height and canonical height for projective points and morphisms #14218

bhutz · 2013-03-03T18:29:52Z

This patch implements height functionality from the initial dynamics functionality problems proposed at the 2012 ICERM semester in Complex and Arithmetic dynamics.

Builds on Trac #13130 and Trac #14217

Implements height functionality:

height of points
height of morphisms
local green's functions
canonical heights

Apply:

Component: algebraic geometry

Keywords: height, canonical, projective, dynamics

Author: Ben Hutz

Reviewer: Joao Alberto de Faria, Adam Towsley

Merged: sage-5.13.beta2

Issue created by migration from https://trac.sagemath.org/ticket/14218

bhutz · 2013-03-03T18:30:00Z

Attachment: heights.patch.gz

fchapoton · 2013-03-06T12:51:25Z

Changed dependencies from 13130, 14217 to #13130, #14217

fchapoton · 2013-05-07T20:06:00Z

comment:3

apply trac_14218_heights.patch

bhutz · 2013-05-16T11:58:11Z

comment:4

apply trac_14218_heights.patch

fchapoton · 2013-08-29T17:49:04Z

comment:8

Attachment: trac_14218_remove_imports.patch.gz

new patch, changed the import of copy

bhutz · 2013-09-04T16:36:05Z

comment:9

apply trac_14218_heights.patch trac_14218_remove_imports.patch

sagetrac-jdefaria · 2013-10-02T16:45:53Z

Reviewer: Joao Alberto de Faria

sagetrac-jdefaria · 2013-10-02T16:45:53Z

comment:10

Confirmed that the functions were returning the correct values. Also tested the functions would not accept undefined variables, here are the list of known issues found

projective_point.py:

green_function: kwd "precision"in should be "prec"
green_function: Joe's name is spelled wrong
global_height: lacking both a number field and precision example
global_height: description still says ZZ or QQ only
canonical_height: lacking a precision example

bhutz · 2013-10-03T12:55:49Z

Changed dependencies from #13130, #14217 to none

bhutz · 2013-10-03T12:55:49Z

comment:11

Fixed all the issues described above. The only change of note was that fixing the 'precision' keyword required more than just a rename. The use of the precision needed to be included throughout the green's function computation.

Since that patchbot seems to be trying to apply the patches from the closed dependencies #13130 and #14217, I've removed those from the dependency field. Hopefully that will allow the patchbot to test this patch.

bhutz · 2013-10-03T12:56:59Z

comment:12

apply trac_14218_heights.patch trac_14218_remove_imports.patch

sagetrac-atowsley · 2013-10-03T18:15:04Z

comment:13

When computing the height of the constant 0 in a function field global_height gives and error. Every other constant seems fine.

R. = PolynomialRing(QQ)

A. = AffineSpace(QQ,1)

H=Hom(A,A)

f=H([0])

f.global_height()

returns

Traceback (most recent call last):
File "", line 1, in
File "_sage_input_100.py", line 10, in
exec compile(u'open("code.py","w").write("# -- coding: utf-8 --
n" + support.preparse_worksheet_cell(base64.b64decode("Ui48eD4gPSBQb2x5bm9taWFsUmluZyhRUSkKQS48eD4gPSBBZmZpbmVTcGFjZShRUSwxKQpIPUhvbShBLEEpCmY9SChbMF0pCmYuZ2xvYmFsX2hlaWdodCgp"),globals())+"
n"); execfile(os.path.abspath("code.py"))
File "", line 1, in

File "/tmp/tmpYiF_cn/code.py", line 7, in
exec compile(u'f.global_height()
File "", line 1, in

File "/home/atowsley/sage-5.12.rc0/local/lib/python2.7/site-packages/sage/schemes/affine/affine_morphism.py", line 542, in global_height
h=max([c.global_height(prec) for c in C])
ValueError: max() arg is an empty sequence

bhutz · 2013-10-03T19:20:01Z

comment:14

Yes, missed that case. Actually, in any dimension if any one of the coordinate functions is 0 it has the same issue. The new patches catches those.

apply trac_14218_heights.patch trac_14218_remove_imports.patch

sagetrac-atowsley · 2013-10-06T19:11:24Z

comment:15

I found no more issues. It passed the long test.

bhutz · 2013-10-07T00:44:30Z

Changed reviewer from Joao Alberto de Faria to Joao Alberto de Faria, Adam Towsley

jdemeyer · 2013-10-12T09:45:25Z

Merged: sage-5.13.beta1

jdemeyer · 2013-10-19T09:18:43Z

Changed merged from sage-5.13.beta1 to none

jdemeyer · 2013-10-19T09:18:43Z

comment:18

Sorry, but this needs work:

there are numerical precision issues on Solaris with green_function:

