Outline

Overview

Ext

Primdec

Normalize

MuPAD

Deform

Classify

Puiseux

Future

Algorithms implemented in Kernel

General standard basis algorithm:

for any monomial ordering. Includes:

well-orderings: Buchberger algorithm

tangent-cone orderings: Mora algorithm

Variants of standard basis algorithm:

Traverso's Hilbert--driven Groebner basis algorithm

weighted--ecart--method, high--corner--method

Factorizing Buchberger algorithm

FGLM for change of monomial ordering

Ideal Theory:

Intersection, ideal quotient, elimination and saturation

Syzygies and free resolutions of modules:

Standard-basis 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