Opened 10 years ago

Closed 7 years ago

#10971 closed enhancement (wontfix)

Finite Field elements in terms of powers of a generator

Reported by: aly.deines Owned by: cpernet
Priority: minor Milestone: sage-duplicate/invalid/wontfix
Component: finite rings Keywords: GF, finite field
Cc: Merged in:
Authors: Reviewers: Jeroen Demeyer
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description (last modified by jdemeyer)

For large values of q, a prime power, GF(q) has elements represented as polynomials over a generator.

sage: F.<a> = GF(2^8)
sage: a^10
a^6 + a^5 + a^4 + a^2

If you further want to compute in a polynomial ring over F, then the polynomials aren't very pretty as they are polynomials with polynomial coefficients.

sage: R.<x> = F[]
sage: a^10*x+1
(a^6 + a^5 + a^4 + a^2)*x + 1

It would be nice to be able to be able to print and work with the elements as powers of the generator.

Change History (10)

comment:1 Changed 10 years ago by lmartel

But I expect it to be slow... How would you compute this efficiently?

sage: K.<a> = GF(17**17)
sage: a + 1
a^24137569    # this would be the result in your representation

comment:2 Changed 8 years ago by jdemeyer

  • Milestone changed from sage-5.11 to sage-5.12

comment:3 Changed 7 years ago by vbraun_spam

  • Milestone changed from sage-6.1 to sage-6.2

comment:4 Changed 7 years ago by vbraun_spam

  • Milestone changed from sage-6.2 to sage-6.3

comment:5 Changed 7 years ago by vbraun_spam

  • Milestone changed from sage-6.3 to sage-6.4

comment:6 Changed 7 years ago by jdemeyer

  • Description modified (diff)

comment:7 Changed 7 years ago by jdemeyer

  • Component changed from group theory to finite rings
  • Owner changed from joyner to cpernet

comment:8 Changed 7 years ago by jdemeyer

  • Milestone changed from sage-6.4 to sage-duplicate/invalid/wontfix
  • Reviewers set to Jeroen Demeyer
  • Status changed from new to needs_review

This requires discrete log computations, which is too inefficient in general.

Close as "wontfix".

comment:9 Changed 7 years ago by jdemeyer

  • Status changed from needs_review to positive_review

comment:10 Changed 7 years ago by vbraun

  • Resolution set to wontfix
  • Status changed from positive_review to closed
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