z63+z64+z66+z68+z71+z72+z76+z78+\ -z81+z82+z83+z84+z85, 2+z, - 2+z+z2+2z3+z4+2z5+2z6+z7+2z9+2z11+z12+2z14+z16+z17+2z18+2z19+2z20+2z21, - 1+2z+2z3+2z4+2z6+2z8+2z9+z11+z12+z14+2z15+2z17+z18+z19+2z21+2z23+z25+2z26+2z\ -27+2z28+2z29+2z30+z32, - 2z+2z3+z8+z9+z12+z15+2z17+2z19+z21+z22+z23+z24+z25+z30+z34+z35+z37+2z38+2z40\ -+z41+2z42+z43, - 2+z+z4+2z6+z7+2z9+z10+2z14+z16+2z19+z20+2z21+2z22+z23+2z25+z26+2z27+z28+2z29\ -+z30+z31+2z34+2z35+z36+z38+z40+z41+z42+z44+2z45+2z47+z51+z52, - 1+z+z4+z6+2z8+z9+z11+2z13+z14+z17+z19+z20+2z21+z23+z25+2z26+z27+z28+z29+z31+\ -z32+z33+z34+z35+2z38+z40+z41+2z42+2z45+z46+2z47+z50+2z51+z52+2z57+z58+2z59+z60\ -+z61+2z62+2z63+2z64+z65, - 1+z2+2z4+z5+2z6+2z7+z8+2z9+2z10+z11+2z12+2z13+z14+z16+2z17+2z18+z21+z22+z24+\ -2z27+2z28+2z29+2z32+z33+z35+z36+z40+2z41+2z42+z45+2z46+2z48+2z49+z51+z52+z53+2\ -z54+z55+z56+z57+2z58+z59+z60+z61+z63+z64+2z65+2z66+2z67+z68+2z73+2z76, 2+z, +z81+z82+z83+z84+z85, 2+z, 2+z+2z3+2z4+2z5+2z7+2z8+2z10+2z11+2z13+z14+z15, + 1+z+z3+z4+2z5+z6+2z11+2z12+z14+2z15+z18+z19+z20+2z23+z26+2z27+z29+2z30+2z31+\ +z32+2z34+2z35+2z36+z38+z39+2z40+2z41+z42+z43+z44+2z45+z46+z47, + 1+2z2+z3+z4+z5+2z7+z8+2z9+z10+z11+z12+z13+2z14+z15, + 1+2z+z2+2z3+z4+2z5+2z6+z8+z9+z11+2z12+z14+2z18+z20+2z22+2z23+2z24+z25+z26+z2\ +7+z28+2z30+2z31+2z33+z34+z35+z36+2z37+2z38+z40+z45+2z46+z47, + z+z2+2z3+2z4+2z5+z7+z9+z10+2z12+z13+2z14+2z15, + 2+z2+z3+2z5+z6+2z7+z8+z9+2z10+z13+z14+z15+2z17+z18+z19+2z20+2z21+z24+z27+z30\ ++z31+z32+z33+z34+z36+2z37+z38+2z39+2z40+2z41+z42+z43+z46+2z47, 2+z, z+z2+2z3+2z4+z7+2z8+z9+z10+2z12+2z13+2z14+z15+2z17+2z18+z19, 2+z2+z3+2z5+z7+2z11+z12+z14+z15+z16+z18+z19+2z20+2z22+z25+z27+z29+2z30+z32+z\ 33+2z34+z35+2z36+2z39+z40+z41+2z43+2z45+z46+2z48+2z49+2z50+z53+2z54+2z55+z56+2\ @@ -311,20 +308,25 @@ z28+2z29+2z31+z32+z33+z34+z36+z37+2z38+z41+z42+2z45+2z46+2z47+2z50+2z52+2z53+2\ z54+z56+z57+z58+z59, 1+z+2z2+z3+z4+2z6+2z7+2z9+z10+z11+2z12+z14+2z15+z16+z19+2z21+2z24+z26+2z28+2\ z29+2z30+z32+z33+z34+z35+2z37+2z40+z41+2z42+2z46+2z48+z49+2z50+2z53+z54+z55+z5\ -6+z58+2z59, 3+z, 12+z2+9z3, 10+9z+13z3+11z4+5z5+10z6+15z7+5z8+13z9+6z10+9z11, - 3+z, 3+z, 17+z, 3+z, 3+z, 2+z, 2+z, 2+z ] +6+z58+2z59, 3+z, 9+z+10z2+15z3+3z5, 14+7z+z2+3z3+16z4+12z5, + 12+12z+9z2+6z3+15z4+7z5+3z6+8z7+11z8+16z9+3z10+8z11, + 10+14z+16z2+7z3+z4+12z5+11z6+12z7+8z8+13z9+6z10+z11+10z12+14z13+9z14+11z15+1\ +3z16+z17+2z18+14z19+11z20+8z21+3z22+11z23+9z24+4z26+10z27+14z28+6z29, 3+z, + 236+32z+148z2+212z3+2z4+2z5, 3+z, 17+z, 3+z, 2+z, 2+z, 2+z ] gap> List(fieldpairs, pdd -> Z(pdd[1],pdd[2])-Z(pdd[1],pdd[3])); -[ 1+z, z+z4+z9+z10+z15+z17+z19+z21+z23+z25+z26+z27+z29+z30+z33, - z2+z3+z6+z10+z13+z15+z16+z18+z19+z20+z24+z25+z35+z38+z39+z40+z41+z44+z46+z48\ -+z49, - 1+z2+z3+z4+z5+z7+z10+z11+z12+z13+z14+z16+z17+z18+z19+z21+z22+z23+z24+z25+z26\ -+z30+z31+z32+z35+z37+z38+z40+z47+z48+z50+z51+z56+z58+z62+z63+z67, - z+z3+z7+z8+z9+z10+z13+z14+z17+z19+z20+z21+z22+z24+z25+z27+z28+z30+z32+z33+z3\ -6+z38+z41+z42+z45+z46+z47+z48+z50+z51+z52+z54+z58+z59+z60+z61+z63+z65+z68+z69+\ -z71+z73+z75+z76+z77+z82, - z2+z3+z5+z7+z10+z11+z13+z16+z18+z19+z20+z21+z22+z25+z26+z27+z28+z30+z31+z32+\ -z34+z35+z37+z38+z39+z40+z44+z45+z47+z54+z55+z56+z58+z60+z61+z63+z65+z67+z69+z7\ -3+z74+z79+z83+z87+z89+z96+z97+z99+z100, <>, 1+z, +[ 1+z, + z2+z4+z6+z10+z11+z14+z15+z16+z17+z18+z19+z21+z26+z30+z34+z35+z37+z43+z47, + 1+z+z2+z3+z5+z8+z12+z14+z17+z18+z21+z22+z23+z24+z25+z27+z28+z30+z33+z41+z44+\ +z45+z46+z47+z49+z51+z54+z55+z57+z61+z62+z66+z68+z70+z72+z73, + z+z4+z6+z7+z8+z11+z12+z15+z16+z17+z18+z23+z24+z27+z28+z30+z31+z33+z34+z35+z3\ +7+z40+z41+z42+z43+z44+z45+z48+z52+z54+z55+z57+z59+z61+z63+z64+z69+z71+z72+z75+\ +z78+z79+z80+z81+z82+z85+z87+z89+z92+z95+z98+z99, + 1+z3+z5+z7+z12+z15+z16+z17+z18+z21+z22+z24, <>, + 1+z3+z4+z5+z7+z8+z9+z15+z18+z25+z26+z28+z29+z30+z33+z34+z38+z40+z42+z43+z45, + 1+z6+z7+z9+z17+z18+z19+z20+z23+z25+z27+z30+z32+z33+z34+z35+z37+z38+z42+z45+z\ +48+z54+z56+z57+z59+z61+z63+z66+z67+z68+z70+z71+z72+z74, + 1+z3+z5+z6+z7+z12+z15+z17+z24+z31+z33+z37+z39+z41+z44+z47+z48+z50+z55+z56+z5\ +9+z61+z67+z72+z73+z75+z76+z78+z82+z84+z87+z90+z92+z93+z99, 1+z, 1+z3+z4+z5+z6+z8+z9+z14+z17+z18+z19+z20+z21+z24+z29+z30, z+z5+z7+z9+z12+z14+z15+z16+z17+z20+z22+z23+z24+z25+z28+z31+z33+z36+z37+z38+z\ 39+z42+z43+z44+z52+z56+z61+z62+z65+z67+z68+z69+z70+z71+z72+z73+z76+z77+z79+z80\ @@ -375,20 +377,15 @@ z44+z45+z46+z48+z49+z52+z53+z56+z57+z60+z63+z64+z65+z69+z70+z71+z73+z74+z75, z77+z79+z81+z83+z84+z86, z+z2+z6+z8+z9+z10+z14+z15+z16+z19+z20+z22+z23+z26+z28+z30+z31+z33+z34+z37+z4\ 1+z46+z50+z51+z54+z55+z56+z57+z58+z59+z60+z61+z63+z64+z66+z68+z71+z72+z76+z78+\ -z81+z82+z83+z84+z85, 1+z, - 2+2z+2z2+2z3+z4+2z5+z8+z9+2z10+z11+z12+z15+z16+2z18+2z19+2z20+z21, - 1+2z+2z2+2z3+z4+z6+z8+2z11+z12+2z13+2z14+2z15+2z16+2z17+z18+z20+2z21+z22+z23\ -+z24+2z25+z26+2z28+z30+2z31, - 2z+z5+2z7+2z8+z9+z10+2z11+z12+z13+z14+z17+z18+2z19+2z20+2z23+2z26+2z28+2z31+\ -2z33+2z35+z36+2z38+z39+z40+2z41+2z42+2z43, - 1+z+z3+2z4+2z5+z6+2z9+z11+z12+z15+2z18+2z19+z20+2z21+z22+2z24+z25+2z27+z28+z\ -29+2z34+z36+2z37+2z38+z40+2z41+2z43+2z45+z47+2z51+z52+2z54, - 1+z+z3+z4+2z5+2z6+z9+z10+z11+z13+2z14+2z15+z16+2z17+2z18+z19+2z22+2z23+2z24+\ -z26+z28+z30+z31+2z33+z34+z35+z37+2z38+z40+2z41+z42+z44+2z45+z46+2z47+z49+2z50+\ -z51+2z52+z54+2z55+z56+z57+z58+z59+2z61+z62+z64, - 