#12170: Genus computation (using singular) and _singular_ object for function
filed
----------------------------------+-----------------------------------------
Reporter: sydahmad | Owner: AlexGhitza
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-5.0
Component: algebraic geometry | Keywords: function field, genus,
singular
Work_issues: | Upstream: N/A
Reviewer: | Author: Syed Ahmad Lavasani
Merged: | Dependencies: #9054
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Comment(by sydahmad):
Replying to [comment:8 saraedum]:
> Thinking about this, is_RationalFunctionField()/is_rational() is
probably not the right name. Take QQ(x) and the extension given by y^2 = x
then that gives you a rational function field but probably that's not what
you want there. In this case what you actually want is probably one
implementation in RationalFunctionField (returning 0) and one in
FunctionField_polymod (calling singular).^
This is why the function is called "is_RationalFunctionField()". This is
because it does not check if (mathematically) the function field is
rational, but it checks, if it is (programatically) of
RationalFunctionField type. I need that because (AFAIUnderstood the
manual) when I ask Singular to create a ring of k(t)[y] form, singular
expects that k be a prime field (you only get to give the characteristic).
so I can not accept k(x)[y]/(y^2 - x) for my purpose:
{{{
sage: singular.eval('ring r = (7^2,a,b),(x,y,z),dp;')
---------------------------------------------------------------------------
RuntimeError Traceback (most recent call
last)
/home/syd/Programmes/sage-4.7.2/devel/sage-sydevel/<ipython console> in
<module>()
/home/syd/Programmes/sage-4.7.2/local/lib/python2.6/site-
packages/sage/interfaces/singular.pyc in eval(self, x, allow_semicolon,
strip, **kw\
ds)
572
573 if s.find("error") != -1 or s.find("Segment fault") != -1:
--> 574 raise RuntimeError, 'Singular error:\n%s'%s
575
576 if get_verbose() > 0:
RuntimeError: Singular error:
? too many parameters
? cannot make ring
? error occurred in or before STDIN line 41: `ring r =
(7^2,a,b),(x,y,z),dp;`
? expected ring-expression. type 'help ring;'
}}}
So, I'm OK with making it a method of FunctionField class but I think we
should keep the name. We can have an additional method of "is_rational()"
if you like (which will involve computing the genus).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12170#comment:11>
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