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

  Copyright (C) 2007, 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 computation with
sesquilinear and quadratic forms on finite vector spaces.
It provides users with the basic tools to 
work with classical groups and polar geometry,
and enables one to specify a form and its corresponding
geometry. Also included in the functionality of the package
are operations which allow a user to change coordinates;
or to ``change form'' and work in an isometric (or similar)
polar space. 

</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 the this package. In Sections <Ref Sect="creating_forms"/>, <Ref 
Sect="properties"/>, and <Ref Sect="changing_forms"/> we provide the details of the operations, 
functions, and attributes entailed in <Package>Forms</Package>.
</Section>

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</Chapter>
