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relevantPrimes -- outputs a list of primes at which the Hasse-Witt invariants of a symmetric bilinear form may be non-trivial



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 = diagonalForm(QQ,(6,7,22));
i2 : relevantPrimes(beta)

o2 = {2, 3, 7, 11}

o2 : List


Ways to use relevantPrimes :

For the programmer

The object relevantPrimes is a method function.