2+z+z5+z6+2z9+2z11+2z13+z14+z16+2z20+z23+2z24+z27+z28+2z29+2z30+z31+2z32+2z3\ -4+2z35+z36+2z37+z38+z39+2z40+2z41+z42+z45+2z46+z47+2z49+2z51+2z52+2z55+z56+2z5\ -7+z58+z61+2z63+z64+2z65+2z67+2z69+2z70+z71+z72+z73+z75+2z76, 1+z, +z81+z82+z83+z84+z85, 1+z, 1+z+z3+z4+z5+z7+z8+z10+z11+z13+2z14+2z15, + 1+2z+2z3+2z6+z7+z8+2z9+z12+z13+z14+z15+z16+2z17+z18+2z20+2z22+z23+2z24+2z26+\ +z30+z32+z33+2z34+z37+z39+z41+2z42+2z46+2z47, + 2+2z+z2+2z3+2z4+2z5+z7+2z8+z9+2z10+2z11+2z12+2z13+z14+2z15, + 1+z+2z2+z3+z6+z7+z9+z11+z12+z13+z14+z16+2z17+z19+2z20+z23+2z25+2z26+z27+2z28\ ++z29+z30+2z32+2z33+z35+z36+2z37+2z38+2z39+z40+z43+z44+z45+z46+2z47, + z+2z2+z3+z4+z5+2z7+2z9+2z10+z12+2z13+z14+z15, + 2z2+2z3+z4+2z6+2z7+z9+z10+2z11+z14+2z15+z16+z18+z20+z21+2z22+z24+z27+z29+2z3\ +0+z31+z32+2z35+z36+2z37+z41+2z42+z44+2z45+2z46+z47, 1+z, z+2z2+z3+z4+2z7+z8+2z9+2z10+z12+z13+z14+2z15+z17+z18+2z19, z4+z5+2z6+2z7+z9+z10+2z12+z14+z15+z17+2z18+2z19+2z20+z21+2z22+2z25+z26+z28+z\ 30+z31+z32+z33+2z35+2z37+z38+z39+2z40+z41+2z42+z43+2z45+z47+z48+z49+2z50+z52+2\ @@ -435,24 +432,27 @@ z57+2z58+2z59, 7+2z58+2z59, 2+z+z2+2z3+2z4+z6+z7+z9+2z10+2z11+z12+2z14+z15+2z16+2z19+z21+z24+2z26+z28+z2\ 9+z30+2z32+2z33+2z34+2z35+z37+z40+2z41+z42+z46+z48+2z49+z50+z53+2z54+2z55+2z56\ -+2z58+z59, 14+z, 5+2z+16z2+8z3, 4z+13z2+8z3+4z4+8z6+16z7+9z8+14z9+16z10+11z11, - 254+z, 254+z, 65504+z, 65534+z, 268435396+z, 4294967289+z, ++2z58+z59, 14+z, 8+z+7z2+2z3+14z5, 3+12z+16z2+14z3+z4+5z5, + 2+16z+13z2+2z3+2z5+2z6+11z7+14z8+6z9+15z10+5z11, + 16+15z+z3+10z4+10z5+9z6+3z7+z8+3z9+12z10+8z11+3z12+15z13+12z14+13z15+7z16+15\ +z17+13z18+3z19+9z20+16z21+5z22+13z23+3z25+4z26+4z27+11z28+6z29, 254+z, + 46+145z+22z2+249z3+239z4+124z5, 254+z, 65504+z, 268435396+z, 4294967289+z, 1152921504606846881+z, 18446744073709551627+z ] gap> List(fieldpairs, pdd -> Z(pdd[1],pdd[2])*Z(pdd[1],pdd[3])); -[ z, 1+z2+z4+z9+z10+z13+z14+z15+z16+z18+z20+z21+z24+z25+z29+z30+z31+z33, - 1+z+z3+z9+z10+z11+z14+z19+z20+z21+z22+z23+z25+z26+z33+z35+z36+z37+z41+z43+z4\ -6+z47+z49, - z+z3+z4+z5+z7+z10+z14+z15+z17+z19+z26+z28+z31+z32+z37+z40+z41+z44+z45+z47+z4\ -8+z51+z53+z55+z57+z60+z62+z64+z65+z66+z67, - 1+z3+z5+z6+z7+z9+z10+z11+z12+z13+z14+z16+z18+z19+z22+z26+z28+z29+z31+z34+z42\ -+z44+z47+z51+z55+z56+z58+z60+z64+z68+z71+z72+z73+z74+z75+z76+z77+z80+z81+z82+z\ -84, - 1+z+z4+z6+z8+z10+z11+z13+z15+z16+z17+z19+z20+z23+z26+z31+z37+z38+z39+z42+z45\ -+z46+z50+z51+z52+z56+z57+z62+z63+z65+z66+z69+z71+z72+z73+z76+z81+z83+z84+z85+z\ -87+z88+z91+z93+z98+z100+z101, - 1+z2+z4+z6+z8+z11+z13+z16+z17+z20+z21+z23+z24+z27+z28+z29+z32+z35+z36+z38+z4\ -0+z48+z49+z51+z52+z54+z55+z56+z58+z59+z61+z68+z69+z70+z72+z75+z77+z78+z79+z80+\ -z81+z87+z91+z92+z96+z101+z102+z107+z109+z111+z112+z113+z115+z118, z, +[ z, z+z2+z4+z5+z6+z11+z14+z15+z16+z21+z31+z32+z34+z37+z38+z40+z42+z44+z48, + z3+z7+z8+z10+z12+z13+z14+z15+z18+z19+z22+z24+z25+z26+z27+z29+z30+z32+z33+z34\ ++z35+z37+z38+z39+z44+z48+z52+z54+z55+z57+z58+z59+z60+z64+z65+z66+z67+z70, + 1+z3+z4+z6+z7+z8+z11+z19+z21+z23+z24+z25+z26+z27+z31+z32+z35+z36+z37+z39+z43\ ++z44+z45+z46+z47+z49+z50+z51+z52+z53+z54+z55+z57+z59+z60+z62+z64+z65+z67+z68+z\ +69+z70+z79+z82+z83+z86+z90+z91+z92+z93+z94+z95+z96+z97+z98+z99, + 1+z+z4+z13+z16+z17+z18+z19+z22+z23, <>, + 1+z+z2+z4+z5+z6+z7+z9+z10+z12+z18+z19+z20+z21+z22+z23+z24+z25+z27+z29+z30+z3\ +4+z40+z41+z42+z44+z45+z46+z48+z49, + 1+z+z2+z5+z6+z10+z11+z13+z14+z20+z22+z23+z25+z27+z28+z29+z31+z32+z33+z35+z37\ ++z40+z42+z43+z45+z47+z49+z50+z51+z55+z56+z57+z60+z64+z67+z68+z69+z70+z71+z72, + z+z2+z6+z7+z8+z9+z10+z12+z16+z19+z20+z21+z27+z29+z32+z33+z34+z35+z36+z40+z43\ ++z46+z47+z48+z49+z54+z55+z56+z60+z62+z64+z66+z69+z71+z74+z75+z77+z78+z80+z81+z\ +82+z83+z84+z88+z89+z90+z92+z94+z95+z98, z, z+z2+z4+z5+z6+z7+z9+z10+z15+z18+z19+z20+z21+z22+z25+z30+z31, z2+z3+z8+z13+z17+z19+z22+z23+z24+z27+z29+z31+z33+z37+z39+z40+z42+z45+z48+z51\ +z52+z54+z55+z58+z59+z60+z63+z64+z68+z69+z70+z76+z78+z79+z81+z82+z83+z86+z87+z\ @@ -504,19 +504,16 @@ z43+z44+z45+z49+z52+z53+z56+z57+z58+z61+z62+z63+z64+z65+z66+z68+z69+z70+z71+z7\ 2+z73+z76+z78+z80+z82+z84+z85, z3+z7+z9+z10+z11+z15+z16+z17+z20+z21+z23+z24+z27+z29+z31+z32+z34+z35+z38+z42\ +z47+z51+z52+z55+z56+z57+z58+z59+z60+z61+z62+z64+z65+z67+z69+z72+z73+z77+z79+z\ -82+z83+z84+z85+z86, 2z, 1+z+2z2+2z3+z4+z5+z9+2z12+2z14+z17+z18, - 1+2z+2z2+z3+2z4+z6+z7+2z8+2z9+2z10+z11+2z13+2z14+2z16+z18+z20+z21+2z22+2z24+\ -2z25+z26+z27+2z31, - 2z+2z2+z3+z6+2z7+z8+2z11+2z12+2z13+z16+2z17+z18+2z22+2z24+2z26+z27+z28+z29+2\ -z30+2z31+2z32+z33+z37+z38+2z41, - 2z2+2z4+z5+z6+2z9+2z11+z12+z13+z16+z17+z18+2z19+z21+z23+z24+z27+z28+2z31+z32\ -+2z33+2z34+2z36+2z39+2z41+2z44+z45+2z46+2z47+2z48+2z51+2z52+2z53+2z54, - 1+z+z2+2z3+z5+z6+2z8+z9+2z13+2z16+2z17+2z18+2z19+z20+z21+z22+2z23+z24+2z25+z\ -26+2z27+z28+z33+2z34+2z35+z36+2z38+2z39+z40+2z41+z42+z44+z45+z47+z48+z49+z50+2\ -z51+2z52+z53+2z54+2z55+z56+2z57+2z59+2z60+2z61+2z62+2z63, - 1+2z+z5+2z8+2z9+z12+z13+2z16+2z17+z19+z20+z24+z25+z27+z29+z30+z31+z32+2z33+2\ -z34+z35+2z38+z39+2z42+z44+z45+2z46+z48+z49+z50+z52+2z54+2z55+2z57+z58+z59+2z62\ -+z64+2z66+z68+z69+z71+2z72+z73+z75, 2z, 1+2z+2z3+z9+2z14+2z15+z16+2z18+2z19, +82+z83+z84+z85+z86, 2z, 1+z+z2+z3+2z5+z7+2z8+2z9+2z11+2z12+2z14+z15, + 1+z+z2+2z6+2z8+z9+z11+z12+2z13+z15+z18+2z20+z22+2z23+2z24+z25+z27+z28+z29+2z\ +35+z36+2z37+2z38+2z39+z40+2z44+z45+z46+z47, + 