Reciprocal transformation and trace polynomial
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)
Branch: 
→ u/kedlaya/reciprocal_transform_for_polynomials_and_its_inverse

Authors: 
→ Kiran S. Kedlaya

Commit: 
→ b59dffe8539db248ce71c730184ef8c5f43d1544

Status: 
new →
needs_review

Commit: 
b59dffe8539db248ce71c730184ef8c5f43d1544 →
314b45fea06ecce0567d73a18ca2e78e80549e6d

Description: 
modified (diff)

Reviewers: 
→ David Roe

Summary: 
Reciprocal transform for polynomials and its inverse →
Trace polynomial transformation and its inverse

Description: 
modified (diff)

Summary: 
Trace polynomial transformation and its inverse →
Reciprocal transformation and trace polynomial

Branch: 
u/kedlaya/reciprocal_transform_for_polynomials_and_its_inverse →
u/roed/reciprocal_transform_for_polynomials_and_its_inverse

Commit: 
314b45fea06ecce0567d73a18ca2e78e80549e6d →
c5af2d4fe2845b73d47f1ced95fac03eef8aa1af

Status: 
needs_review →
positive_review

Branch: 
u/roed/reciprocal_transform_for_polynomials_and_its_inverse →
c5af2d4fe2845b73d47f1ced95fac03eef8aa1af

Resolution: 
→ fixed

Status: 
positive_review →
closed

Authors: 
Kiran S. Kedlaya →
Kiran Kedlaya

Commit: 
c5af2d4fe2845b73d47f1ced95fac03eef8aa1af

Here it is!
New commits:
Implement reciprocal transform, inverse reciprocal transform