Opened 5 years ago

Last modified 4 years ago

#21996 closed enhancement

Factorization in iterated extensions of finite fields — at Initial Version

Reported by: saraedum Owned by:
Priority: major Milestone: sage-7.5
Component: finite rings Keywords: factorization, finite field, sd86.5, sd87
Cc: jpflori Merged in:
Authors: Julian Rüth Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description

At the moment there is no factorization implemented in iterated extensions of finite fields:

sage: K = GF(2)
sage: R.<x> = K[]
sage: L.<x> = K.extension(x^2 + x + 1)
sage: R.<y> = L[]
sage: M.<y> = L.extension(y^2 + y + x)
sage: R.<T> = M[]
sage: (T^2 + T + x).factor()

The reason is that M in the above example is just a quotient of a polynomial ring over L. Here, we implement isomorphisms (for this special case) to a simple extensions of a prime field over which factorization is implemented. We also implement univariate factorization for polynomial quotient rings if an isomorphism to a field which supports such factorization is known.

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