getSumDecomposition beta
Given a symmetric bilinear form beta over $\mathbb{Q},$ $ \mathbb{R},$ $\mathbb{C}$ or a finite field of characteristic not 2, we decompose it as a sum of some number of hyperbolic and rank one forms.
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Over $\mathbb{R}$ there are only two square classes and a form is determined uniquely by its rank and signature [L05, II Proposition 3.2]. A form defined by the $3\times 3$ Gram matrix M above is isomorphic to the form $\langle 1,-1,1\rangle $.
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Over $\mathbb{F}_{q}$ forms can similarly be diagonalized, in the above case as $\langle 1,-1,1,-6 \rangle$.
Citations:
The object getSumDecomposition is a method function.
The source of this document is in A1BrouwerDegrees/Documentation/DecompositionDoc.m2:32:0.