This chapter should give you a quick guide to create your first example in &homalg;.
<Section Label="Why ZZ">
<Heading>Why are all examples in this manual over &ZZ; or <M>&ZZ;/m&ZZ;</M>?</Heading>
As the reader might notice, all examples in this manual will be either
over &ZZ; or over one of its residue class rings
<M>&ZZ;/m&ZZ;</M>. There are two reasons for this. The first reason is
that &GAP; does not natively support rings other than &ZZ; in a
<E>sufficient</E> way (&see; <Ref Sect="SufficientSupport" Text="Rings
supported in a sufficient way"/>).
<P/>
The second and more important reason is to underline the fact the all
effective homological constructions that are relevant for &Modules;
have only as much to do with the Gröbnerbasis algorithm as they do
with the Hermite algorithm for the ring &ZZ;; both algorithms are used
to effectively solve inhomogeneous linear systems over the respective
ring. And &Modules; is designed to use rings and matrices over these
rings together with all their operations as a black box. In other
words: Because &Modules; works for <M>&ZZ;</M>, it works by its design
for all other computable rings.
<!-- (see also <Ref Sect="black box" Text="The black box concept"/>)
-->
To quickly create a ring for use with &Modules; enter<Br/><Br/>
<C>ExamplesForHomalg();</C><Br/><Br/>
which will load the package &ExamplesForHomalg; (if installed) and
provide a step by step guide to create the ring. For the full core
functionality you need to install the packages &homalg;,
&HomalgToCAS;, &IO_ForHomalg;, &RingsForHomalg;, &Gauss;, and
&GaussForHomalg;. They are part of the &homalg; project.
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Bemerkung:
Die farbliche Syntaxdarstellung ist noch experimentell.
