1#@local R,a,b,c,d 2gap> START_TEST("zmodnze.tst"); 3gap> R:=RingInt(CF(4)) mod 5; 4(RingInt(CF(4)) mod 5) 5gap> IsFinite(R); 6true 7gap> Size(R); 825 9gap> IsFinite(R); 10true 11gap> AsList(R); 12[ ( 0 mod 5 ), ( 1 mod 5 ), ( 2 mod 5 ), ( 3 mod 5 ), ( 4 mod 5 ), 13 ( E(4) mod 5 ), ( 2*E(4) mod 5 ), ( 3*E(4) mod 5 ), ( 4*E(4) mod 5 ), 14 ( 1+E(4) mod 5 ), ( 1+2*E(4) mod 5 ), ( 1+3*E(4) mod 5 ), 15 ( 1+4*E(4) mod 5 ), ( 2+E(4) mod 5 ), ( 2+2*E(4) mod 5 ), 16 ( 2+3*E(4) mod 5 ), ( 2+4*E(4) mod 5 ), ( 3+E(4) mod 5 ), 17 ( 3+2*E(4) mod 5 ), ( 3+3*E(4) mod 5 ), ( 3+4*E(4) mod 5 ), 18 ( 4+E(4) mod 5 ), ( 4+2*E(4) mod 5 ), ( 4+3*E(4) mod 5 ), 19 ( 4+4*E(4) mod 5 ) ] 20gap> One(R); 21( 1 mod 5 ) 22gap> IsUnit(One(R)); 23true 24gap> Zero(R); 25( 0 mod 5 ) 26gap> IsUnit(Zero(R)); 27false 28gap> a:=E(4)*One(R); 29( E(4) mod 5 ) 30gap> b:=-One(R); 31( 4 mod 5 ) 32gap> c:=a+b; 33( 4+E(4) mod 5 ) 34gap> d:=E(4)+c; 35( 4+2*E(4) mod 5 ) 36gap> c+2; 37( 1+E(4) mod 5 ) 38gap> d*E(4); 39( 3+4*E(4) mod 5 ) 40gap> d*3; 41( 2+E(4) mod 5 ) 42gap> ZmodnZObj(2,4)*d; 43( 3+4*E(4) mod 5 ) 44gap> d*ZmodnZObj(2,4); 45( 3+4*E(4) mod 5 ) 46gap> a*c; 47( 4+4*E(4) mod 5 ) 48gap> IsUnit(a); 49true 50gap> Zero(a); 51( 0 mod 5 ) 52gap> One(a); 53( 1 mod 5 ) 54gap> Zero(a) in R; 55true 56gap> One(a) in R; 57true 58gap> Cyclotomic(d); 594+2*E(4) 60gap> a*a^-1; 61( 1 mod 5 ) 62gap> a*a^-1=One(R); 63true 64gap> d^-1; 65fail 66gap> Number(R,IsUnit); 6716 68gap> Number(R,x->IsUnit(R,x)); 6916 70gap> RingInt(GF(2)); 71Error, RingOfIntegralCyclotomics : an argument is not cyclotomic field ! 72gap> STOP_TEST( "zmodnze.tst", 1); 73