#23947 closed enhancement (fixed)
Reciprocal transformation and trace polynomial
Reported by: | kedlaya | Owned by: | |
---|---|---|---|
Priority: | minor | Milestone: | sage-8.1 |
Component: | algebra | Keywords: | sd91 |
Cc: | dzb | Merged in: | |
Authors: | Kiran Kedlaya | Reviewers: | David Roe |
Report Upstream: | N/A | Work issues: | |
Branch: | c5af2d4 (Commits) | Commit: | |
Dependencies: | Stopgaps: |
Description (last modified by )
This ticket implements what we are calling the reciprocal transform for polynomials, and its inverse. For a fixed parameter q
, the reciprocal transform applied to P(x)
returns x^deg(P)*P(x+q/x)
. This operation transforms polynomials with all roots in the interval [-2*sqrt(q), 2*sqrt(q)]
into polynomials with all roots having absolute value sqrt(q)
, and accounts for all such polynomials up to multiplication by a factor of x^2-q
.
Change History (12)
comment:1 Changed 2 years ago by
- Branch set to u/kedlaya/reciprocal_transform_for_polynomials_and_its_inverse
comment:2 Changed 2 years ago by
- Commit set to b59dffe8539db248ce71c730184ef8c5f43d1544
- Status changed from new to needs_review
comment:3 Changed 2 years ago by
There does seem to be some precedent for referring to what I've called the inverse reciprocal transform as the trace polynomial associated to the original polynomial.
comment:4 Changed 2 years ago by
- Commit changed from b59dffe8539db248ce71c730184ef8c5f43d1544 to 314b45fea06ecce0567d73a18ca2e78e80549e6d
Branch pushed to git repo; I updated commit sha1. New commits:
314b45f | Rename inverse transform as trace polynomial
|
comment:5 Changed 2 years ago by
- Description modified (diff)
- Reviewers set to David Roe
- Summary changed from Reciprocal transform for polynomials and its inverse to Trace polynomial transformation and its inverse
Changing title and description to match new name.
comment:6 Changed 2 years ago by
- Description modified (diff)
- Summary changed from Trace polynomial transformation and its inverse to Reciprocal transformation and trace polynomial
Oops; reverting.
comment:7 Changed 2 years ago by
- Branch changed from u/kedlaya/reciprocal_transform_for_polynomials_and_its_inverse to u/roed/reciprocal_transform_for_polynomials_and_its_inverse
comment:8 Changed 2 years ago by
- Commit changed from 314b45fea06ecce0567d73a18ca2e78e80549e6d to c5af2d4fe2845b73d47f1ced95fac03eef8aa1af
Positive review if you're happy with my changes.
New commits:
c5af2d4 | Fix docstring formatting, add doctests, fix error in cofactor of trace_polynomial
|
comment:9 Changed 2 years ago by
- Status changed from needs_review to positive_review
I'm happy with the changes, yes.
comment:10 Changed 2 years ago by
For the record, all tests passed on k8s.
comment:11 Changed 2 years ago by
- Branch changed from u/roed/reciprocal_transform_for_polynomials_and_its_inverse to c5af2d4fe2845b73d47f1ced95fac03eef8aa1af
- Resolution set to fixed
- Status changed from positive_review to closed
comment:12 Changed 2 years ago by
- Commit c5af2d4fe2845b73d47f1ced95fac03eef8aa1af deleted
Here it is!
New commits:
Implement reciprocal transform, inverse reciprocal transform