#18281: implement critical point functionality including is_pcf for projective
morphisms
-------------------------------------+-------------------------------------
Reporter: bhutz | Owner: bhutz
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.7
Component: algebraic | Resolution:
geometry | Merged in:
Keywords: | Reviewers: Grayson Jorgenson
Authors: Ben Hutz | Work issues:
Report Upstream: N/A | Commit:
Branch: | 83242df1ca8b49344cc0cbc58c4b197d36a2c41b
u/bhutz/ticket/18281 | Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
Changes (by gjorgenson):
* status: needs_review => needs_work
* reviewer: => Grayson Jorgenson
Comment:
change_ring (for both SchemeMorphism_polynomial and SchemeMorphism_point):
- Before creating an embedding into QQbar, need check that the map is
defined over a number field, change_ring breaks otherwise:
{{{
P.<x,y> = ProjectiveSpace(ZZ,1)
H = End(P)
f = H([3*x^2,y^2])
f.change_ring(QQbar)
}}}
- There is also an issue when trying to change_ring from QQbar to QQbar:
{{{
P.<x,y> = ProjectiveSpace(QQbar,1)
H = End(P)
f = H([3*x^2,y^2])
f.change_ring(QQbar)
}}}
_preperiodic_points_to_cyclegraph:
- maybe add more comments explaining how equal points with different
representations are dealt with
wronskian_ideal:
- in line 2497, change format of NotImplementedError to the standard
format
- change "== false" checks to "not" for faster performance
critical_points:
- rational_points should return a list, so the list conversion in the
return statement is not needed
is_postcritically_finite
- remove extra lines in documentation, lines 2560 and 2595
- subscheme check not needed since the check is present in critical_points
- perhaps restrict to only maps defined over number fields
critical_point_portrait:
- copying crit_points list not needed, instead could loop over crit_points
by index, stopping when the index is the original length of the
crit_points list
- subscheme and endomorphism checks not needed since they are present in
critical_points
critical_height:
- maybe include a note that the keywords are optional
- subscheme and endomorphism checks are already done in critical_points
--
Ticket URL: <http://trac.sagemath.org/ticket/18281#comment:3>
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