#10540: Spec and patches for singular affine toric varieties / algebraic schemes
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Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.7.1
Component: algebraic geometry | Keywords:
Work_issues: | Upstream: N/A
Reviewer: Andrey Novoseltsev | Author: Volker Braun
Merged: | Dependencies: #9918, #10525, #10023,
#10529
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Comment(by vbraun):
I've added a possibility to specify the polynomial ring directly and
documentation.
As for the base ring, really you only have to work over `GF(2)`. During
the Buchberger algorithm, all S-polynomials are of the form
`monomial=monomial`. This is a very special case and implementing
Buchbergers algorithm in this special case is probably faster than any
general-purpose code. But then, its been fast enough for me so far. If you
use smaller coefficient rings then converting it back into an ideal over
QQ, say, gets more difficult. For example, if you use `GF(2)` then you
have to manually give each generator alternating signs. So its probably
most convenient to work over QQ.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10540#comment:8>
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