This extension for [polymake] (https://www.polymake.org) contains my private code for experimenting with toric geometry. It is not well documented and many methods might do different things from what you expect. If you have any questions, please send me an email.
There is sample code for building a proof-of-concept type interface to [Singular] (http://www.singular.uni-kl.de/) in the file [apps/fulton/rules/singular.rules] (https://github.com/lkastner/pmExperiments/blob/master/apps/fulton/rules/singular.rules). This code uses the singular_eval method from the polymake core to execute Singular commands. The polymake objects get equipped with string properties, containing the variable names of the Singular objects.
The file [apps/fulton/rules/cyclic_quotient.rules] (https://github.com/lkastner/pmExperiments/blob/master/apps/fulton/rules/cyclic_quotient.rules) contains all algorithms developed in my [thesis] (http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000101520) that were too specific to go into the polymake core. Some of these may be different than from the print version, since polymake has had numerous updates making small changes necessary.
The file [apps/fulton/rules/dgla.rules] (https://github.com/lkastner/pmExperiments/blob/master/apps/fulton/rules/dgla.rules) contains code for dealing with differential graded Lie algebras of toric varieties. I am not really sure what this does, please ask [Klaus Altmann] (http://www.math.fu-berlin.de/altmann/) for the mathematical details. You can ask me, if you know the mathematical details and have questions about the implementation.
There are several files dealing with toric deformation theory:
- apps/fulton/rules/t1.rules
- apps/fulton/rules/deformations.rules
- apps/fulton/rules/downgrading.rules
- apps/fulton/rules/subvarietyInTV*.rules
You can determine the age of these files using git or estimating from the cleanliness of the code.