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Algorithms implemented in 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
