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 1.2.9, released on 2022-10-14. 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 1.2.9 (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.