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I am looking for a computer algebra system, which is able to some of the following (in theory equivalent) things for a smooth projective variety defined over a finite field:

-Count the number of points definied over a certain field extension.

-Compute the Eigenvalues of Frobenius on etale Cohomology.

-Compute the Zeta function.

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I'm no expert, but Sage would be my guess –  Juan S Aug 29 '12 at 10:15
In the past my colleagues have used MAGMA to find answers to (at least) the first question. –  Jyrki Lahtonen Aug 30 '12 at 10:23

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