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Check whether point is on a projective variety

asked 2019-09-16 11:08:25 -0500

ConfusedMark gravatar image

I have a projective variety X (defined via .subscheme(polynomials) on a projective space). I have a projective point P. How can I check whether my point is on my variety?

The obvious answer is to try X.point(P). This throws an error if it's not a point, and constructs a point on X otherwise. Is there something like this that will simply give me true or false, rather than an error?

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answered 2019-09-16 11:21:06 -0500

rburing gravatar image

Sure, you can take a point from the ambient projective space and do a membership test:

sage: PP.<x,y,z,w,u,v> = ProductProjectiveSpaces([3,1],QQ)
sage: W = PP.subscheme([y^2*z-x^3,z^2-w^2,u^3-v^3])
sage: PP.point([1,1,1,1,1,1]) in W
sage: PP.point([1,1,1,1,1,2]) in W

Internally this does a try - except block around W.point(...).

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Thank you so much! Didn't even think to try that.

ConfusedMark gravatar imageConfusedMark ( 2019-09-16 11:24:37 -0500 )edit

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Asked: 2019-09-16 11:08:25 -0500

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Last updated: Sep 16 '19