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Quaternion Algebras
New Features:
- The ConjugacyClasses of maximal orders or Eichler orders in definite
quaternion algebras can now be computed.
- A routine IsConjugate (or IsIsomorphic) is provided for quaternion orders.
- Representatives of the TwoSidedIdealClasses, and the TwoSidedIdealClassGroup
can be computed for an order in a definite quaternion algebra; the Support of
the representatives can be specified by the user.
- The Factorization of a two-sided ideal (in a definite quaternion order)
can be obtained.
- An alternative algorithm for the LeftIdealClasses and RightIdealClasses
is provided, which is more efficient in many cases; the Support of the
representatives can be specified by the user.
- A more sophisticated UnitGroup algorithm, using results about the structure
of the unit group, has been implemented for orders in definite quaternion algebras.
- An intrinsic NormOneGroup is included.
Bug fixes:
- A number of errors in enumeration of units and right ideal classes for orders
in definite quaternion algebras over number fields have been corrected.
- The pMatrixRing routine is now stable and available in all cases.
- Trivial bugs in Embed have been fixed.
Next: Orders in Associative Algebras
Up: Algebras
Previous: Finite Dimensional Algebras
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