Closed tornaria closed 15 years ago
Attachment: patch.5411.clifford_invariant.gz
same file with correct name
Attachment: trac_5411.clifford_invariant.patch.gz
Positive review.
Cheers,
Michael
Jon expressed some further wishes, so "needs review" again for now :-)
Cheers,
Michael
replaces previous patch --- this one doesn't remove hasse_conductor
Attachment: trac_5411.clifford_invariant.2nd.patch.gz
The new patch (2nd patch) preserves hasse_conductor
as requested by Jon, and it also fixes the imports in quadratic_form.py
, so it is meant to be applied on top of #5403.
Looks good. Positive review.
Merged trac_5411.clifford_invariant.2nd.patch in Sage 3.4.rc0.
Cheers,
Michael
The
hasse_invariant
of a quadratic form doesn't match the standard invariant (brauer class) for quaternion algebras (e.g. for ternary quadratic forms, the ramification of the corresponding quaternion algebra).The
clifford_invariant
can defined in terms of the clifford algebra of the quadratic form. See Lam (AMS GSM 67) p. 117 for the definition, and p. 119 for the formula relating it to the Hasse invariant.It also has the property that hyperbolic spaces have
clifford_invariant == +1
at all primes.It also makes more sense to define a
clifford_conductor
instead of ahasse_conductor
as the product of all the primes withclifford_invariant == -1
.Component: quadratic forms
Issue created by migration from https://trac.sagemath.org/ticket/5411