#23947 closed enhancement (fixed)
Reciprocal transformation and trace polynomial
Reported by:  kedlaya  Owned by:  

Priority:  minor  Milestone:  sage8.1 
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^2q
.
Change History (12)
comment:1 Changed 3 years ago by
 Branch set to u/kedlaya/reciprocal_transform_for_polynomials_and_its_inverse
comment:2 Changed 3 years ago by
 Commit set to b59dffe8539db248ce71c730184ef8c5f43d1544
 Status changed from new to needs_review
comment:3 Changed 3 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 3 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 3 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 3 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 3 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 3 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 3 years ago by
 Status changed from needs_review to positive_review
I'm happy with the changes, yes.
comment:10 Changed 3 years ago by
For the record, all tests passed on k8s.
comment:11 Changed 3 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 3 years ago by
 Commit c5af2d4fe2845b73d47f1ced95fac03eef8aa1af deleted
Here it is!
New commits:
Implement reciprocal transform, inverse reciprocal transform