#5159: [with new patch, needs review] Add functionality to Galois groups
---------------------------+------------------------------------------------
Reporter: davidloeffler | Owner: davidloeffler
Type: enhancement | Status: assigned
Priority: major | Milestone: sage-3.4.2
Component: number theory | Keywords: galois groups, number theory
---------------------------+------------------------------------------------
Comment(by davidloeffler):
I've rebased it to a patch based on (3.4 + the patch for #5508).
This version actually adds quite a bit that wasn't in the previous
version: based on the debate on sage-nt, I've made it return the Galois
group of the splitting field when the given field isn't Galois, and also
added a method fixed_field for subgroups of Galois groups based on Pari's
"galoisfixedfield".
In an ideal world, when given a non-Galois field, it would return the
Galois group of the Galois closure of the given field, but represented as
permutations of the roots of the defining polynomial of the original
field. I couldn't work out an easy way of doing this which wouldn't be
horribly slow in general, so elements are represented as permutations of
the Galois conjugates of some single element generating the Galois
closure.
I've also ReSTified class_group.py and number_field_ideal.py (the latter
because I was editing it anyway, and the former because it was easy to
do); and deprecated galois_group and is_galois for relative fields in
favour of explicitly relative and absolute variants.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5159#comment:5>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected]
To unsubscribe from this group, send email to
[email protected]
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en
-~----------~----~----~----~------~----~------~--~---
