commutative algebra

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• Gröbner bases
• normal forms
• elimination of variables
• IntegralClosure -- routines for integral closure of affine domains and ideals
• PrimaryDecomposition -- primary decomposition and associated primes routines for ideals and modules
• hilbertFunction -- the Hilbert function
• hilbertSeries -- compute the Hilbert series
• hilbertPolynomial -- compute the Hilbert polynomial
• syz -- the syzygy matrix
• koszul -- Koszul complex or specific matrix in the Koszul complex
• eagonNorthcott -- Eagon-Northcott complex of a matrix of linear forms
• regularity -- compute the Castelnuovo-Mumford regularity
• presentation -- presentation of a module or ring
• resolution -- projective resolution
• quotient -- quotient or division
• quotient' -- factor a map through another with the same source
• quotientRemainder -- matrix quotient and remainder
• quotientRemainder' -- matrix quotient and remainder (opposite)
• remainder -- matrix remainder
• remainder' -- matrix remainder (opposite)
• pseudoRemainder -- compute the pseudo-remainder
• rank -- compute the rank
• dim -- compute the Krull dimension
• codim -- compute the codimension
• pdim -- compute the projective dimension
• depth -- depth of an object
• height -- height of an object
• length -- length of an object
• complete
• trim -- minimize generators and relations
• prune -- prune, e.g., compute a minimal presentation
• numgens -- the number of generators
• mingens -- minimal generator matrix
• minimize
• minimalPresentation -- compute a minimal presentation
• tensor -- tensor product
• directSum -- direct sum of modules or maps
• directProduct -- direct product
• monomialCurveIdeal -- make the ideal of a monomial curve
• isBorel -- whether an ideal is fixed by upper triangular changes of coordinates
• isCommutative -- whether a ring is commutative
• isAffineRing -- whether something is an affine ring