#5411: QuadraticForm: implement clifford_invariant and replace hasse_conductor
with clifford_conductor
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Reporter: tornaria | Owner: gonzalo
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.4
Component: quadratic forms | Keywords:
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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 a
{{{hasse_conductor}}} as the product of all the primes with
{{{clifford_invariant == -1}}}.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5411>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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