This package is intended computing and manipulating local and global $\mathbb{A}^1$-Brouwer degrees. Global Brouwer degrees are non-degenerate symmetric bilinear forms valued in the Grothendieck-Witt ring of a field $\text{GW}(k)$.
In order to simplify the forms produced, this package produces invariants of symmetric bilinear forms, including their Witt indices, their discriminants, and their Hasse Witt invariants. Quadratic forms can furthermore be decomposed into their isotropic and anisotropic parts. Finally, and perhaps most crucially, we can certify whether two symmetric bilinear forms are isomorphic in the Grothendieck-Witt ring.
This documentation describes version 1.0 of A1BrouwerDegrees.
The source code from which this documentation is derived is in the file A1BrouwerDegrees.m2. The auxiliary files accompanying it are in the directory A1BrouwerDegrees/.
The object A1BrouwerDegrees is a package.