I'm currently reading through Hess' paper on calculating bases for Riemann-Roch spaces (http://linkinghub.elsevier.com/retrieve/pii/ S0747717101905139), hoping to be able to implement it for Sage. I'd like to be able to learn how to compute a basis in Magma so that I'll be able to check my results when I begin coding.
For example, at http://www.sagemath.org/doc/ref/module-sage.schemes.plane-curves.projective-curve.html, one of the examples toward the bottom is a demonstration of an incorrect basis that Singular gives. So far, I've set this up in Magma as R<x,y,z> := ProjectiveSpace(GF(5),2); C := Curve(R,x^7 + y^7 + z^7); pts := RationalPoints(C); I haven't figured out how to do the next step in Magma, creating the divisor. In the Sage example, the code is: D = C.divisor([ (3, pts[0]), (-1,pts[1]), (10, pts[5]) ]) pts[0] = (0:4:1) corresponds to pts[5] by Magma's calculation. Likewise, pts[1] = (1:2:1) in Sage corresponds to pts[3] in Magma, and pts[5] = (4:1:0) in Sage corresponds to pts[6] in Magma. Once I have the divisor D, I understand that Basis(D) computes the basis, and that it should be [x/(y + x), (z + y)/(y + x)]. I'd also like to be able to do Hess' Example 6.3 in Magma. Magma's documentation is clear, I'm just not sure which functions to use to correctly create the fields, places, and divisors in question. Specific solutions to the above, some more examples, or a general template on how to set up Magma with a curve C over a field F and how to find/get divisors would be helpful. The ultimate goal is to have a large number of examples (a field, a curve, a divisor of the curve, and the Riemann-Roch basis as calculated by Hess' algorithm in Magma) that I can use as test cases for my implementation. --Francisco --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
