Gap Polymake Singular Applications

Polymake - Singular projects

• Normalization of monomial ideals
  People: Christian Eder.
  Abstract: Christian, please drop a couple of lines here
  Implementation: Available in Singular
  System: Singular with polymake.so
  References: C. Eder, https://github.com/ederc/Sources/tree/int-clos

• Computation of GIT fans
  People: Simon Keicher (to be contacted), Janko Boehm, Yue Ren
  Abstract: More to come after Simon's invitation to Kaiserslautern.
  Implementation: The plan is to convert Simon's implementation, which uses Maple/convex and Groebner bases in Maple to Singular+Polymake
  System: Singular with polymake.so
  References S. Keicher: Computing the GIT-fan, http://arxiv.org/abs/1205.4204)

• Computation of Groebner fans
  (Bogart, Jensen, Speyer, Sturmfels, Thomas: Computing Tropical Varieties, http://arxiv.org/abs/math/0507563)
  currently Gfan computes the Groebner fan for polynomial ideals over rationals, data stored in gfanlib; possible complete extention to gfanlib by Anders, reuse M. Monerjan's code for Groebner fan computation of polynomial ideal over more general ground fields.

• Computation of tropical varieties
  (Bogart, Jensen, Speyer, Sturmfels, Thomas: Computing Tropical Varieties, http://arxiv.org/abs/math/0507563)
  currently Gfan computes the tropcial variety for polynomial ideals over rationals, data stored in gfanlib; possible complete extention to gfanlib by Anders, direct implementation of the algorithm in Singular for more general polynomial rings (possibly over valued fields)

• Framework for polyhedral divisors
  (Altmann, Hausen: Polyhedral Divisors and Algebraic Torus Actions, http://arxiv.org/abs/math/0306285)

• Generators of multigraded algebras
  (Ilten, Kastner: Generators of multigraded algebras, http://arxiv.org/abs/1203.5382)

• Regularity of semigroup algebras
  (Boehm, Eisenbud, Nitsche: Decomposition of semigroup algebras, http://arxiv.org/abs/1110.3653)

• Ring theoretic properties of semigroup algebras
  (Boehm, Eisenbud, Nitsche: Decomposition of Monomial Algebras: Applications and Algorithms, http://arxiv.org/abs/1206.1735)

• Deformations with constant Milnor number
  People: H. Schönemann, J. Boehm

• Computation of Weyl Algebras of line bundles over toric varieties
  People: M. Cuntz, Y. Ren, G. Trautmann
  References: http://arxiv.org/abs/1108.1886

##Gap - Singular projects

• Homalg project
  People: Mohamed Barakat
  Abstract: Mohamed please drop some lines here
  References: http://homalg.math.rwth-aachen.de/

• Computation of cohomology rings
  People: Probably a student could redo the sage implementation using GAP and Singular/Plural for the Groebner computations
  Abstract:
  References: Green, King: The computation of the cohomology rings of all groups of order 128, http://arxiv.org/abs/1001.2577