getAnisotropicDimensionQQp -- returns the anisotropic dimension of a rational symmetric bilinear form over the p-adic rational numbers

Usage:

getAnisotropicDimensionQQp(beta, p)
Inputs:
- beta, a Grothendieck-Witt Class, over $\mathbb{Q}$
- p, an integer, a prime number
Outputs:
- an integer, the rank of the anisotropic part of $\beta$ over $\mathbb{Q}_{p}$

Description

This is an implementation of [KC18, Algorithm 8], which computes the anisotropic dimension of rational forms over the $p$-adic rational numbers. Any form of rank $\ge 5$ is isotropic, so this method will always return 0, 1, 2, 3, or 4.

References

[KC18] P. Koprowski, A. Czogala, "Computing with quadratic forms over number fields," Journal of Symbolic Computation, 2018.

Ways to use getAnisotropicDimensionQQp:

getAnisotropicDimensionQQp(GrothendieckWittClass,ZZ)

For the programmer

The object getAnisotropicDimensionQQp is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/AnisotropicDimensionDoc.m2:25:0.

getAnisotropicDimensionQQp -- returns the anisotropic dimension of a rational symmetric bilinear form over the p-adic rational numbers

Description

References

See also

Ways to use getAnisotropicDimensionQQp:

For the programmer