Reciprocal transformation and trace polynomial

[kedlaya]

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.

[kedlaya]

Here it is!

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New commits:

​b59dffe

Implement reciprocal transform, inverse reciprocal transform

[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.

[git]

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

​314b45f

Rename inverse transform as trace polynomial

[roed]

Changing title and description to match new name.

[roed]

Oops; reverting.

[roed]

Positive review if you're happy with my changes.

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New commits:

​c5af2d4

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

[kedlaya]

I'm happy with the changes, yes.

[kedlaya]

For the record, all tests passed on k8s.