#16934: Fix factory keys for finite fields to avoid repeated construction
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Reporter: jdemeyer | Owner:
Type: defect | Status: positive_review
Priority: major | Milestone: sage-6.4
Component: finite rings | Resolution:
Keywords: | Merged in:
Authors: Peter Bruin | Reviewers: Jeroen Demeyer
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/pbruin/16934-FiniteField_factory_key|
9cbdcde41b4783e7adf3f56451b9dedd36842f1d
Dependencies: #16930 | Stopgaps:
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Comment (by nbruin):
Replying to [comment:24 jdemeyer]:
> Replying to [comment:22 pbruin]:
> > This commit adds back the warning. Alternatively, it could have been
put outside the `if impl == 'modn'`, but in this way it is easier to
remove again for non-`modn` implementations.
> I would prefer to have the warning in one place. If we ever allow a
custom modulus, we should allow it for all implementations.
>
> My vision for this "modulus" argument is that the following should
assign to `a` a primitive root:
> {{{
> sage: K.<a> = GF(7, modulus='primitive')
> }}}
The word "modulus" here is definitely wrong. If anything is a modulus for
`GF(7)`, it is 7, because the natural way to construct `GF(7)` as
''quotient'' of `ZZ` by `7ZZ`.
In general, even for field *extensions*, the word modulus is confusing.
That only applies if you're making the field as a quotient of a polynomial
ring. For the purpose proposed, `generator` would cover the notion much
better. I see from the doc that we have legacy against us on this one.
--
Ticket URL: <http://trac.sagemath.org/ticket/16934#comment:28>
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