Opened 5 years ago

Closed 5 years ago

Last modified 5 years ago

#23947 closed enhancement (fixed)

Reciprocal transformation and trace polynomial

Reported by: Kiran Kedlaya Owned by:
Priority: minor Milestone: sage-8.1
Component: algebra Keywords: sd91
Cc: David Zureick-Brown Merged in:
Authors: Kiran Kedlaya Reviewers: David Roe
Report Upstream: N/A Work issues:
Branch: c5af2d4 (Commits, GitHub, GitLab) Commit:
Dependencies: Stopgaps:

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Description (last modified by David Roe)

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 5 years ago by Kiran Kedlaya

Branch: u/kedlaya/reciprocal_transform_for_polynomials_and_its_inverse

comment:2 Changed 5 years ago by Kiran Kedlaya

Authors: Kiran S. Kedlaya
Commit: b59dffe8539db248ce71c730184ef8c5f43d1544
Status: newneeds_review

Here it is!

New commits:

b59dffeImplement reciprocal transform, inverse reciprocal transform

comment:3 Changed 5 years ago by Kiran Kedlaya

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 5 years ago by git

Commit: b59dffe8539db248ce71c730184ef8c5f43d1544314b45fea06ecce0567d73a18ca2e78e80549e6d

Branch pushed to git repo; I updated commit sha1. New commits:

314b45fRename inverse transform as trace polynomial

comment:5 Changed 5 years ago by David Roe

Description: modified (diff)
Reviewers: David Roe
Summary: Reciprocal transform for polynomials and its inverseTrace polynomial transformation and its inverse

Changing title and description to match new name.

comment:6 Changed 5 years ago by David Roe

Description: modified (diff)
Summary: Trace polynomial transformation and its inverseReciprocal transformation and trace polynomial

Oops; reverting.

comment:7 Changed 5 years ago by David Roe

Branch: u/kedlaya/reciprocal_transform_for_polynomials_and_its_inverseu/roed/reciprocal_transform_for_polynomials_and_its_inverse

comment:8 Changed 5 years ago by David Roe

Commit: 314b45fea06ecce0567d73a18ca2e78e80549e6dc5af2d4fe2845b73d47f1ced95fac03eef8aa1af

Positive review if you're happy with my changes.

New commits:

c5af2d4Fix docstring formatting, add doctests, fix error in cofactor of trace_polynomial

comment:9 Changed 5 years ago by Kiran Kedlaya

Status: needs_reviewpositive_review

I'm happy with the changes, yes.

comment:10 Changed 5 years ago by Kiran Kedlaya

For the record, all tests passed on k8s.

comment:11 Changed 5 years ago by Volker Braun

Branch: u/roed/reciprocal_transform_for_polynomials_and_its_inversec5af2d4fe2845b73d47f1ced95fac03eef8aa1af
Resolution: fixed
Status: positive_reviewclosed

comment:12 Changed 5 years ago by Jeroen Demeyer

Authors: Kiran S. KedlayaKiran Kedlaya
Commit: c5af2d4fe2845b73d47f1ced95fac03eef8aa1af
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