Minimal Resultant Locus

[EnderWannabe]

We aim to implement the algorithm given in https://arxiv.org/pdf/1304.1201.pdf to compute the minimal resultant locus using number fields.

Given a dynamical system, we can compute the resultant of the system as the resultant of the defining polynomials. The resultant, however, is not constant under conjugacy. We can therefore conjugate by appropriate linear maps to reduce the absolute value of the resultant. The minimal resultant locus is the segment of Berkovich space where the minimal order of the resultant is achieved.

This ticket depends heavily on the implementation of Berkovich space in #29844, the implementation of dynamical systems on Berkovich space in #29949, as well as the additional normalize_coordinates() functionality added in #30409.

CC: @bhutz @pfili

Component: dynamics

Keywords: gsoc20

Author: Alexander Galarraga

Branch/Commit: u/gh-EnderWannabe/min_res_locus @ 06b98de

Issue created by migration from https://trac.sagemath.org/ticket/30294

[EnderWannabe]

Branch: u/gh-EnderWannabe/min_res_locus

[sagetrac-git]

Commit: 4b25e19

[sagetrac-git]

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

71af818	30294: added example
18cddd9	29949: added resultant and base_ring methods
4b25e19	30294: Merge branch 'berkovich_dynamical' into min_res_locus

[sagetrac-git]

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

145c045	Merge branch 'u/gh-EnderWannabe/berkovich_dynamical' of git://trac.sagemath.org/sage into berkovich_dynamical
b45cb40	Merge branch 'u/gh-EnderWannabe/berkovich_dynamical' of git://trac.sagemath.org/sage into berkovich_dynamical
5db8e66	Merge branch 'u/gh-EnderWannabe/min_res_locus' of git://trac.sagemath.org/sage into min_res_locus
894e1e1	Merge branch 'u/gh-EnderWannabe/min_res_locus' of git://trac.sagemath.org/sage into min_res_locus
da49a8b	30294: added step 4b

[sagetrac-git]

Changed commit from 4b25e19 to da49a8b

[sagetrac-git]

Changed commit from da49a8b to 085282b

[sagetrac-git]

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

6502126	29844: added more examples
bb264b1	Merge branch 'berkovich_number_field' into min_res_locus
ad55ab7	29949: added matrix imports
fbfef60	Merge branch 'berkovich_number_field' into berkovich_dynamical
2f7742b	Merge branch 'develop' into berkovich_dynamical
cb0b8c6	Merge branch 'berkovich_number_field' into berkovich_dynamical
3878f2e	29949: added tests, removed unused imports
1523bd4	29949: fixed spacing issues, better error messages
42ed3ab	Merge branch 'u/gh-EnderWannabe/berkovich_dynamical' of git://trac.sagemath.org/sage into berkovich_dynamical
085282b	Merge branch 'berkovich_dynamical' into min_res_locus

[fchapoton]

comment:7

You should fill the "Author" field above here with your real name

First line of doc should use Return instead of Returns

[EnderWannabe]

Author: Alexander Galarraga

[sagetrac-git]

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

c274cbe	Merge branch 'develop' into berkovich_dynamical
c6fc21f	Merge branch 'berkovich_dynamical' into min_res_locus
8cbbbc9	Merge branch 'normalize_coordinates_enhancement' into min_res_locus
51bae01	30294: merged in updated 29949 and 30409, fixed return

[sagetrac-git]

Changed commit from 085282b to 51bae01

[fchapoton]

comment:10

and do not import metaclass from six, but use python3 syntax for metaclass

Please look at the patchbot plugins for this kind of stuff.

[sagetrac-git]

Changed commit from 51bae01 to 06b98de

[sagetrac-git]

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

0cdf6e4	29949: fixed patchbot errors
06b98de	Merge branch 'berkovich_dynamical' into min_res_locus

[mkoeppe]

comment:13

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

[mkoeppe]

comment:14

Setting a new milestone for this ticket based on a cursory review.

[mkoeppe]

comment:15

Stalled in needs_review or needs_info; likely won't make it into Sage 9.5.