**********************************************************************
File "devel/sage/sage/schemes/projective/projective_morphism.py", line 1236, in sage.schemes.projective.projective_morphism.SchemeMorphism_polynomial_projective_space.green_function
Failed example:
    f.green_function(P.point([5,2],False),0,N=30)
Expected:
    1.7315451844777406965714211646
Got:
    1.7315451844777406965172110560
**********************************************************************
File "devel/sage/sage/schemes/projective/projective_morphism.py", line 1238, in sage.schemes.projective.projective_morphism.SchemeMorphism_polynomial_projective_space.green_function
Failed example:
    f.green_function(P.point([2,1],False),0,N=30)
Expected:
    0.86577259223181085968927265240
Got:
    0.86577259223181085966216759809
**********************************************************************
File "devel/sage/sage/schemes/projective/projective_morphism.py", line 1240, in sage.schemes.projective.projective_morphism.SchemeMorphism_polynomial_projective_space.green_function
Failed example:
    f.green_function(P.point([1,1],False),0,N=30)
Expected:
    0.43288629610862337434550672337
Got:
    0.43288629610862337433195419621
**********************************************************************
File "devel/sage/sage/schemes/projective/projective_point.py", line 727, in sage.schemes.projective.projective_point.SchemeMorphism_point_projective_ring.green_function
Failed example:
    Q.green_function(f,0,N=200,prec=200)
Expected:
    1.6460930160038721221892751679783564477424287857689424150860
Got:
    1.6460930160038721221892751679783564477424287857689424150656
**********************************************************************

This actually shows a bigger problem: it shows that some computations depend on machine floats and therefore are done only to 53 bits precision. In the code I see:

RealField(prec)(log(m))

this should be

RealField(prec)(m).log()

(the best solution to avoid this is simply removing from math import log)

Also, I recommend you to write once

R = RealField(prec)

and then use R(a) every where.

Also, comparisons to None should be done with is: a is None or a is not None.

bhutz · 2013-10-20T12:59:53Z

comment:19

apply trac_14218_heights.patch trac_14218_remove_imports.patch

Removed the math.log function and replaced with R.log() everywhere it occurred. That should fix the precision issue.

Fixed comparisons to None everywhere they occurred.

Also, added another input check to the error_bound kwd.

fchapoton · 2013-10-20T17:35:57Z

Attachment: trac_14218_addon1.patch.gz

fchapoton · 2013-10-20T17:38:36Z

comment:21

Hello,

I have added a patch which mainly cleans the doc a little bit.

for the patchbot:

apply trac_14218_heights.patch trac_14218_remove_imports.patch trac_14218_addon1.patch

By the way, did you know that you could run your own patchbot on your own tickets instead of waiting for the bot of someone else ?

jdemeyer · 2013-10-21T12:05:32Z

comment:22

I suggest removing the added

from math import log

(the addon patch removes only 1 out of 2)

bhutz · 2013-10-21T12:24:29Z

comment:23

Yes, thanks, I'll upload a new version that gets the missed one in affine_point.py as soon as my tests are done.

bhutz · 2013-10-21T17:30:40Z

Attachment: trac_14218_heights.patch.gz

removed the log import from affine_point.py

bhutz · 2013-10-21T17:34:05Z

comment:24

apply trac_14218_heights.patch trac_14218_remove_imports.patch trac_14218_addon1.patch

all I have to say is that I can't wait to switch to git instead of dealing with a stack of patches like this...

jdemeyer · 2013-10-22T06:36:44Z

comment:25

Replying to @bhutz:

all I have to say is that I can't wait to switch to git instead of dealing with a stack of patches like this...

It is perfectly fine to fold all patches into one patch.

sagetrac-atowsley · 2013-10-24T18:02:12Z

comment:26

Green's function works and is accurate on my computer.

jdemeyer · 2013-10-31T19:16:24Z

Merged: sage-5.13.beta2

jdemeyer · 2013-12-15T08:44:05Z

Changed author from Ben Hutz to Benjamin Hutz

fchapoton · 2016-04-15T20:26:44Z

Changed author from Benjamin Hutz to Ben Hutz

bhutz added this to the sage-5.11 milestone Mar 3, 2013

bhutz added c: algebraic geometry labels Mar 3, 2013

bhutz self-assigned this Mar 3, 2013

This comment has been minimized.

