<!-- 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. --> <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> <!-- ############################################################ --> </Chapter>