Opened 3 years ago

Closed 3 years ago

Last modified 3 years ago

#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 roed)

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 3 years ago by kedlaya

  • Branch set to u/kedlaya/reciprocal_transform_for_polynomials_and_its_inverse

comment:2 Changed 3 years ago by kedlaya

  • Authors set to Kiran S. Kedlaya
  • Commit set to b59dffe8539db248ce71c730184ef8c5f43d1544
  • Status changed from new to needs_review

Here it is!

New commits:

​b59dffeImplement reciprocal transform, inverse reciprocal transform

comment:3 Changed 3 years ago by 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 3 years ago by git

  • Commit changed from b59dffe8539db248ce71c730184ef8c5f43d1544 to 314b45fea06ecce0567d73a18ca2e78e80549e6d

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

​314b45fRename inverse transform as trace polynomial

comment:5 Changed 3 years ago by roed

  • 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 3 years ago by roed

  • Description modified (diff)
  • Summary changed from Trace polynomial transformation and its inverse to Reciprocal transformation and trace polynomial

Oops; reverting.

comment:7 Changed 3 years ago by roed

  • 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 3 years ago by roed

  • Commit changed from 314b45fea06ecce0567d73a18ca2e78e80549e6d to c5af2d4fe2845b73d47f1ced95fac03eef8aa1af

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 3 years ago by kedlaya

  • Status changed from needs_review to positive_review

I'm happy with the changes, yes.

comment:10 Changed 3 years ago by kedlaya

For the record, all tests passed on k8s.

comment:11 Changed 3 years ago by vbraun

  • 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 3 years ago by jdemeyer

  • Authors changed from Kiran S. Kedlaya to Kiran Kedlaya
  • Commit c5af2d4fe2845b73d47f1ced95fac03eef8aa1af deleted
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