This section describes how to construct rings for use with &MatricesForHomalg;,
which exploit the &GAP4;-built-in abilities to perform the necessary
ring operations. By this we also mean necessary matrix operations over
such rings. For the purposes of &MatricesForHomalg; only the ring of integers is
properly supported in &GAP4;. The &GAP4; extension packages &Gauss;
and &GaussForHomalg; extend these built-in abilities to operations
with sparse matrices over the ring <M>&ZZ; / p^n</M> for <M>p</M>
prime and <M>n</M> positive.<P/>
If a ring <M>R</M> is supported in &MatricesForHomalg; any of its residue class
rings <M>R/I</M> is supported as well, provided the ideal <M>I</M> of
relations admits a finite set of generators as a left resp. right
ideal (&see; <Ref Oper="\/"
Label="constructor for residue class rings" Style="Number"/>).
This is immediate for commutative noetherian rings.
The following properties are declared for &homalg; rings. Note that
(apart from so-called true and immediate methods (&see;
<Ref Sect="Rings:LIRNG"/>)) there are no methods installed for ring
properties. This means that if the value of the ring
property <C>Prop</C> is not set for a &homalg; ring <A>R</A>, then
<P/>
<C>Prop</C>( <A>R</A> ); <P/>
will cause an error. One can use the usual &GAP4; mechanism to check if
the value of the property is set or not <P/>
<C>HasProp</C>( <A>R</A> ); <P/>
If you discover that a specific property <C>Prop</C> is missing for a
certain &homalg; ring <A>R</A> you can it add using the usual &GAP4;
mechanism <P/>
<C>SetProp</C>( <A>R</A>, true ); <P/>
or <P/>
<C>SetProp</C>( <A>R</A>, false ); <P/>
Be very cautious with setting "missing" properties to &homalg;
objects: If the value you set is mathematically wrong &homalg; will
probably draw wrong conclusions and might return wrong results.
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