Opened 11 years ago
Closed 10 years ago
#10464 closed enhancement (fixed)
m-th power residue symbol
Reported by: | katestange | Owned by: | davidloeffler |
---|---|---|---|
Priority: | minor | Milestone: | sage-4.7.2 |
Component: | number fields | Keywords: | cubic residue |
Cc: | katestange | Merged in: | sage-4.7.2.alpha3 |
Authors: | Katherine Stange | Reviewers: | Francis Clarke, David Loeffler |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
implement m-th power residue symbol (generalising Legendre/Kronecker? symbol)
Apply only trac_10464_residue_symbol.4.patch to the Sage library.
Attachments (4)
Change History (16)
Changed 11 years ago by
comment:1 Changed 11 years ago by
- Status changed from new to needs_review
comment:2 Changed 11 years ago by
- Cc katestange added
comment:3 Changed 11 years ago by
- Status changed from needs_review to needs_work
- Work issues set to docstring formatting
comment:4 Changed 11 years ago by
I think there are a couple of things which will make the ideal residue_symbol
function a little faster:
- There should be no need to have the default
check=True
when recursively applying the function to the prime factors of the ideal since all the checks will have already been performed. - The final loop can be avoided by calculating a discrete log in the residue field.
Thus I think the last few lines of the definition should read something like:
if not self.is_prime(): return prod(Q.residue_symbol(e, m, check=False)**i for Q, i in self.factor()) k = self.residue_field() r = k(e)**((k.order() - 1)/m) resroot = primroot**(rootorder/m) from sage.groups.generic import discrete_log j = discrete_log(k(resroot), k(r), ord=m) return resroot**j
One other little thing. I think it is safer to write self.smallest_integer()
rather than ZZ(self.gens()[0])
.
Changed 10 years ago by
comment:5 Changed 10 years ago by
- Status changed from needs_work to needs_review
Thanks all for the comments and suggestions; they were very helpful. I've uploaded a new version of the patch that has taken into account all of them. (I couldn't figure out how to replace the file with one of the same name as suggested in the development walkthrough guide.)
comment:6 Changed 10 years ago by
- Status changed from needs_review to needs_work
- Work issues changed from docstring formatting to patch corrupted?
There is something messed up with this patch: each new method is defined twice over.
Changed 10 years ago by
comment:7 Changed 10 years ago by
- Status changed from needs_work to needs_review
Sorry! I must have cloned the wrong branch at some point, but I should have noticed in the diff -- newbie mistake. Anyway, it's now been fixed. (I also see now how to replace the old patch, but at this point I think that would be more confusing, so this is labelled '3'.)
comment:8 Changed 10 years ago by
It's all fine now. I'd give it a positive review but for one thing. The docstring for sage.rings.number_field.number_field_element.NumberFieldElement.residue_symbol
says
- ``P`` - proper ideal of the number field (or an extension)
I think that there needs to be a doctest illustrating the case where P is an ideal in an extension.
Changed 10 years ago by
comment:9 Changed 10 years ago by
Thanks for pointing that out. I've fleshed out the documentation somewhat, and in the process found a small bug which has been fixed (the faster routine kronecker_symbol was called on some inappropriate cases).
comment:10 Changed 10 years ago by
- Reviewers set to Francis Clarke
- Status changed from needs_review to positive_review
- Work issues patch corrupted? deleted
All looks good now. Positive review.
comment:11 Changed 10 years ago by
- Description modified (diff)
- Reviewers changed from Francis Clarke to Francis Clarke, David Loeffler
Please put into the ticket's description which patches to apply [in which order, i.e., in the order they should be applied, and perhaps to which repository].
(The trac wiki syntax for referring to attached files is [attachment:here_comes_the_filename]
, hence in this case [attachment:trac_10464_residue_symbol.4.patch]
.)
Also, using the comment field of attachments isn't bad.
comment:12 Changed 10 years ago by
- Merged in set to sage-4.7.2.alpha3
- Resolution set to fixed
- Status changed from positive_review to closed
I like the look of this, but the formatting of the docstrings isn't quite right -- the text
"Quadratic Residue (7 is not a square modulo 11)"
shouldn't be inside the code block. You should remove the double colon afterEXAMPLES
, unindent the description lines and put a double colon at the end of each one. Other than that very trivial fix this looks absolutely fine.