getWittIndex -- returns the Witt index of a symmetric bilinear form

Usage:

getWittIndex beta
Inputs:
- beta, a Grothendieck-Witt Class, a GrothendieckWittClass denoted by $\beta\in\text{GW}(k)$, where $k$ is $\mathbb{Q}$, $\mathbb{R}$, $\mathbb{C}$, or a finite field of characteristic not 2
Outputs:
- an integer, the rank of the totally isotropic 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 integer $n$ is called the Witt index of $\beta$. See for instance [L05, I.4.3].

References

[L05] T.Y. Lam, "Introduction to quadratic forms over fields," American Mathematical Society, 2005.

Ways to use getWittIndex:

getWittIndex(GrothendieckWittClass)

For the programmer

The object getWittIndex is a method function.

The source of this document is in A1BrouwerDegrees/Documentation/AnisotropicDimensionDoc.m2:76:0.

getWittIndex -- returns the Witt index of a symmetric bilinear form

Description

References

See also

Ways to use getWittIndex:

For the programmer