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

  • Count the number of points defined 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](http://www.sagemath.org/) would be my guess2012-08-29
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    In the past my colleagues have used MAGMA to find answers to (at least) the first question.2012-08-30

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