LocalRings : Table of Contents

• LocalRings -- Localizations of polynomial rings at prime ideals

  • LocalRing -- The class of all local rings

    • localRing -- Constructor for local rings
    • liftUp -- Lifts various objects over R_P to R.
    • baseRing(LocalRing) -- produce the ring from which a ring was formed
    • char(LocalRing) -- computes the characteristic of the ring or field
    • coefficientRing(LocalRing) -- get the coefficient ring
    • degreeLength(LocalRing) -- the length of the degree vector
    • degrees(LocalRing) -- degrees of generators
    • dim(LocalRing) -- compute the Krull dimension
    • frac(LocalRing) -- construct a fraction field
    • generators(LocalRing) -- the list of generators of a ring
    • isCommutative(LocalRing) -- whether a ring is commutative
    • isWellDefined(LocalRing) -- whether a local ring is well defined
    • numgens(LocalRing) -- number of generators of a polynomial ring
• hilbertSamuelFunction -- Computes the Hilbert-Samuel Function of Modules over Local Rings
• replacements for functions from version 1.0

  • setMaxIdeal -- set the maximal ideal for local ring methods
  • localComplement -- find the splitting of the target of a map
  • localsyz -- find syzygies
  • localMingens -- finds a minimal set of generators
  • localModulo -- find the pre-image (pullback) of image of a map over a local ring
  • localPrune -- find a minimal presentation
  • localResolution -- find a resolution over a local ring