On 1/14/08, D. Benjamin Antieau <[EMAIL PROTECTED]> wrote: > To all, > > I've created a sage file to calculate, among other things, the Hodge numbers > of an arbitrary complete intersection. Attached is the .sage file. I also > attempted to create a .spkg file, but it does not seem to work. Mine > contains simply a .py file that the install script puts it > $SAGE_ROOT/local/bin. But, I cannot seem to use it from within sage. Any > help on that front would be appreciated. On the other hand, loading the > .sage file works fine. > > The file itself is well-documented. I would love suggestions for further > methods to add. For instance, at some point I will add the ability to > compute the degrees of the top Chern classes of a threefold.
I don't know enough about the area to suggest anything right off, but I skimmed through your code and it looks well written and documented. Especially the references to the literature and formulas you are using are good. > I don't see putting this in sage at the moment, but it does lead to the > question: should there be a CompleteIntersection class, which would inherit > from AlgebraicScheme_subscheme_projective. If so, then I > could put this code in that class in the characteristic zero case. > > Ben Antieau > > Example: > > The Hodge numbers of a crazy fourfold. The list of integers is the list of > degrees of the complete intersection. > sage: hodge_numbers_ci([2,4,6,3,6,4,3,2,9,5],4) > [ 1 0 0 0 2658146543] > [ 0 1 0 22238665343 0] > [ 0 0 42452753184 0 0] > [ 0 22238665343 0 1 0] > [ 2658146543 0 0 0 1] > > The file provides the following functions: > chiy_characteristic_ci(degrees,index,yprecision,zprecision) > hodge_numbers_ci(degrees,dimension) > betti_numbers_ci(degrees,dimension) > euler_characteristic_ci(degrees,dimension) > topological_euler_characteristic_ci(degrees,dimension) > arithmetic_genus_ci(degrees,dimension) > geometric_genus_ci(degrees,dimension) > [==arithmetic_genus_ci] > K_squared_surface_ci(degrees,dimension) [computes the > degree of K^2 of a complete intersection surface] > c2_surface_ci(degrees,dimension) [computes the degree of > the second Chern class of a complete intersection surface] > > > > > > -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
