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Computing graded Betti tables of toric surfaces

This is a preliminary version of the software developed as part of the paper Computing graded Betti tables of toric surfaces by Wouter Castryck, Filip Cools, Jeroen Demeyer and Alexander Lemmens.

Installation

This package requires a recent version of Sage and the recommended way to install this package is within Sage. Download the sources and then run

sage --python setup.py install

Usage

Start Sage the usual way and then execute the following commands to compute the graded Betti table of 5 Sigma in characteristic 40009 in just a few seconds:

sage: from betti.all import *
sage: P = polygon_normalized([(0,0), (5,0), (0,5)])
sage: T = ToricSurfaceBettiTable(P, GF(40009))
sage: T.betti_table()
[     1      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0]
[     0    165   1830  10710  41616 117300 250920 417690 548080 568854 464100 291720 134640  39780   4858    375      0      0      0]
[     0      0      0      0      0      0      0      0      0      0      0      0      0   2002   4200   2160    595     90      6]

Useful keywords are verbose and threads:

sage: T = ToricSurfaceBettiTable(P, GF(40009), verbose=2, threads=2)
sage: T.betti_table()
...
[     1      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0      0]
[     0    165   1830  10710  41616 117300 250920 417690 548080 568854 464100 291720 134640  39780   4858    375      0      0      0]
[     0      0      0      0      0      0      0      0      0      0      0      0      0   2002   4200   2160    595     90      6]