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getRelevantPrimes -- outputs a list containing all primes p where the Hasse-Witt invariant of a symmetric bilinear form is nontrivial

Description

It is a classical result that the Hasse-Witt invariants of a quadratic form are equal to 1 for all but finitely many primes (see e.g. [S73, IV Section 3.3]). As the Hasse-Witt invariants are computed as a product of Hilbert symbols of the pairwise entries appearing on a diagonalization of the symbol, it suffices to consider primes dividing diagonal entries.

i1 : beta = makeDiagonalForm(QQ, (6,7,22));
i2 : getRelevantPrimes beta

o2 = {2, 3, 7, 11}

o2 : List

Citations:

See also

Ways to use getRelevantPrimes:

  • getRelevantPrimes(GrothendieckWittClass)

For the programmer

The object getRelevantPrimes is a method function.


The source of this document is in A1BrouwerDegrees/Documentation/GWInvariantsDoc.m2:83:0.