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 1.2.12, released on 2024-08-30. For more information, please refer to the package manual. There is also a README file.

License: GPL-2.0-or-later

An example of how it works

gap> LoadPackage("forms");<br>
true<br>
gap> gf := GF(8);<br>
GF(2^3)<br>
gap> r := PolynomialRing( gf, 3 );<br>
PolynomialRing(..., [ x_1, x_2, x_3 ])<br>
gap> poly := r.1^2 + r.2 * r.3;<br>
x_1^2+x_2\*x_3<br>
gap> form := QuadraticFormByPolynomial( poly, r );<br>
&lt; quadratic form ><br>
gap> Display( form );<br>
Quadratic form<br>
Gram Matrix:<br>
 1 . .<br>
 . . 1<br>
 . . .<br>
Polynomial: x_1^2+x_2\*x_3<br>
<br>
gap> IsDegenerateForm( form );<br>
#I  Testing degeneracy of the \*associated bilinear form\*<br>
true<br>
gap> IsSingularForm( form );<br>
false<br>
gap> WittIndex( form );<br>
1<br>
gap> IsParabolicForm( form );<br>
true<br>
gap> form;<br>
< non-singular parabolic quadratic form ><br>

Dependencies

This package requires GAP version >=4.9

Authors

John Bamberg, Jan De Beule.

Citing

Please, cite this package as

[BBH24] Bamberg, J., De Beule, J. and Horn, M., Forms, Sesquilinear and Quadratic, Version 1.2.12 (2024)
(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.