  
  [1X1 Introduction[0X
  
  
  [1X1.1 Philosophy[0X
  
  [5XForms[0m  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:
  
  --    the construction of sesquilinear and quadratic forms;
  
  --    operations  which  allow  a  user  to  change coordinates, that is, to
        ``change  form''  and  work in an isometric (or similar) formed vector
        space; and
  
  --    a way to determine the form(s) left invariant by a matrix group (up to
        a scalar).
  
  
  [1X1.2 Overview over this manual[0X
  
  The  next  chapter ([14X2[0m) gives some basic examples of the use of this package.
  In  "Background  Theory of Forms" (Chapter [14X3[0m) 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  [14X4[0m), 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 [14X5[0m) 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.
  
  
  [1X1.3 How to read this manual[0X
  
  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.
  
  
  [1X1.4 Release notes[0X
  
  Version  1.2.1  of  [5XForms[0m contains some changed and extra functionality with
  relation  to  trivial  forms. The changed and new functionality is described
  completely  in Section [14X4.9[0m. We greatfully acknowledge the useful feedback of
  Alice Niemeyer.
  
