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# 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) -- get 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