#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:
Authors: Joao de Faria | Work issues:
Report Upstream: N/A | Commit:
Branch: | df867c1288da3a89d8a1df1d9cceb6f5dd5bacb9
u/jdefaria/ticket/16986 | Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
Changes (by bhutz):
* status: needs_review => needs_work
Comment:
The cases of number fields and finite fields work fine, but many other
fields fail. Also there are some issues in the documentation:
- The descriptions of both functions reference QQ only
- The description of all_rational_preimages reference parallel (which it
is not)
- The text is after the :: in examples so is not formatted correctly
- number field is 2 words and not capitalized
For functionality: here are some examples which fail. They fail in at
least 3 distinct ways.
{{{
R.<t>=FunctionField(QQ)
P.<x,y>=ProjectiveSpace(R,1)
H=End(P)
f=H([x^2-y^2,y^2])
f.rational_preimages(P([0,1]))
}}}
{{{
R.<t>=PolynomialRing(QQ)
P.<x,y>=ProjectiveSpace(FractionField(R),1)
H=End(P)
f=H([x^2-y^2,y^2])
f.rational_preimages(P([0,1]))
}}}
{{{
R.<t>=PolynomialRing(QuadraticField(2))
P.<x,y>=ProjectiveSpace(FractionField(R),1)
H=End(P)
f=H([x^2-y^2,y^2])
f.rational_preimages(P([0,1]))
}}}
{{{
P.<x,y>=ProjectiveSpace(Qp(3),1)
H=End(P)
f=H([x^2-y^2,y^2])
f.rational_preimages(P([0,1]))
}}}
{{{
P.<x,y>=ProjectiveSpace(CC,1)
H=End(P)
f=H([x^2-y^2,y^2])
f.rational_preimages(P([0,1]))
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/16986#comment:4>
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