anisotropicDimensionQp -- returns the anisotropic dimension of a rational symmetric bilinear form over the p-adics

Synopsis

• Usage:

  anisotropicDimensionQp(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] in Macaulay2, which computes the anisotropic dimension of rational forms over the $p$-adics. Note that any form of rank $\ge 5$ is always isotropic, so this method will return 0, 1, 2, 3, or 4.

Citations:

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

See also

• anisotropicDimension -- returns the anisotropic dimension of a symmetric bilinear form