#20511: Not all empty schemes are created equal
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Reporter: kedlaya | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-7.2
Component: algebraic geometry | Resolution:
Keywords: schemes, empty | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by kedlaya):
Replying to [comment:1 nbruin]:
> Projective scheme comparison should compare ideals saturated with
respect to the irrelevant ideal:
>
> {{{
> sage: U=P2.subscheme([x,y,z])
> sage: V=P2.subscheme([x,y^2,z])
> sage: J=U.defining_ideal()
> sage: U.defining_ideal().saturation(J)[0] ==
V.defining_ideal().saturation(J)[0]
> True
> }}}
>
Agreed. I guess we don't want to transform the generating set at creation,
so we can recover the generators as specified, but maybe we want to cache
the saturation?
> Similarly, the `is_empty` should do:
> {{{
> sage: one_ideal= J^0 #just get the ideal generated by 1
> sage: U.defining_ideal().saturation(J)[0] == one_ideal
> }}}
> decomposing in irreducible components is a more expensive operation.
Agreed again.
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Ticket URL: <http://trac.sagemath.org/ticket/20511#comment:2>
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