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  intro.xml            'Forms' package documentation 
                                                                  John Bamberg
                                                               and Jan De Beule
                                                                  

  Copyright (C) 2008, Ghent University

This chapter gives a short introduction to the package.

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<Chapter Label="intro">
<Heading>Introduction</Heading>

<Section Label="philosophy">
<Heading>Philosophy</Heading>

<Package>Forms</Package> is a package for computing with
sesquilinear and quadratic forms on finite vector spaces.
It provides users with the basic algebraic tools to 
work with classical groups and polar geometries,
and enables one to specify a form and its corresponding
geometry. The functionality of the package includes:
<List>
 <Item>the construction of sesquilinear and quadratic forms;</Item>
 <Item>operations which allow a user to change coordinates, that is,
to ``change form'' and work in an isometric (or similar)
formed vector space; and</Item>
 <Item>a way to determine the form(s) left invariant by a matrix group (up to a scalar).</Item>
</List>


</Section>

<Section Label="overview">
<Heading>Overview over this manual</Heading>

The next chapter (<Ref Chap="examples"/>) gives some basic examples of
the use of this package. In "Background Theory of Forms" (Chapter
<Ref Chap="theory"/>) we revise the basic notions of the theory of
sesquilinear and quadratic forms, where we also set the notation
and conventions adopted by this package. In "Constructing forms and basic
functionality" (Chapter <Ref Chap="functionality"/>), we describe all operations
to construct sesquilinear and quadratic forms and basic attributes and
properties that do not require morphisms. In "Morphims of forms" (Chapter
<Ref Chap="morphisms"/>) we revise the basic notions of morphisms of forms, and
the classification of sesquilinear and quadratic forms on vector spaces over
finite fields. Operations, attributes and properties that are related to the
computation of morphisms of forms, are also described in this chapter. 
</Section>

<Section Label="howto">
<Heading>How to read this manual</Heading>

We have tried to make this manual pleasant to read for the general
reader. So it is inevitable that we will use Greek symbols and simple
mathematical formulas. To make these visible in the HTML version of this
documentation, you may have to change the default character set
of your browser to UTF-8.
</Section>

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</Chapter>
