#15448: cartesian products of projective space
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Reporter: bhutz | Owner: bhutz
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.13
Component: algebraic geometry | Resolution:
Keywords: | Merged in:
Authors: bhutz | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by nbruin):
Replying to [comment:3 bhutz]:
> As far as I'm aware there is no native way to use multiply graded rings
in Sage. I'd be happy to look into another way to do things, that's why
I've put this up here as 'mostly done'.
The arithmetic in a multiply graded ring only depends on the ring
structure, so in that respect nothing extra is necessary. You just need to
interpret the results properly, i.e., that the ideal
(x-y,u-v) in k[x,y,u,v] describes a point in P1xP1 and not a line in P3. I
guess knowing you're working with bihomogeneously generated ideals might
affect your choice of term ordering if you need to compute groebner bases.
Basically what I expect is that it's possible to use/adapt the toric
variety framework for dynamic purposes as well. I haven't looked into it
myself. I'm just sharing my experience that in cases where I needed
products of projective varieties, I found using multiple gradings
initially daunting but eventually not bad at all and much more convenient
and efficient.
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Ticket URL: <http://trac.sagemath.org/ticket/15448#comment:4>
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