#8335: Finite Field lattices
-------------------------+--------------------------------------------------
Reporter: roed | Owner: AlexGhitza
Type: defect | Status: new
Priority: major | Milestone: sage-4.3.4
Component: algebra | Keywords:
Author: David Roe | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Implements coercion within lattices of finite fields lying above the same
prime.
{{{
sage: k = GF(9)
sage: l = GF(27)
sage: x = k.gen() + l.gen(); x
z6^5 + 2*z6^4 + 2*z6^3 + z6^2 + 2*z6 + 1
sage: x.parent()
Finite Field in z6 of size 3^6
}}}
This feature is implemented for fields outside the range of the Conway
polynomial database by the implementation of a function for finding
pseudo-Conway polynomials: polynomials that satisfy all of the algebraic
constraints on Conway polynomials without the lexicographic constraint
that imposes uniqueness.
Finite fields no longer require an explicit variable name (though they
still accept one). If a variable name is given, then outside the range of
the Conway polynomial database a random or sparse polynomial is used for
speed reasons; if no variable name is given then either a Conway
polynomial or pseudo-Conway polynomial is used.
Also adds methods `any_root` and `squarefree_decomposition` to polynomials
over finite fields.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8335>
Sage <http://www.sagemath.org>
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