Algorithms implemented in Kernel

General standard basis algorithm: for any monomial ordering. Includes:

Buchberger algorithm (well-orderings)

Mora algorithm (tangent-cone orderings)

Variants of standard basis algorithm:

Traverso's Hilbert-driven Gröbner 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