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SAGBIBasis -- The type of all subalgebra bases

Description

A computation object for subalgebra bases. It stores a partial subalgebra bases computation for picking up a computation where it left off. For many uses, it is superior to use a subring, as the computation SAGBIBases are handled behind the scenes, and the user experience is more streamlined. To create a SAGBIBasis, use the function sagbiBasis. The SAGBIBasis type is the main output type of the function sagbi. Applying subring to a SAGBIBasis returns the original subring that generated the SAGBIBasis.

See also

Functions and methods returning a SAGBIBasis:

  • sagbi -- Compute a subalgebra basis (sagbi basis)
  • sagbiBasis -- Constructs a computation object from a subring.

Methods that use a SAGBIBasis:

  • ambient(SAGBIBasis) -- The ambient ring of a SAGBIBasis computation object
  • flattenedRing(SAGBIBasis) -- see flattenedRing -- The flattened ring of a subring or sagbiBasis
  • forceSB(SAGBIBasis) -- declare the generators to be a complete subalgebra basis
  • generators(SAGBIBasis) -- Returns generators of a SAGBIBasis computation object
  • isSAGBI(SAGBIBasis) -- Check if the generators are a subalgebra basis
  • net(SAGBIBasis) -- Short summary of a subalgebra basis computation object
  • numgens(SAGBIBasis) -- The number of generators of a SAGBIBasis
  • Matrix % SAGBIBasis -- see Reduction in subrings -- Remainder modulo a subring
  • RingElement % SAGBIBasis -- see Reduction in subrings -- Remainder modulo a subring
  • ring(SAGBIBasis) -- The lifted ring of a SAGBIBasis computation object
  • sagbi(SAGBIBasis) -- see sagbi -- Compute a subalgebra basis (sagbi basis)
  • sagbiDegree(SAGBIBasis) -- see sagbiDegree -- The current degree of the subalgebra bases computation
  • sagbiLimit(SAGBIBasis) -- see sagbiLimit -- The current limit of the subalgebra bases computation
  • sagbiStatus(SAGBIBasis) -- see sagbiStatus -- checks if the subalgebra bases computation is done
  • status(SAGBIBasis) -- status of the subalgebra bases computation
  • subduction(SAGBIBasis,Matrix) -- see subduction -- Subduction against a set elements
  • subduction(SAGBIBasis,RingElement) -- see subduction -- Subduction against a set elements
  • subring(SAGBIBasis) -- see subring -- Constructs a subring of a polynomial ring.

For the programmer

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

The source of this document is in SubalgebraBases/documentation.m2:1859:0.