1+2z4+z5+2z6+z7+2z8+z9+2z10+z11+z12+z13+z14+2z15, + 2+z+z2+2z4+2z5+z7+z8+z10+2z11+z12+z14+2z15+2z16+2z17+z19+2z20+z22+z23+z24+2z\ +25+z26+z29+2z30+z33+z34+z35+2z37+z38+2z40+z41+z42+z44+z45+z46+2z47, + 2+z+2z2+z4+2z5+z6+2z7+z8+z10+z11+2z13+z14+2z15, + 1+2z2+2z3+2z4+z5+2z6+2z7+z8+2z11+2z14+2z16+2z17+z18+z19+2z20+2z23+2z24+2z25+\ +2z26+2z27+2z28+2z29+2z30+z31+z33+z35+2z36+z38+2z40+z41+2z44+z46+2z47, 2z, + 1+2z+2z3+z9+2z14+2z15+z16+2z18+2z19, 2+2z+2z2+z6+z7+2z10+z17+z19+2z20+2z21+z24+2z25+2z27+z28+z29+2z30+z31+2z32+2z\ 35+z36+2z37+z38+2z40+2z41+2z42+z44+2z46+z47+z49+z51+z52+z54+z56+2z57+2z58+z59, 1+z2+2z3+2z6+z7+2z9+2z10+2z11+2z12+z14+z15+z16+2z17+z18+z19, @@ -561,24 +558,28 @@ z27+z28+z30+2z31+2z34+2z35+2z36+2z37+z38+2z39+z41+2z42+z44+z45+2z46+z48+z49+z5\ 54+2z55+z57+z58+z59, 2+z+2z2+z3+2z5+2z6+2z7+z8+z12+2z13+z14+z16+z17+2z20+z21+z22+2z24+2z25+2z26+2\ z28+2z29+2z31+z32+2z34+2z35+z38+2z39+z40+z41+z42+2z43+z44+2z47+2z49+z50+2z51+2\ -z54+z55+z56+z57+z59, 3z, 7+7z+4z2+z3, - 5+12z+z2+11z3+3z5+8z6+z7+11z8+10z9+16z10+7z11, 3z, 3z, 17z, 3z, 3z, 2z, 2z, - 2z ] +z54+z55+z56+z57+z59, 3z, 8+4z2+10z3+9z4, 15+12z+5z2+z3+13z4+16z5, + 5+13z+12z2+12z3+11z4+10z5+4z6+z7+8z8+5z9+2z10+8z11, + 7z+7z2+8z3+9z4+z5+z6+16z7+12z8+2z9+11z10+3z11+12z13+10z14+2z15+5z16+10z17+11\ +z19+4z20+13z21+15z22+4z23+7z24+5z25+7z26+13z27+3z29, 3z, + 17+156z+205z2+13z3+10z4+62z5, 3z, 17z, 3z, 2z, 2z, 2z ] gap> List(fieldpairs, pdd -> Z(pdd[1],pdd[2])/Z(pdd[1],pdd[3])); -[ z, z+z4+z7+z8+z9+z10+z13+z14+z17+z18+z19+z23+z24+z25+z26+z27+z28+z29+z32, - 1+z+z9+z10+z12+z13+z20+z21+z26+z28+z30+z31+z32+z33+z34+z37+z39+z46+z48+z49+z\ -50, - z+z5+z6+z10+z11+z12+z15+z16+z20+z24+z25+z28+z34+z36+z37+z38+z40+z43+z44+z45+\ -z46+z47+z48+z49+z53+z55+z57+z58+z59+z63+z64, - z+z2+z5+z8+z9+z13+z14+z15+z16+z20+z21+z22+z24+z26+z27+z28+z29+z30+z31+z32+z3\ -3+z38+z41+z42+z44+z46+z48+z49+z50+z53+z55+z59+z62+z63+z65+z66+z68+z70+z72+z75+\ -z77+z78+z79+z80+z82+z83, - 1+z2+z7+z8+z9+z10+z11+z12+z13+z16+z17+z19+z20+z22+z27+z28+z29+z30+z34+z36+z3\ -7+z39+z40+z41+z45+z47+z51+z52+z54+z56+z58+z59+z60+z63+z65+z67+z68+z69+z72+z74+\ -z81+z84+z88+z89+z90+z93+z95+z97+z101, - 1+z2+z3+z4+z8+z10+z11+z12+z14+z15+z16+z21+z22+z24+z32+z33+z34+z36+z39+z40+z4\ -4+z50+z51+z52+z54+z62+z63+z65+z68+z70+z71+z74+z77+z80+z88+z89+z92+z94+z101+z10\ -2+z104+z107+z108+z109+z110+z111+z118, z, +[ z, + 1+z2+z4+z5+z9+z10+z12+z14+z16+z17+z18+z19+z20+z23+z25+z29+z32+z36+z37+z39+z4\ +0+z41+z42+z43+z44+z45+z47+z48, + z+z2+z4+z6+z7+z9+z16+z17+z18+z21+z22+z29+z31+z32+z34+z37+z38+z39+z40+z43+z45\ ++z47+z48+z50+z53+z55+z56+z57+z58+z59+z60+z63+z64+z65+z68+z71+z74, + 