Opened 5 years ago

Closed 4 years ago

Last modified 18 months ago

#14218 closed enhancement (fixed)

height and canonical height for projective points and morphisms

Reported by: bhutz Owned by: bhutz
Priority: major Milestone: sage-5.13
Component: algebraic geometry Keywords: height, canonical, projective, dynamics
Cc: Merged in: sage-5.13.beta2
Authors: Ben Hutz Reviewers: Joao Alberto de Faria, Adam Towsley
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description (last modified by chapoton)

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:

Attachments (4)

heights.patch (14.4 KB) - added by bhutz 5 years ago.
trac_14218_remove_imports.patch (1.4 KB) - added by chapoton 4 years ago.
trac_14218_addon1.patch (57.5 KB) - added by chapoton 4 years ago.
trac_14218_heights.patch (22.5 KB) - added by bhutz 4 years ago.
removed the log import from affine_point.py

Download all attachments as: .zip

Change History (33)

Changed 5 years ago by bhutz

comment:1 Changed 5 years ago by chapoton

  • Dependencies changed from 13130, 14217 to #13130, #14217

comment:2 Changed 5 years ago by bhutz

  • Description modified (diff)
  • Status changed from new to needs_review

comment:3 Changed 4 years ago by chapoton

apply trac_14218_heights.patch

comment:4 Changed 4 years ago by bhutz

apply trac_14218_heights.patch

comment:5 Changed 4 years ago by jdemeyer

  • Milestone changed from sage-5.11 to sage-5.12

comment:6 Changed 4 years ago by chapoton

  • Description modified (diff)

comment:7 Changed 4 years ago by chapoton

  • Description modified (diff)

Changed 4 years ago by chapoton

comment:8 Changed 4 years ago by chapoton

new patch, changed the import of copy

comment:9 Changed 4 years ago by bhutz

apply trac_14218_heights.patch trac_14218_remove_imports.patch

comment:10 Changed 4 years ago by jdefaria

  • Reviewers set to Joao Alberto de Faria
  • Status changed from needs_review to needs_work

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

comment:11 Changed 4 years ago by bhutz

  • Dependencies #13130, #14217 deleted
  • Status changed from needs_work to needs_review

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.

comment:12 Changed 4 years ago by bhutz

apply trac_14218_heights.patch trac_14218_remove_imports.patch

comment:13 Changed 4 years ago by atowsley

  • Status changed from needs_review to needs_work

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

R.<x> = PolynomialRing?(QQ)

A.<x> = AffineSpace?(QQ,1)

H=Hom(A,A)

f=H([0])

f.global_height()

returns

Traceback (most recent call last):

File "<stdin>", line 1, in <module> File "_sage_input_100.py", line 10, in <module>

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 <module>

File "/tmp/tmpYiF_cn/_code_.py", line 7, in <module>

exec compile(u'f.global_height()

File "", line 1, in <module>

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

Last edited 4 years ago by atowsley (previous) (diff)

comment:14 Changed 4 years ago by bhutz

  • Status changed from needs_work to needs_review

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

comment:15 Changed 4 years ago by atowsley

  • Status changed from needs_review to positive_review

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

comment:16 Changed 4 years ago by bhutz

  • Reviewers changed from Joao Alberto de Faria to Joao Alberto de Faria, Adam Towsley

comment:17 Changed 4 years ago by jdemeyer

  • Merged in set to sage-5.13.beta1
  • Resolution set to fixed
  • Status changed from positive_review to closed

comment:18 Changed 4 years ago by jdemeyer

  • Merged in sage-5.13.beta1 deleted
  • Resolution fixed deleted
  • Status changed from closed to new

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.

comment:19 Changed 4 years ago by bhutz

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.

comment:20 Changed 4 years ago by bhutz

  • Status changed from new to needs_review

Changed 4 years ago by chapoton

comment:21 Changed 4 years ago by chapoton

  • Description modified (diff)

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 ?

comment:22 Changed 4 years ago by jdemeyer

I suggest removing the added

from math import log

(the addon patch removes only 1 out of 2)

Last edited 4 years ago by jdemeyer (previous) (diff)

comment:23 Changed 4 years ago by bhutz

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

Changed 4 years ago by bhutz

removed the log import from affine_point.py

comment:24 follow-up: Changed 4 years ago by bhutz

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...

comment:25 in reply to: ↑ 24 Changed 4 years ago by jdemeyer

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.

comment:26 Changed 4 years ago by atowsley

  • Status changed from needs_review to positive_review

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

comment:27 Changed 4 years ago by jdemeyer

  • Merged in set to sage-5.13.beta2
  • Resolution set to fixed
  • Status changed from positive_review to closed

comment:28 Changed 4 years ago by jdemeyer

  • Authors changed from Ben Hutz to Benjamin Hutz

comment:29 Changed 18 months ago by chapoton

  • Authors changed from Benjamin Hutz to Ben Hutz
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