Unimodular quadratic forms over global function fields

1979 ◽  
Vol 11 (4) ◽  
pp. 529-541 ◽  
Author(s):  
Larry J. Gerstein
Keyword(s):  
Quadratic Forms ◽  
Function Fields ◽  
Global Function ◽  
Global Function Fields

scholarly journals Algorithms for quadratic forms over global function fields of odd characteristic

2021 ◽  
Vol 55 (3) ◽  
pp. 68-72
Author(s):  
Mawunyo Kofi Darkey-Mensah
Keyword(s):  
Quadratic Form ◽  
Quadratic Forms ◽  
Function Fields ◽  
Number Fields ◽  
Global Function ◽  
Global Function Fields ◽  
Anisotropic Part ◽  
Pythagoras Number ◽  
Present Algorithm

This paper presents an adaptation of recently developed algorithms for quadratic forms over number fields in [4] to global function fields of odd characteristics. First, we present algorithm for checking if a given non-degenerate quadratic form is isotropic or hyperbolic. Next we devise a method for computing the dimension of the anisotropic part of a quadratic form. Finally we present algorithms computing two field invariants: the level and the Pythagoras number.

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