This paper presents algorithms for quadratic forms over a formally real algebraic function field K of one variable over a fixed real closed field k. The algorithms introduced in the paper solve the following problems: test whether an element is a square, respectively a local square, compute Witt index of a quadratic form and test if a form is isotropic/hyperbolic. Finally, we remark on a method for testing whether two function fields are Witt equivalent.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc108-0-10,
author = {Konrad Ja\l owiecki and Przemys\l aw Koprowski},
title = {Algorithms for quadratic forms over real function fields},
journal = {Banach Center Publications},
volume = {108},
year = {2016},
pages = {133-141},
zbl = {06622290},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc108-0-10}
}
Konrad Jałowiecki; Przemysław Koprowski. Algorithms for quadratic forms over real function fields. Banach Center Publications, Tome 108 (2016) pp. 133-141. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc108-0-10/