Fri 2018-04-13 10:56:17 UTC, David Joyner:
>
> PS: About 3 years ago, a related question was posted:
>
> https://groups.google.com/forum/#!topic/sage-support/s59iDjhu2zU
>
> For some reason, the method described there is no longer implemented.
Regarding the example in the discussion you point to,
a minor change gets it to work: instead of
sage: C.cardinality()
you can use
sage: C.point_set().cardinality()
Illustration below:
Sage version:
$ sage -v
SageMath version 8.2.rc1, Release Date: 2018-03-31
Define the finite field F:
sage: F.<q> = GF(13^2)
sage: F
Finite Field in q of size 13^2
The projective plane over F:
sage: P2.<x,y,z> = toric_varieties.P2(base_ring=F)
sage: P2
2-d CPR-Fano toric variety covered by 3 affine patches
The curve (as a scheme):
sage: C = P2.subscheme(x^8 + y^8 + z^8)
sage: C
Closed subscheme of 2-d CPR-Fano toric variety covered by 3 affine
patches defined by:
x^8 + y^8 + z^8
Trying to get the cardinality fails for this scheme:
sage: C.cardinality()
Traceback (most recent call last)
...
AttributeError: 'AlgebraicScheme_subscheme_toric_with_category' object
has no attribute 'cardinality'
We need to go through the point set:
sage: P = C.point_set()
sage: P
Set of rational points of Closed subscheme of 2-d CPR-Fano toric
variety covered by 3 affine patches defined by:
x^8 + y^8 + z^8
Now we can get the cardinality:
sage: c = P.cardinality()
sage: c
512
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