
Algorithms in the
SINGULAR
Kernel
Algorithms which are implemented in the
SINGULAR
kernel
include the following:

General standard basis algorithm:
for any monomial ordering. Includes:
 Buchberger algorithm (wellorderings)
 Mora algorithm (tangentcone orderings)

Variants of standard basis algorithm:
 Traverso's Hilbertdriven Gröbner 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
One of the main design goals of
SINGULAR
is efficiency.
And, indeed,
SINGULAR
is
one of the fastest CAS for polynomial computations.
