Multiplier Spectra for P^N, N > 1

EnderWannabe commented 3 years ago

Currently the multiplier spectra function for dynamical systems on P^N throws a NotImplementedError when N > 1.

This ticket aims to implement that functionality.

Depends on #31944 Depends on #32041

CC: @bhutz

Component: dynamics

Keywords: gsoc2021

Author: Alexander Galarraga

Branch/Commit: 4a0e9a1

Reviewer: Ben Hutz

Issue created by migration from https://trac.sagemath.org/ticket/32035

EnderWannabe commented 3 years ago

Description changed:

--- 
+++ 
@@ -1,3 +1,3 @@
-Currently the multiplier spectra function for dynamical systems on P^N throws a NotImplementedError when N > 1.
+Currently the multiplier spectra function for dynamical systems on P<sup>N</sup> throws a NotImplementedError when N > 1.

 This ticket aims to implement that functionality.

EnderWannabe commented 3 years ago

Branch: u/gh-EnderWannabe/multiplier_spectra

EnderWannabe commented 3 years ago

Last 10 new commits:

`27888da`	`31954: initial commit with working code and examples`
`22201d7`	`Merge branch 'hyperplane_transform' into periodic_points_improvement`
`c324844`	`31944: added computation for formal periodic points`
`91ebb22`	`31944: removed changes in tickets 31906 and 31896 from this ticket`
`df038ca`	`31944: initial formal preperiodic points`
`5d142bf`	`31944: examples for formal preperiodic points, fixed return scheme for formal preperiodic points`
`d4957f4`	`Merge branch 'u/gh-EnderWannabe/periodic_points_improvement' of trac.sagemath.org:sage into multiplier_spectra`
`254b1a8`	`working on number fields`
`ab0b37c`	`Merge branch 'develop' into multiplier_spectra`
`d23769a`	`32035: added tests, functionality for QQbar and algebraic closures of finite fields`

EnderWannabe commented 3 years ago

Changed dependencies from 31944 to #31944

EnderWannabe commented 3 years ago

Commit: d23769a

EnderWannabe commented 3 years ago

Changed dependencies from #31944 to #31944, #32041

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

`9a2c01c`	`32041: added fix and test`
`0903a77`	`Merge branch 'reduced_form_fix' into multiplier_spectra`
`558c255`	`32035: cleaned up code, added documentation`
`dbbd3dc`	`32035: added test for algebraic closure`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from d23769a to dbbd3dc

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

`083b6fa`	`32035: minor code cleanup`
`2f064fd`	`32035: added comments, fixed output documentation`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from dbbd3dc to 2f064fd

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from 2f064fd to 732b08a

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

`b4ec7c1`	`31944: minor fixes`
`6b810a2`	`31944: fixed periodic typo and added test`
`b8ce4b7`	`31906: actual fix for warning message`
`dc36d19`	`Merge branch 'u/gh-EnderWannabe/point_matrix_improvement' of trac.sagemath.org:sage into point_transformation_improvement`
`e7e8930`	`31906: fixed denominator bug`
`e49e34c`	`Merge branch 'point_transformation_improvement' into periodic_points_improvement`
`3a04a8d`	`31944: fixed bug with formal=True over ring`
`4a62742`	`Merge branch 'develop' into periodic_points_improvement`
`e3693f0`	`31944: added error message for fraction fields of m polynomial rings`
`732b08a`	`Merge branch 'periodic_points_improvement' into multiplier_spectra`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from 732b08a to 27de53e

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

`b82de34`	`Merge branch 'u/gh-EnderWannabe/hyperplane_transform' of trac.sagemath.org:sage into hyperplane_transform`
`379a732`	`Merge branch 'hyperplane_transform' into affine_preperiodic`
`15f206c`	`32166: fixed typos, added subscheme example`
`b4246d2`	`32166: fixed identity matrix return`
`eaebd33`	`32166: added test for identity`
`57a4b39`	`Merge branch 'affine_preperiodic' into periodic_points_improvement`
`81d7c97`	`32166: fixed documentation`
`a63927e`	`Merge branch 'affine_preperiodic' into periodic_points_improvement`
`9b5e74f`	`31944: fixed calls to affine preperiodic model`
`27de53e`	`Merge branch 'periodic_points_improvement' into multiplier_spectra`

bhutz commented 3 years ago

Reviewer: Ben Hutz

bhutz commented 3 years ago

comment:10

I see no issues with functionality. A few minor doc things and one extra if.

the default is formal=False, so the first main paragraph should not say it computes the formal unless the user specifies otherwise (i.e., that logic should be reversed)
end of second paragraph - "critical points" should be "periodic points"
If False, and he map is -> "the"
use_algebraic_closure - "critical points" should be "periodic points"
no examples of algebraic closures in dimension > 1
line 4711 -- need line wrap
line 4798 -- extra word in comment ("which point the point")
line 4817 -- aren't we already in the dimension == 1 case?
looks like this needs to be updated for the latest preperiodic point ticket (31944)

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from 27de53e to 2ab4ac6

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

`b695b25`	`Merge branch 'u/gh-EnderWannabe/multiplier_spectra' of git://trac.sagemath.org/sage into multiplier_spectra`
`f1e1958`	`31944: fix for subscheme issue`
`d3ea2be`	`31944: added check for morphisms`
`268bc83`	`31944: fixed if statement`
`6f2857f`	`31944: added example for formal preperiodic`
`8827e74`	`Merge branch 'u/gh-EnderWannabe/periodic_points_improvement' of git://trac.sagemath.org/sage into periodic_points_improvement`
`c35b14a`	`Merge branch 'periodic_points_improvement' into multiplier_spectra`
`2ab4ac6`	`32035: doc fixes`

bhutz commented 3 years ago

Changed branch from u/gh-EnderWannabe/multiplier_spectra to u/bhutz/multiplier_spectra

bhutz commented 3 years ago

comment:14

The commit fixed a couple of the missed doc issues, but the use_algebraic_closure example is still an issue and exposes an problem. If you only use the base_field when it is false you are missing periodic points and hence not returning the full multiplier spectrum.

One option is to count the number of points you have (with multiplicity) and throw an error if the base field doesn't contain them all.

New commits:

25b19e2 32035: minor doc fixes

bhutz commented 3 years ago

Changed commit from 2ab4ac6 to 25b19e2

EnderWannabe commented 3 years ago

Changed branch from u/bhutz/multiplier_spectra to u/gh-EnderWannabe/multiplier_spectra

EnderWannabe commented 3 years ago

comment:16

Replying to @bhutz:

One option is to count the number of points you have (with multiplicity) and throw an error if the base field doesn't contain them all.

Good catch. Added such a check.

New commits:

5fcf96d 32035: added check for if the full spectra was computed

EnderWannabe commented 3 years ago

Changed commit from 25b19e2 to 5fcf96d

vbraun commented 3 years ago

comment:19

Merge conflict

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 2 years ago

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

4a0e9a1 Merge branch 'u/gh-EnderWannabe/multiplier_spectra' of trac.sagemath.org:sage into 32035

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 2 years ago

Changed commit from 5fcf96d to 4a0e9a1

bhutz commented 2 years ago

comment:26

The merge conflict resolution looks ok with all tests passing.

vbraun commented 2 years ago

Changed branch from u/gh-EnderWannabe/multiplier_spectra to 4a0e9a1

sagemath / sage

Multiplier Spectra for P^N, N > 1 #32035