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The theory of ideals of Z is very elementary but for completeness
the general machinery for ring ideals applies. Such ideals will have
type RngInt, that is, the same type as the ring of integers itself
(ideal<Integers() | 1>).
In the case of Z any subring is an ideal so that the
sub-constructor creates the same object as does the
ideal-constructor.
Given the ring of integers Z and an integer a, return the ideal
of Z generated by a.
We construct some ideals of Z.
> Z := IntegerRing();
> I13 := ideal< Z | 13 >;
> I13;
Ideal of Integer Ring generated by 13
> 1 in I13;
false
> 0 in I13;
true
> -13 in I13;
true
> I0 := ideal< Z | 0 >;
> 0 in I0;
true
> 1 in I0;
false
We check that that Z is regarded as an ideal.
> I1 := ideal< Z | 1 >;
> I1 eq Z;
true
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