#13379: Add a splitting field function for polynomials over a finite field
---------------------------------+------------------------------------------
Reporter: abrochard | Owner: davidloeffler
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.8
Component: number fields | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
---------------------------------+------------------------------------------
Comment (by robharron):
For p a prime and q = p^n^, the field F,,q,, is Galois over F,,p,,, i.e.
it is the splitting field of any irreducible polynomial of degree n over
F,,p,,. Moreover, the field with p^n^ elements contains the one with p^m^
elements if and only if m divides n. Thus, starting from a polynomial over
F,,p,,, the splitting field is simply given by taking the lcm of the
degrees of the factors. This would be quicker than what you are doing. If
you start with a polynomial over F,,q,,, a simple modification of what
I've said would work too.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13379#comment:5>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac?hl=en.
For more options, visit https://groups.google.com/groups/opt_out.
