diff --git a/A1-Brouwer/Documentation/AnisotropicDimensionDoc.m2 b/A1-Brouwer/Documentation/AnisotropicDimensionDoc.m2 index 57d1f66..a13d2ad 100644 --- a/A1-Brouwer/Documentation/AnisotropicDimensionDoc.m2 +++ b/A1-Brouwer/Documentation/AnisotropicDimensionDoc.m2 @@ -44,10 +44,10 @@ document{ Headline => "Returns the anisotropic dimension of a symmetric bilinear form", Usage => "anisotropicDimension(beta)", Inputs => { - GrothendieckWittClass => "beta" => {"Any class ", TEX///$\beta\in\text{GW}(k)$///, " where ", TEX///$k$///, " is the complex numbers, reals, rationals, or a finite field."}, + GrothendieckWittClass => "beta" => {"over a field ", TEX///$k$///, " where ", TEX///$k$///, " is the complex numbers, reals, rationals, or a finite field."}, }, Outputs => { - ZZ => {"The rank of the anisotropic part of ", TEX///$\beta$///, "."}, + ZZ => {"the rank of the anisotropic part of ", TEX///$\beta$///, "."}, }, PARA{"By Witt decomposition, any form decomposes uniquely as ", TEX///$\beta \cong k \mathbb{H} \oplus \beta_a$///," where the form ", TEX///$\beta_a$///," is anisotropic. The rank of ", TEX///$\beta_a$///, " is called the ", EM "anisotropic dimension", " of ", TEX///$\beta$///, "."}, PARA{"The anisotropic dimension of a form defined over the rationals is the maximum of the ", TO2(anisotropicDimensionQp,"anistropic dimension at each of the completions"), " of ", TEX///$\mathbb{Q}$///, "."},