|
|
Next: Quadratic Fields
Up: Extensions of Rings
Previous: Extensions of Rings
Algebraic Number Fields
New Features:
- NumberField for parents of places and divisors of number fields
has been included.
- The support for infinite places of number fields has been improved,
in particular it is now easy to get access to all real places and test
for positivitiy at any or all real places.
- The computation of Galois group for polynomials of degree > 23 over
extensions of
Q is now supported. The functionality to compute
arbitray subfields of a normal closure has been extended to
compute arbitrary subfield towers correspoding to subgroup chains.
- The computation of splitting fields for polynomials over
Q can
now be based on the computation of the Galois group to gain efficiency.
- For polynomials over
Z with solvable Galois group, it is now
possible to express the roots as radicals.
- Given a 2-cocycle with values in the multiplicative group of
a number field, it is now possible to determine if this cocycle
splits, and in this case, to compute a 1-cochain to verify this.
- Linear dependecies of arbitrary elements of the splitting field
of a polynomial can be compututed.
- A routine NiceRepresentativeModuloPowers for number field elements
has been provided.
Bug Fixes:
- As a result of the re-write of the computation of Galois groups
over number fields, a number of bugs in this module have been removed.
Next: Quadratic Fields
Up: Extensions of Rings
Previous: Extensions of Rings
|
|