1+z+z2+z4+z6+z11+z15+z16+z17+z18+z19+z20+z24+z25+z27+z31+z34+z35+z42+z45+z47\ ++z48+z51+z52+z53+z55+z56+z58+z61+z62+z63+z65+z66+z69+z70+z71+z74+z76+z78+z80+z\ +82+z85+z92+z94+z95+z96+z97+z98+z99, + 1+z+z2+z8+z9+z12+z13+z14+z15+z16+z18+z19+z21, <>, + 1+z3+z4+z8+z10+z12+z13+z18+z19+z20+z21+z23+z24+z28+z30+z31+z33+z34+z40+z41+z\ +42+z43+z45+z46+z48, + 1+z2+z3+z6+z11+z12+z14+z15+z19+z20+z23+z24+z25+z26+z27+z28+z29+z33+z40+z41+z\ +42+z45+z46+z47+z48+z49+z50+z51+z52+z55+z56+z57+z59+z61+z63+z65, + 1+z2+z4+z5+z6+z7+z10+z11+z12+z22+z23+z26+z31+z32+z39+z41+z43+z44+z46+z48+z49\ ++z53+z54+z56+z59+z61+z63+z65+z66+z67+z69+z70+z71+z73+z74+z76+z77+z82+z84+z90+z\ +94+z95+z96+z98+z99, z, z2+z4+z5+z6+z7+z9+z10+z15+z18+z19+z20+z21+z22+z25+z30+z31, 1+z3+z8+z9+z10+z12+z13+z16+z17+z18+z20+z23+z24+z28+z29+z31+z34+z36+z38+z40+z\ 42+z43+z46+z47+z48+z51+z55+z56+z57+z59+z63+z64+z65+z66+z69+z71+z72+z73+z77+z79\ @@ -643,20 +644,14 @@ z44+z46+z48+z50+z51+z53+z58+z61+z62+z63+z64+z65+z66+z67+z68+z69+z70+z71+z72+z7\ 72+z73+z74+z75+z77+z79+z80+z84+z86, z2+z4+z7+z9+z12+z13+z18+z19+z21+z22+z24+z25+z28+z29+z30+z33+z34+z36+z39+z43+\ z45+z46+z50+z51+z52+z55+z57+z58+z60+z61+z62+z65+z66+z69+z71+z73+z74+z75+z77+z7\ -8+z79+z80+z81+z82, 2z, - 2+z+2z2+2z5+2z6+z7+z8+z9+2z10+z12+z14+z15+2z16+2z17+2z18+z19+z20, - 2+2z5+2z6+2z7+2z8+2z9+2z11+2z13+2z14+2z16+2z19+z21+z22+z23+2z24+z25+2z26+z29\ -+z30+2z31+2z32, - 1+z+z2+2z3+z6+z7+z8+z9+2z10+2z11+z12+2z14+z15+z26+z27+2z29+z30+z31+2z33+2z34\ -+z35+z36+z41+2z42, - 2+2z+z2+2z3+z4+z5+z7+z8+z11+2z13+2z14+2z20+2z21+2z22+2z26+z28+z29+z30+z31+2z\ -32+z33+2z34+2z35+2z38+z39+z40+2z41+2z42+2z43+z44+z46+z48+z49+2z52+2z53+2z54, - 1+z+z2+z4+2z5+2z7+z8+z9+z10+2z11+z13+z14+2z16+2z18+2z19+z20+2z22+2z25+z26+2z\ -28+z29+z30+2z31+2z32+z33+2z36+z38+2z39+2z42+2z43+z44+2z45+2z46+2z48+2z49+2z50+\ -2z54+2z55+z57+z58+z60+2z65, - 2+z+z3+2z4+2z5+2z6+2z7+z8+2z10+z11+z14+2z15+2z18+z19+z24+2z25+z26+z27+z30+z3\ -1+2z32+2z33+2z35+z36+z38+z39+2z40+z41+2z43+2z45+z46+2z48+2z50+z52+2z53+z55+z59\ -+2z60+z61+z63+z65+2z66+z67+2z68+z69+z70+z73+z75+z76, 2z, +8+z79+z80+z81+z82, 2z, 1+z2+z3+2z5+z7+2z8+2z9+2z11+2z12+2z14+z15, + 1+2z2+z5+z6+z8+2z10+z12+z14+z16+2z17+2z19+z20+z21+2z23+z25+2z26+z27+z28+2z29\ ++z33+z34+z35+z36+2z38+2z39+2z40+2z41+z45, 2z+z2+z4+2z5+z9+z10+z11+z12+z14+z15, + 2z+z2+z3+z4+z5+z7+z8+2z10+2z11+z12+z13+z14+2z15+z18+z19+2z21+2z22+z23+2z24+2\ +z26+2z28+2z29+2z31+2z33+z35+2z36+z37+2z39+z42+2z44+z46+2z47, + 1+z+z2+z3+2z4+2z5+z6+z7+2z10+z11+z12+z13+2z15, + 1+z+z2+2z3+2z4+2z5+2z6+2z8+z10+z11+z12+z13+2z14+2z15+2z17+2z18+z21+z25+z26+z\ +28+z29+z30+2z31+2z32+z33+2z34+2z35+2z37+z41+2z42+2z43+2z44+2z45+2z46+z47, 2z, 1+z+2z3+z9+2z14+2z15+z16+2z18+2z19, 