#16986: Enhance rational_preimages and all_rational_preimages to work over
Number
Fields
-------------------------------------+-------------------------------------
Reporter: jdefaria | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.4
Component: algebraic | Resolution:
geometry | Merged in:
Keywords: | Reviewers: Ben Hutz
Authors: Joao de Faria | Work issues:
Report Upstream: N/A | Commit:
Branch: | 07592c745b9d0c24fd137d95d949ba8130d0a0f0
u/jdefaria/ticket/16986 | Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
Changes (by bhutz):
* status: needs_review => needs_work
Comment:
The code snippents above are resolved now, but here are a couple more
issues:
- the docs are still wrong see comment 4 above
- for subschemes the points being returned are in the ambient space and
not the subscheme
- the following two examples fail
{{{
P.<x,y>=ProjectiveSpace(CC,1)
H=End(P)
f=H([x^2-2*y^2,y^2])
f.rational_preimages(P([0,1]))
}}}
The previous example also fails for RR
{{{
z = var('z')
K.<w>=NumberField(z^3+2)
R.<z>=PolynomialRing(K)
L.<v>=K.extension(z^2+z+1)
P.<x,y>=ProjectiveSpace(L,1)
H=End(P)
f=H([x^3-2*y^3,v*y^3])
f.rational_preimages(P([0,1]))
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/16986#comment:11>
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