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LineageTable -- a hash table of Gr\"obner basis polynomials and their lineages

Description

A lineage table is a hashtable whose values are a Gr\"obner basis for the ideal I or the ideal generated by L, and keys are the lineages of the corresponding elements.

A lineage of a polynomial is a natural number, or an ordered pair of lineages, tracing its history in the given Gr\"obner basis computation. Lineages that are natural numbers are assigned to the original input polynomials.

See also

Functions and methods returning an object of class LineageTable:

  • minimize(LineageTable) -- turn a Gr\"obner basis computed using threaded Gr\"obner bases into a minimal one
  • reduce -- produce a reduced Gr\"obner basis from one computed by threaded Gr\"obner bases
  • reduce(LineageTable) -- see reduce -- produce a reduced Gr\"obner basis from one computed by threaded Gr\"obner bases
  • tgb -- threaded Gr\"obner bases
  • tgb(List) -- see tgb -- threaded Gr\"obner bases

Methods that use an object of class LineageTable:

  • matrix(LineageTable) -- extract a matrix of polynomials from values of a LineageTable after deleting null values

For the programmer

The object LineageTable is a type, with ancestor classes HashTable < Thing.

The source of this document is in ThreadedGB.m2:482:0.