Added multiplier computation to affine morphism

[sagetrac-gjorgenson]

Implement function to compute multipliers for periodic points of affine morphisms.

Component: algebraic geometry

Author: Grayson Jorgenson

Branch/Commit: e83be23

Reviewer: Ben Hutz

Issue created by migration from https://trac.sagemath.org/ticket/17118

[sagetrac-gjorgenson]

Branch: u/gjorgenson/ticket/17118

[sagetrac-gjorgenson]

New commits:

d5856dc

Added function that computes the multipliers of periodic points of affine morhpisms

[sagetrac-gjorgenson]

Commit: d5856dc

[bhutz]

comment:5

A few things here

• The docs say: 'at the QQ-rational point', but it does not need to be a QQ point

• I don't understand this example: It seems to me that period 0 is bad input. Perhaps as part of 'check' you should check that period > 0.

sage: P.<x> = AffineSpace(CC,1)
sage: H = End(P)
sage: f = H([x^2 + 1/2])
sage: f.multiplier(P([0.5 + 0.5*I]),0)

• I think

NotImplementedError("Must be an endomorphism of affine space")

should be TypeError, since you can't iterate a non-endomorphism

• You didn't quite get subschemes working fully, see the error on this example:

sage: P.<x,y> = AffineSpace(QQ,2)
sage: X=P.subscheme([x^2-y^2])
sage: H = End(X)
sage: f = H([x^2,y^2])
sage: f.multiplier(X([1,1]),1)

[bhutz]

Reviewer: Ben Hutz

[sagetrac-git]

Changed commit from d5856dc to e7a9d14

[sagetrac-git]

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

a5af987	Minor changes to multiplier function for both affine/projective morphisms.
886e95f	Minor doctest change in multiplier for affine morphisms
2cc284a	Merged ticket with newest beta.
e7a9d14	Merge branch 'master' into ticket/17118

[bhutz]

comment:8

Almost there, just a couple minor things since the functionality seems fine.

• the comment
  #get the correct order for chain rule matrix multiplication
  does not need the 'get the correct order' as that is only an issue for projective

• Since you're allowing subschemes, all the places that say
  must be an endomorphism of xxx space
  just need to say 'must be an endomorphism'. I count 4 such places.

[sagetrac-git]

Changed commit from e7a9d14 to e83be23

[sagetrac-git]

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

e83be23

Minor changes in comments/documentation for multiplier function

[bhutz]

comment:11

Looks good.

[vbraun]

Changed branch from u/gjorgenson/ticket/17118 to e83be23