Outline
Overview
Ext
Primdec
Normalize
MuPAD
Deform
Classify
Puiseux
Future

Algorithms implemented in Kernel
 General standard basis algorithm:
 for any monomial ordering. Includes:
 wellorderings: Buchberger algorithm
 tangentcone orderings: Mora algorithm
 Variants of standard basis algorithm:
 Traverso's Hilbertdriven Groebner basis algorithm
 weightedecartmethod, highcornermethod
 Factorizing Buchberger algorithm
 FGLM for change of monomial ordering
 Ideal Theory:
 Intersection, ideal quotient, elimination and
saturation
 Syzygies and free resolutions of modules:
 Standardbasis driven, Schreyer's, and La Scala's algorithm
 Combinatorics:
 dimensions, Hilbert series, multiplicities,
etc
 Multivariate polynomial computations:
 gcd, resultant, factorization
 Characteristic sets:
 Wu's method
SINGULAR: one of the fastest CAS for polynomial computations
