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#W  gaussian.tst                GAP library                     Thomas Breuer
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#H  @(#)$Id: gaussian.tst,v 4.9 2002/04/15 10:08:40 sal Exp $
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#Y  Copyright (C)  1996,  Lehrstuhl D fuer Mathematik,  RWTH Aachen,  Germany
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gap> START_TEST("$Id: gaussian.tst,v 4.9 2002/04/15 10:08:40 sal Exp $");

gap> 257 in GaussianIntegers;
true
gap> 257 + 17*E(4) in GaussianIntegers;
true
gap> 1/2 in GaussianIntegers;
false
gap> 1 + E(3) in GaussianIntegers;
false

gap> 257 in GaussianRationals;
true
gap> 257 + 17*E(4) in GaussianRationals;
true
gap> 1/2 in GaussianRationals;
true
gap> 1 + E(3) in GaussianRationals;
false

gap> IsSubset( GaussianRationals, GaussianIntegers );
true

gap> Quotient( GaussianIntegers, 35, 5 );
7
gap> Quotient( GaussianIntegers, 35, 1+2*E(4) );
7-14*E(4)
gap> Quotient( GaussianIntegers, 35, 1+E(4) );
fail

gap> IsAssociated( GaussianIntegers, 4, -4*E(4) );
true
gap> IsAssociated( GaussianIntegers, 4*E(4), -4 );
true
gap> IsAssociated( GaussianIntegers, 4*E(4), 5 );
false

gap> StandardAssociate( GaussianIntegers,      4 );
4
gap> StandardAssociate( GaussianIntegers,     -4 );
4
gap> StandardAssociate( GaussianIntegers, 1-E(4) );
1+E(4)
gap> StandardAssociate( GaussianIntegers, 1+E(4) );
1+E(4)

gap> EuclideanDegree( GaussianIntegers, 1+E(4) );
2
gap> EuclideanDegree( GaussianIntegers,      2 );
4

gap> EuclideanRemainder( GaussianIntegers, 35, 7 );
0
gap> EuclideanRemainder( GaussianIntegers, 5, 1+2*E(4) );
0
gap> EuclideanRemainder( GaussianIntegers, 5, 1+E(4) );
-1
gap> EuclideanRemainder( GaussianIntegers, 5-2*E(4), 1+E(4) );
-1

gap> EuclideanQuotient( GaussianIntegers, 35, 7 );
5
gap> EuclideanQuotient( GaussianIntegers, 5, 1+2*E(4) );
1-2*E(4)
gap> EuclideanQuotient( GaussianIntegers, 5, 1+E(4) );
3-3*E(4)
gap> EuclideanQuotient( GaussianIntegers, 5-2*E(4), 1+E(4) );
2-4*E(4)

gap> QuotientRemainder( GaussianIntegers, 35, 7 );
[ 5, 0 ]
gap> QuotientRemainder( GaussianIntegers, 5, 1+2*E(4) );
[ 1-2*E(4), 0 ]
gap> QuotientRemainder( GaussianIntegers, 5, 1+E(4) );
[ 3-3*E(4), -1 ]
gap> QuotientRemainder( GaussianIntegers, 5-2*E(4), 1+E(4) );
[ 2-4*E(4), -1 ]

gap> IsPrime( GaussianIntegers, 3 );
true
gap> IsPrime( GaussianIntegers, 5 );
false
gap> IsPrime( GaussianIntegers, 2+E(4) );
true
gap> IsPrime( GaussianIntegers, 1+2*E(4) );
true
gap> IsPrime( GaussianIntegers, 5-E(4) );
false

gap> Factors( GaussianIntegers, 35 );
[ 2-E(4), 2+E(4), 7 ]
gap> Factors( GaussianIntegers, 255 );
[ -3, 1+2*E(4), 2+E(4), 1+4*E(4), 4+E(4) ]
gap> Factors( GaussianIntegers, 2+E(4) );
[ 2+E(4) ]
gap> Factors( GaussianIntegers, 1+2*E(4) );
[ 1+2*E(4) ]
gap> Factors( GaussianIntegers, 5-E(4) );
[ 1-E(4), 3+2*E(4) ]

gap> STOP_TEST( "gaussian.tst", 640000 );


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#E  gaussian.tst  . . . . . . . . . . . . . . . . . . . . . . . . . ends here
