#14218: height and canonical height for projective points and morphisms
-------------------------------------+-------------------------------------
Reporter: bhutz | Owner: bhutz
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.13
Component: algebraic | Resolution:
geometry | Merged in:
Keywords: height, | Reviewers: Joao Alberto de
canonical, projective, dynamics | Faria, Adam Towsley
Authors: Ben Hutz | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
Changes (by jdemeyer):
* status: closed => new
* resolution: fixed =>
* merged: sage-5.13.beta1 =>
Comment:
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`.
--
Ticket URL: <http://trac.sagemath.org/ticket/14218#comment:18>
Sage <http://www.sagemath.org>
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