Macaulay2 » Documentation
Packages » A1BrouwerDegrees :: getAnisotropicDimension
next | previous | forward | backward | up | index | toc

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

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 anistropic dimension at each of the completions of $\mathbb{Q}$.

See also

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 /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/AnisotropicDimensionDoc.m2:35:0.