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Outdated suggestions cannot be applied.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: Dual basis of power basis wrt trace form #8835
[Merged by Bors] - feat: Dual basis of power basis wrt trace form #8835
Changes from all commits
0c84179
54993e3
9ea5306
1d04ede
0ad71d8
ea811c3
cdce2fd
44cd7c4
319cc11
2f4423a
75410f3
89b5f76
9aa6eae
d6f45a5
9812c56
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 created #9071 which may make some lemmas easier, including this.
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 failed to use them to make the proofs shorter.
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'll try later. I think several lemmas could be easier using what we know about divByMonic, instead of using the characterization you introduced.
I've started wondering whether we should prove something general about upper/lower triangular matrices (with 1 on the diagonal) or such linear systems ...but #9071 was merged really quickly (thanks!)Edit: sorry there's probably nothing general. It's about the inverse of a particular type of bidiagonal matrix. There exists a general formula for the inverse of bidiagonal matrices, but it's probably too complicated for the use case here.
It might help to prove the stronger statement that the submodule spanned by the first i coefficients is equal to that spanned by the first i powers of x.