Opened 4 years ago

Closed 4 years ago

# Added multiplier computation to affine morphism

Reported by: Owned by: gjorgenson minor sage-6.4 algebraic geometry Grayson Jorgenson Ben Hutz N/A e83be23 (Commits) e83be23b16a2cc68be090f6067af132ca403fc92

### Description

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

### comment:1 Changed 4 years ago by gjorgenson

• Branch set to u/gjorgenson/ticket/17118
• Created changed from 10/08/14 16:46:55 to 10/08/14 16:46:55
• Modified changed from 10/08/14 16:46:55 to 10/08/14 16:46:55

### comment:2 Changed 4 years ago by gjorgenson

• Commit set to d5856dcf887886622e0739b0cee3495f994f90d8
• Status changed from new to needs_review

New commits:

 ​d5856dc `Added function that computes the multipliers of periodic points of affine morhpisms`

### comment:3 Changed 4 years ago by gjorgenson

• Status changed from needs_review to needs_work

### comment:4 Changed 4 years ago by gjorgenson

• Status changed from needs_work to needs_review

### comment:5 Changed 4 years ago by bhutz

• Reviewers set to Ben Hutz
• Status changed from needs_review to needs_work

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)
```

### comment:6 Changed 4 years ago by git

• Commit changed from d5856dcf887886622e0739b0cee3495f994f90d8 to e7a9d145a1adab1bf9ec6b287b4a07078c9500b9

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`

### comment:7 Changed 4 years ago by gjorgenson

• Status changed from needs_work to needs_review

### comment:8 Changed 4 years ago by bhutz

• Status changed from needs_review to needs_work

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.

### comment:9 Changed 4 years ago by git

• Commit changed from e7a9d145a1adab1bf9ec6b287b4a07078c9500b9 to e83be23b16a2cc68be090f6067af132ca403fc92

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

 ​e83be23 `Minor changes in comments/documentation for multiplier function`

### comment:10 Changed 4 years ago by gjorgenson

• Status changed from needs_work to needs_review

### comment:11 Changed 4 years ago by bhutz

• Status changed from needs_review to positive_review

Looks good.

### comment:12 Changed 4 years ago by vbraun

• Branch changed from u/gjorgenson/ticket/17118 to e83be23b16a2cc68be090f6067af132ca403fc92
• Resolution set to fixed
• Status changed from positive_review to closed
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