Opened 11 years ago
Closed 8 years ago
#10971 closed enhancement (wontfix)
Finite Field elements in terms of powers of a generator
Reported by: | aly.deines | Owned by: | cpernet |
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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: |
Description (last modified by )
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 11 years ago by
comment:2 Changed 9 years ago by
- Milestone changed from sage-5.11 to sage-5.12
comment:3 Changed 9 years ago by
- Milestone changed from sage-6.1 to sage-6.2
comment:4 Changed 8 years ago by
- Milestone changed from sage-6.2 to sage-6.3
comment:5 Changed 8 years ago by
- Milestone changed from sage-6.3 to sage-6.4
comment:6 Changed 8 years ago by
- Description modified (diff)
comment:7 Changed 8 years ago by
- Component changed from group theory to finite rings
- Owner changed from joyner to cpernet
comment:8 Changed 8 years ago by
- 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 8 years ago by
- Status changed from needs_review to positive_review
comment:10 Changed 8 years ago by
- Resolution set to wontfix
- Status changed from positive_review to closed
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But I expect it to be slow... How would you compute this efficiently?