As already mentioned in the introduction of this chapter the objects
GaussianIntegers are the domains of Gaussian
rationals and integers respectively. All set theoretic functions, i.e.,
Intersection, are applicable to these domains and their
elements (see chapter Domains). There does not seem to be an important
use of this however. All functions not mentioned here are not treated
specially, i.e., they are implemented by the default function mentioned
in the respective section.
The membership test for Gaussian rationals is implemented via
IsGaussRat (IsGaussRat). The membership test for Gaussian integers
is implemented via
IsGaussInt (see IsGaussInt).
A random Gaussian rational
a + b*E(4) is computed by combining two
random rationals a and b (see Set Functions for Rationals).
Likewise a random Gaussian integer
a + b*E(4) is computed by
Set Functions for Integers).
gap> Size( GaussianRationals ); "infinity" gap> Intersection( GaussianIntegers, [1,1/2,E(4),-E(6),E(4)/3] ); [ 1, E(4) ]
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