1+2z2+2z3+2z4+z5+2z6+2z8+2z9+z10+z13+2z16+2z17+z18+z19+2z20+z22+2z25+z27+2z2\ 8+z29+2z31+z32+z33+z35+z37+2z40+z41+2z48+2z50+z52+z53+z54+2z55+2z57+z58, @@ -701,9 +696,12 @@ z30+2z31+2z32+2z34+2z35+2z36+z38+z39+z40+2z42+z45+2z46+2z49+2z51+z52+z53+2z54+\ 33+z35+2z37+2z38+z40+2z41+z44+z45+2z46+2z48+2z49+2z50+z52+z56+2z58+z59, 2z+2z2+2z4+z5+2z7+z8+2z9+2z10+2z12+z14+2z15+z16+z17+2z18+z19+z20+z21+2z22+z2\ 5+2z26+z28+2z29+z30+z32+z33+2z34+z35+2z36+z39+z40+2z41+z42+z44+2z46+z47+2z48+z\ -49+z51+2z52+z53+z54+z57+z58+2z59, 6z, 9+15z+10z2+11z3, - 5+7z+14z2+13z3+10z4+10z5+4z6+13z7+5z8+12z9+3z10+7z11, 86z, 86z, 42396z, - 21846z, 178956933z, 2147483646z, 576460752303423442z, 9223372036854775815z ] +49+z51+2z52+z53+z54+z57+z58+2z59, 6z, 3+6z+10z2+8z3+14z4, + 11+12z+13z2+2z3+13z4+5z5, 4+15z+3z2+9z3+3z6+12z7+4z9+4z10, + 9+9z+15z2+10z3+12z4+12z5+4z6+13z7+5z8+6z9+5z10+4z11+13z12+2z13+13z14+11z15+1\ +1z16+16z17+3z18+6z19+10z20+z21+5z22+11z23+3z24+14z25+z26+3z27+10z28+7z29, + 86z, 105+125z+16z2+114z3+152z4+191z5, 86z, 42396z, 178956933z, 2147483646z, + 576460752303423442z, 9223372036854775815z ] gap> ForAll(fieldsizes, pd -> ForAll(DivisorsInt(pd[2]), d2 -> > Z(pd[1],pd[2])^((pd[1]^pd[2]-1)/(pd[1]^d2-1)) = Z(pd[1],d2) )); true @@ -713,17 +711,17 @@ gap> AsInternalFFE(Z(2,10)^0); Z(2)^0 gap> AsInternalFFE(Z(2,10)); Z(2^10) -gap> AsInternalFFE(0*Z(7,6)); +gap> AsInternalFFE(0*Z(7,11)); 0*Z(7) -gap> AsInternalFFE(Z(7,6)^0); +gap> AsInternalFFE(Z(7,11)^0); Z(7)^0 -gap> AsInternalFFE(Z(7,6)); +gap> AsInternalFFE(Z(7,11)); fail -gap> AsInternalFFE(0*Z(65537,2)); +gap> AsInternalFFE(0*Z(NextPrimeInt(MAXSIZE_GF_INTERNAL),2)); fail -gap> AsInternalFFE(Z(65537,2)^0); +gap> AsInternalFFE(Z(NextPrimeInt(MAXSIZE_GF_INTERNAL),2)^0); fail -gap> AsInternalFFE(Z(65537,2)); +gap> AsInternalFFE(Z(NextPrimeInt(MAXSIZE_GF_INTERNAL),2)); fail gap> SetInfoLevel(InfoPrimeInt,iPI); gap> SetInfoLevel(InfoFactor,iF); diff --git a/tst/testinstall/hpc/tasks.tst b/tst/testinstall/hpc/tasks.tst index 29549c042c0..ba72c294f26 100644 --- a/tst/testinstall/hpc/tasks.tst +++ b/tst/testinstall/hpc/tasks.tst @@ -21,7 +21,7 @@ gap> CallAsTask(ZmodnZ,33); (Integers mod 33) gap> CallAsTask(ZmodnZ,70001); GF(70001) -gap> CallAsTask( Z, 2, 17); +gap> CallAsTask( Z, 2, 35); z gap> z:=CallAsTask( Z, 65537, 2 ); z diff --git a/tst/testinstall/zmodnz.tst b/tst/testinstall/zmodnz.tst index baff2fa49e8..0dd1474ad3e 100644 --- a/tst/testinstall/zmodnz.tst +++ b/tst/testinstall/zmodnz.tst @@ -145,15 +145,15 @@ GF(7) # # large prime field # -gap> p:= NextPrimeInt( MAXSIZE_GF_INTERNAL ); -65537 +gap> p:= NextPrimeInt( 2^32 ); +4294967311 