Algebraic Number Fields [HB 52]

Changes:

• The checks on the creation of homomorphisms from number fields and fields of fractions of orders have been increased. The codomain of the homomorphism must cover the coefficient ring of the domain if a coefficient map is not given.

• Norm equations over number fields have been completely rewritten including a new, stringent precision analysis for most of the algorithm.
• Element arithmetic has been sped up.

New Features:

• It is now possible to create a VectorSpace or Algebra representing any algebraic field (not just cyclotomics) over any subfield.

• The map from a number field into a vector space or algebra can be extended to vector and matrix spaces over the number field into a larger dimensional space over a subfield using InducedMap.

• Elements can now have product representations.