getAnisotropicDimension -- returns the anisotropic dimension of a symmetric bilinear form

Usage:

getAnisotropicDimension beta
Inputs:
- beta, a Grothendieck-Witt Class, a GrothendieckWittClass over a field $k$, where $k$ is $\mathbb{Q}$, $\mathbb{R}$, $\mathbb{C}$, or a finite field of characteristic not 2
Outputs:
- an integer, the rank of the anisotropic part of $\beta$

Description

By the Witt Decomposition Theorem, any non-degenerate form decomposes uniquely as $\beta \cong n \mathbb{H} \oplus \beta_a$ where the form $\beta_a$ is anisotropic. The rank of $\beta_a$ is called the anisotropic dimension of $\beta$.

The anisotropic dimension of a form defined over the rational numbers is the maximum of the getAnisotropicDimensionQQp anistropic dimension at each of the completions of $\mathbb{Q}$ at the relevant primes.

References

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

Ways to use getAnisotropicDimension:

getAnisotropicDimension(GrothendieckWittClass)
getAnisotropicDimension(Matrix)

For the programmer

The object getAnisotropicDimension is a method function.

The source of this document is in A1BrouwerDegrees/Documentation/AnisotropicDimensionDoc.m2:53:0.

getAnisotropicDimension -- returns the anisotropic dimension of a symmetric bilinear form

Description

References

See also

Ways to use getAnisotropicDimension:

For the programmer