#12170: Genus computation (using singular) and _singular_ object for function
filed
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Reporter: sydahmad | Owner: AlexGhitza
Type: enhancement | Status: needs_review
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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Changes (by sydahmad):
* status: new => needs_review
Comment:
if we have:
kx.<x> = FunctionField(QQ)
kxY.<Y> = PolynomialRing(QQ)
kxY._singular_ should be k(x)[Y] (which is what this code generates)
however, singular only computes the genus of an ideal of k[x][Y] ring. So,
I have to generate a tmpR = k[x][Y] each time I need to compute the genus.
Maybe it's worth it to add __singular_deg2_ private object to store this
ring as well.
Also, it makes sense to store the genus in __genus. But I'm not sure how
should I check it's validity. Can the defining polynomial of the function
field change after its creation. If not then we can set __genus = -1 and
if it's non-negative then it's valid.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12170#comment:1>
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