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anisotropicPart -- returns the anisotropic part of a Grothendieck Witt class



Given a form $\beta$ we may compute its anisotropic part inductively by reference to its anisotropic dimension. Over the complex numbers and the reals this is trivial, and over finite fields it is a fairly routine computation, however over the rationals some more sophisticated algorithms are needed from the literature. For this methods we implement algorithms developed for number fields by Koprowski and Rothkegel [KR23]. Note also that a Chinese Remainder Theorem method is needed in reducing from anisotropic dimension three as in [KR23, Algorithm 7], so we import one from the Parametrization package.

i1 : alpha = diagonalForm(QQ,(3,-3,2,5,1,-9));
i2 : anisotropicPart(alpha)

o2 = GrothendieckWittClass{cache => CacheTable{}}
                           matrix => | 2 0  |
                                     | 0 20 |

o2 : GrothendieckWittClass


See also

Ways to use anisotropicPart :

For the programmer

The object anisotropicPart is a method function.