Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
New issue
Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.
By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.
Already on GitHub? Sign in to your account
[Merged by Bors] - feat: improve
polyrith
by testing for membership in the radical #7790[Merged by Bors] - feat: improve
polyrith
by testing for membership in the radical #7790Changes from all commits
67e53ae
acbdf91
4006550
5278e4d
74c822d
93445f9
8d7e896
e4685b3
1a199f9
c30c045
bc33e63
d8873f0
0a410d0
bbcb66d
677d35e
File filter
Filter by extension
Conversations
Jump to
There are no files selected for viewing
There was a problem hiding this comment.
Choose a reason for hiding this comment
The reason will be displayed to describe this comment to others. Learn more.
I don't really understand why this is done with this trick of checking if 1 is in the ideal
<hyps, 1/goal>
, I would expect singular/sage has a way to ask for a lift to the radical ideal directly which I would hope would be easier to maintain in the long run (especially if we have aspirations of making this work for non-char 0 rings properly). Did you consider this approach?I'm not completely against merging this, but the whole thing is starting to look a bit scary ;)
There was a problem hiding this comment.
Choose a reason for hiding this comment
The reason will be displayed to describe this comment to others. Learn more.
After experimenting a bit I believe that using the builtin radical support, while probably a better algorithm underneath, is not very convenient to use with the way things are set up here, so I'm happy with this I guess
There was a problem hiding this comment.
Choose a reason for hiding this comment
The reason will be displayed to describe this comment to others. Learn more.
Yeah, I remember looking for this when I first implemented this (granted, a year and a half ago) and not turning up anything useful. Sage/Singular will check for membership in the radical just fine but extracting the power and coefficient is a pain. My impression is that what I do in this PR is a "standard" approach and that a native Sage implementation would do roughly the same, although I'm somewhat out of my element here.
There was a problem hiding this comment.
Choose a reason for hiding this comment
The reason will be displayed to describe this comment to others. Learn more.
When I read the sage docstring for radical earlier it said:
but I have no idea how accurate that is!
There was a problem hiding this comment.
Choose a reason for hiding this comment
The reason will be displayed to describe this comment to others. Learn more.
Right -- but there's space between the membership check$p \in \sqrt{\langle H_1, \ldots, H_n \rangle}$ , and explicitly producing $k$ and $Q_i$ such that $p^k = \sum Q_iH_i$ . Sage's
radical
makes the former easy, but I don't see how to get from there to the latter. Maybe there's a way, I'd love to hear it.(It sounds like you came to a similar conclusion, just leaving this comment for reference later!)