Forms

Sesquilinear and Quadratic

Version 1.2.8
Released 2022-07-09

This project is maintained by John Bamberg, Jan De Beule, Max Horn

GAP Package Forms

This package can be used for work with sesquilinear and quadratic forms on finite vector spaces; objects that are used to describe polar spaces and classical groups.

The current version of this package is version 1.2.8, released on 2022-07-09. For more information, please refer to the package manual. There is also a README file.

An example of how it works

gap> LoadPackage(“forms”);
true
gap> gf := GF(8);
GF(2^3)
gap> r := PolynomialRing( gf, 3 );
PolynomialRing(…, [ x_1, x_2, x_3 ])
gap> poly := r.1^2 + r.2 * r.3;
x_1^2+x_2*x_3
gap> form := QuadraticFormByPolynomial( poly, r );
< quadratic form >
gap> Display( form );
Quadratic form
Gram Matrix:
1 . .
. . 1
. . .
Polynomial: x_1^2+x_2*x_3

gap> IsDegenerateForm( form );
#I Testing degeneracy of the *associated bilinear form*
true
gap> IsSingularForm( form );
false
gap> WittIndex( form );
1
gap> IsParabolicForm( form );
true
gap> form;
< non-singular parabolic quadratic form >

Dependencies

This package requires GAP version >=4.9

Authors

John Bamberg, Jan De Beule.

Citing

Please, cite this package as

[BBH22] Bamberg, J., De Beule, J. and Horn, M., Forms, Sesquilinear and Quadratic, Version 1.2.8 (2022)
(Refereed GAP package), https://gap-packages.github.io/forms.

You can get more info by typing Cite("Forms"); in the gap prompt.

Feedback

For bug reports, feature requests and suggestions, please use the issue tracker.