Changes between Version 3 and Version 8 of Ticket #20264


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Timestamp:
06/04/18 21:43:59 (2 years ago)
Author:
edgarcosta
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  • Ticket #20264

    • Property Status changed from new to needs_review
    • Property Branch changed from to u/edgarcosta/cycliccovers
    • Property Commit changed from to 7b51922af08c4002fc36f565025fcad8955cfe12
  • Ticket #20264 – Description

    v3 v8  
    1 We plan to add code to compute the Hasse-Weil Zeta function of a cyclic cover of P1 over finite fields using p-adic methods.
     1We add a new method to compute the zeta function of a cyclic cover of {{{P^1}}}, this is the result of a forthcoming paper generalizing the work of Kedlaya, Harvey, Minzlaff and Gonçalves.
     2In particular, we add two classes for cyclic covers, one over a generic ring and a specialized one over finite fields.
     3This requires wrapping David Harvey's code for computing products of matrices already in Sage but not accessible to Sage, see #25366
     4
     5Here is a quick example:
     6
     7{{{
     8sage: p = 4999;
     9sage: x = PolynomialRing(GF(p),"x").gen();
     10sage: C = CyclicCover(5, x^5 + 1)
     11sage: C
     12Cyclic Cover of P^1 over Finite Field of size 4999 defined by y^5 = x^5 + 1
     13sage: C.frobenius_polynomial()
     14x^12 + 29994*x^10 + 374850015*x^8 + 2498500299980*x^6 + 9367502249700015*x^4 + 18731257498500149994*x^2 + 15606259372500374970001
     15sage: C.genus()
     166
     17}}}