  
  
                              [1m[4m[31mGAP 4 Package [1mForms[1m[4m[31m[0m
  
  
                           [1m[4m[31mSesquilinear and Quadratic[0m
  
  
                                      1.0
  
  
                                    May 2007
  
  
                                  John Bamberg
  
                                  Jan De Beule
  
  
  
  John Bamberg
      Email:    [34mmailto:bamberg@cage.ugent.be[0m
      Homepage: [34mhttp://cage.ugent.be/~bamberg[0m
      Address:  Department  of Pure Mathematics, Ghent University, Galglaan 2,
                9000 Ghent, Belgium
  
  
  Jan De Beule
      Email:    [34mmailto:jdebeule@cage.ugent.be[0m
      Homepage: [34mhttp://cage.ugent.be/~jdebeule[0m
      Address:  Department  of Pure Mathematics, Ghent University, Galglaan 2,
                9000 Ghent, Belgium
  
  
  
  -------------------------------------------------------
  [1m[4m[31mCopyright[0m
  (C) 2007 by the authors
  
  This  package  may  be distributed under the terms and conditions of the GNU
  Public License Version 2 or higher.
  
  
  -------------------------------------------------------
  
  
  [1m[4m[31mContent (Forms)[0m
  
  1. Introduction
    1.1 Philosophy
    1.2 Overview over this manual
  2. Examples
    2.1 A conic of PG(2,8)
    2.2 A form for W(5,3)
  3. Background Theory on Forms
    3.1 Sesquilinear forms, dualities, and polarities
      3.1-1 Example
    3.2 Quadratic forms
      3.2-1 Example
    3.3 Morphisms of forms
    3.4 An important convention
      3.4-1 Example
    3.5 Canonical forms
  4. Functionality
    4.1 Functions for creating forms
      4.1-1 BilinearFormByMatrix
      4.1-2 QuadraticFormByMatrix
      4.1-3 HermitianFormByMatrix
      4.1-4 BilinearFormByPolynomial
      4.1-5 QuadraticFormByPolynomial
      4.1-6 HermitianFormByPolynomial
    4.2 Attributes and properties of forms
      4.2-1 IsReflexiveForm
      4.2-2 IsAlternatingForm
      4.2-3 IsSymmetricForm
      4.2-4 IsDegenerateForm
      4.2-5 BaseField
      4.2-6 GramMatrix
      4.2-7 WittIndex
      4.2-8 RadicalOfForm
      4.2-9 PolynomialOfForm
      4.2-10 DiscriminantOfForm
    4.3 Functions for changing forms
      4.3-1 BaseChangeToCanonical
      4.3-2 IsometricCanonicalForm
    4.4 Operations on forms
      4.4-1 BaseChangeHomomorphism
      4.4-2 EvaluateForm
  
  
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