gap> Famp:= ElementsFamily( FamilyObj( Integers mod p ) );; gap> z1:= ZmodnZObj( Famp, -3 ); -ZmodpZObj( 65534, 65537 ) +ZmodpZObj( 4294967308, 4294967311 ) gap> z2:= ZmodnZObj( Famp, 1 ); -ZmodpZObj( 1, 65537 ) +ZmodpZObj( 1, 4294967311 ) gap> z3:= ZmodnZObj( Famp, 10 ); -ZmodpZObj( 10, 65537 ) +ZmodpZObj( 10, 4294967311 ) gap> z1 = z2; z2 = z3; false false @@ -168,51 +168,51 @@ gap> z1 = Zero( GF(p) ); Zero( GF(p) ) = z1; false false gap> z1 + z2; z1 + z3; z2 + z3; z1 + 1; 2 + z2; -ZmodpZObj( 65535, 65537 ) -ZmodpZObj( 7, 65537 ) -ZmodpZObj( 11, 65537 ) -ZmodpZObj( 65535, 65537 ) -ZmodpZObj( 3, 65537 ) +ZmodpZObj( 4294967309, 4294967311 ) +ZmodpZObj( 7, 4294967311 ) +ZmodpZObj( 11, 4294967311 ) +ZmodpZObj( 4294967309, 4294967311 ) +ZmodpZObj( 3, 4294967311 ) gap> z1 - z2; z1 - z3; z2 - z3; z1 - 1; 2 - z2; -ZmodpZObj( 65533, 65537 ) -ZmodpZObj( 65524, 65537 ) -ZmodpZObj( 65528, 65537 ) -ZmodpZObj( 65533, 65537 ) -ZmodpZObj( 1, 65537 ) +ZmodpZObj( 4294967307, 4294967311 ) +ZmodpZObj( 4294967298, 4294967311 ) +ZmodpZObj( 4294967302, 4294967311 ) +ZmodpZObj( 4294967307, 4294967311 ) +ZmodpZObj( 1, 4294967311 ) gap> z1 * z2; z1 * z3; z2 * z3; z1 * 1; 2 * z2; -ZmodpZObj( 65534, 65537 ) -ZmodpZObj( 65507, 65537 ) -ZmodpZObj( 10, 65537 ) -ZmodpZObj( 65534, 65537 ) -ZmodpZObj( 2, 65537 ) +ZmodpZObj( 4294967308, 4294967311 ) +ZmodpZObj( 4294967281, 4294967311 ) +ZmodpZObj( 10, 4294967311 ) +ZmodpZObj( 4294967308, 4294967311 ) +ZmodpZObj( 2, 4294967311 ) gap> z1 / z2; z1 / z3; z2 / z3; z1 / 1; 2 / z2; -ZmodpZObj( 65534, 65537 ) -ZmodpZObj( 58983, 65537 ) -ZmodpZObj( 45876, 65537 ) -ZmodpZObj( 65534, 65537 ) -ZmodpZObj( 2, 65537 ) +ZmodpZObj( 4294967308, 4294967311 ) +ZmodpZObj( 1288490193, 4294967311 ) +ZmodpZObj( 3865470580, 4294967311 ) +ZmodpZObj( 4294967308, 4294967311 ) +ZmodpZObj( 2, 4294967311 ) gap> z2^3; z2^(-2); z2^0; -ZmodpZObj( 1, 65537 ) -ZmodpZObj( 1, 65537 ) -ZmodpZObj( 1, 65537 ) +ZmodpZObj( 1, 4294967311 ) +ZmodpZObj( 1, 4294967311 ) +ZmodpZObj( 1, 4294967311 ) gap> DegreeFFE( z1 ); DegreeFFE( z2 ); DegreeFFE( z3 ); 1 1 1 gap> Int( z1 ); Int( z2 ); Int( z3 ); -65534 +4294967308 1 10 gap> SquareRoots( GF(p), z1 ); -[ ] +[ ZmodpZObj( 122581002, 4294967311 ), ZmodpZObj( 4172386309, 4294967311 ) ] gap> SquareRoots( GF(p), z2 ); -[ ZmodpZObj( 1, 65537 ), ZmodpZObj( 65536, 65537 ) ] +[ ZmodpZObj( 1, 4294967311 ), ZmodpZObj( 4294967310, 4294967311 ) ] gap> SquareRoots( GF(p), z3 ); -[ ] +[ ZmodpZObj( 495820313, 4294967311 ), ZmodpZObj( 3799146998, 4294967311 ) ] gap> ModulusOfZmodnZObj( z1 ); -65537 +4294967311 gap> DefaultRingByGenerators( [ z1 ] ); -GF(65537) +GF(4294967311) # # ring that is not a field