NumericalSemigroups : Table of Contents

• NumericalSemigroups -- Compute the Apery set and invariants of a numerical semigroup ring
• allSemigroups -- Compute the Hilbert basis and module generators of a cone of semigroups
• apery -- Compute the apery set, multiplicity and conductor
• aperyConeEquations -- Inequalities defining the Kunz cones
• aperyFacetRays (missing documentation)
• aperySemigroupRing -- computes the semigroup ring using both the multiplicity and the full Apery set
• aperySet -- Compute the apery set of a numerical semigroup
• arfClosure -- Compute the Arf closure of a numerical semigroup
• arfIndex -- Computes the Arf index of a numerical semigroup
• buchweitz -- An example of a semigroup that is not a Weierstrass semigroup
• buchweitzCriterion -- Does L satisfies the Buchweitz criterion?
• buchweitzSemigroups -- Finds semigroups that are not Weierstrass semigroups by the Buchweitz test
• burchIndex -- Compute the burchIndex of the Burch ring of a semigroup
• conductor(List) -- conductor of a semigroup
• coneRays -- All the rays of the (homogeneous) Kunz cone
• def1 -- degrees of a basis of T^1
• ewt -- Effective weight of a semigroup (Pflueger)
• facetRays -- computes the rays spanning the face in which a semigroup lies
• findSemigroups -- Find all semigroups with a given number of gaps, multiplicity and/or conductor
• fractionalIdeal -- turn a fractional ideal into a proper ideal
• gaps -- The gap sequence of a semigroup
• genus(List) -- Compute the number of gaps (genus) of a semigroup
• infinitelyNearModules -- The sequence of blowups of a semigroup ring as fractional ideals
• infinitelyNearSemigroups -- The sequence of blowup semigroups of a numerical semigroup
• isArf -- test whether a numerical semigroup is Arf
• isGapSequence -- test whether a list of integers can be the list of gaps of a semigroup
• isKnownExample -- Is L a known Weierstrass semigroup?
• isMinimalMultiplicity (missing documentation)
• isSymmetric -- test whether the semigroup generated by L is symmetric
• kunzMatrix -- determine the set of facet equations satisfied by a semigroup
• kunzPoset (missing documentation)
• kunzRing -- artinian reduction of a semigroup ring
• mingens(List) -- Find a mininmal set of semigroup generators
• mu -- Compute the point representing a semigroup in the Kunz cone
• muFacetRays (missing documentation)
• randomSemigroup -- Random semingroup on a given face of the Kunz cone
• reduceByList (missing documentation)
• semigroup -- Compute the semigroup generated by a list of positive integers
• semigroupFromMu -- Inverse of the function mu
• semigroupIdeal -- The ideal defining the semigroup ring
• semigroupRing -- forms the semigroup ring over "BaseField"
• semigroupsFromMatrix -- applies semigroupFromMu to the columns of a matrix
• socle -- elements of the semigroup that are in the socle mod the multiplicity
• sums -- sum of two sequences
• syzFormat (missing documentation)
• type -- type of the local semigroup ring
• weight -- weight of a semigroup