Sign in to view

bhutz added the s: needs review label Mar 18, 2013

jdemeyer modified the milestones: sage-5.11, sage-5.12 Aug 13, 2013

This comment has been minimized.

Sign in to view

sagetrac-jdefaria mannequin added s: needs work and removed s: needs review labels Oct 2, 2013

bhutz added s: needs review and removed s: needs work labels Oct 3, 2013

sagetrac-atowsley mannequin added s: needs work and removed s: needs review labels Oct 3, 2013

bhutz added the s: needs review label Oct 3, 2013

sagetrac-atowsley mannequin added s: positive review and removed s: needs review labels Oct 6, 2013

jdemeyer removed the s: positive review label Oct 12, 2013

jdemeyer closed this as completed Oct 12, 2013

jdemeyer reopened this Oct 19, 2013

bhutz added the s: needs review label Oct 20, 2013

This comment has been minimized.

Sign in to view

sagetrac-atowsley mannequin added s: positive review and removed s: needs review labels Oct 24, 2013

jdemeyer removed the s: positive review label Oct 31, 2013

jdemeyer closed this as completed Oct 31, 2013

bhutz mentioned this issue Apr 15, 2016

rational preperiodic points for projective morphisms #14219

Closed

Provide feedback

Saved searches

Use saved searches to filter your results more quickly

height and canonical height for projective points and morphisms #14218

height and canonical height for projective points and morphisms #14218

bhutz commented Mar 3, 2013

bhutz commented Mar 3, 2013

fchapoton commented Mar 6, 2013

This comment has been minimized.

fchapoton commented May 7, 2013

bhutz commented May 16, 2013

This comment has been minimized.

This comment has been minimized.

fchapoton commented Aug 29, 2013

bhutz commented Sep 4, 2013

sagetrac-jdefaria mannequin commented Oct 2, 2013

sagetrac-jdefaria mannequin commented Oct 2, 2013

bhutz commented Oct 3, 2013

bhutz commented Oct 3, 2013

bhutz commented Oct 3, 2013

sagetrac-atowsley mannequin commented Oct 3, 2013

bhutz commented Oct 3, 2013

sagetrac-atowsley mannequin commented Oct 6, 2013

bhutz commented Oct 7, 2013

jdemeyer commented Oct 12, 2013

jdemeyer commented Oct 19, 2013

jdemeyer commented Oct 19, 2013

bhutz commented Oct 20, 2013

fchapoton commented Oct 20, 2013

fchapoton commented Oct 20, 2013

This comment has been minimized.

jdemeyer commented Oct 21, 2013

bhutz commented Oct 21, 2013

bhutz commented Oct 21, 2013

bhutz commented Oct 21, 2013

jdemeyer commented Oct 22, 2013

sagetrac-atowsley mannequin commented Oct 24, 2013

jdemeyer commented Oct 31, 2013

jdemeyer commented Dec 15, 2013

fchapoton commented Apr 15, 2016

height and canonical height for projective points and morphisms #14218

height and canonical height for projective points and morphisms #14218

Comments

bhutz commented Mar 3, 2013

bhutz commented Mar 3, 2013

fchapoton commented Mar 6, 2013

This comment has been minimized.

fchapoton commented May 7, 2013

bhutz commented May 16, 2013

This comment has been minimized.

This comment has been minimized.

fchapoton commented Aug 29, 2013

bhutz commented Sep 4, 2013

sagetrac-jdefaria mannequin commented Oct 2, 2013

sagetrac-jdefaria mannequin commented Oct 2, 2013

bhutz commented Oct 3, 2013

bhutz commented Oct 3, 2013

bhutz commented Oct 3, 2013

sagetrac-atowsley mannequin commented Oct 3, 2013

bhutz commented Oct 3, 2013

sagetrac-atowsley mannequin commented Oct 6, 2013

bhutz commented Oct 7, 2013

jdemeyer commented Oct 12, 2013

jdemeyer commented Oct 19, 2013

jdemeyer commented Oct 19, 2013

bhutz commented Oct 20, 2013

fchapoton commented Oct 20, 2013

fchapoton commented Oct 20, 2013

This comment has been minimized.

jdemeyer commented Oct 21, 2013

bhutz commented Oct 21, 2013

bhutz commented Oct 21, 2013

bhutz commented Oct 21, 2013

jdemeyer commented Oct 22, 2013

sagetrac-atowsley mannequin commented Oct 24, 2013

jdemeyer commented Oct 31, 2013

jdemeyer commented Dec 15, 2013

fchapoton commented Apr 15, 2016