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periods
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JordyLopez27 committed Nov 6, 2023
1 parent da49c73 commit 1261b11
Showing 1 changed file with 2 additions and 2 deletions.
4 changes: 2 additions & 2 deletions A1-Brouwer/Documentation/AnisotropicDimensionDoc.m2
Original file line number Diff line number Diff line change
Expand Up @@ -44,10 +44,10 @@ document{
Headline => "returns the anisotropic dimension of a symmetric bilinear form",
Usage => "anisotropicDimension(beta)",
Inputs => {
GrothendieckWittClass => "beta" => {"over a field ", TEX///$k$///, " 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///$\mathbb{Q}$///, "."},
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