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# 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.

## See also

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

## Ways to use getWittIndex:

- `getWittIndex(GrothendieckWittClass)`

## For the programmer

The object getWittIndex 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.m2:76:0.