sagbiBasis -- Constructs a computation object from a subring.

• Usage:

  B = sagbiBasis S

• Inputs:
  • S, a subring,
• Optional inputs:
  • AutoSubduce => a Boolean value, default value true, a flag indicating when to perform autosubduction on the generators before performing the subalgebra basis computation
  • ReduceNewGenerators => a Boolean value, default value true, a flag indicating whether to reduce (via Gaussian elimination) to new subalgebra generators before adding them to the current subalgebra basis
  • StorePending => a Boolean value, default value true, a flag that indicates whether the pending list should be stored in the result.
  • Strategy => a string, default value "Master", the name of the update strategy at the beginning of each loop: "DegreeByDegree", "Incremental", and "Master". The strategy "Master" is a hybrid method that combines the other two; starting with "DegreeByDegree" for low degrees and switching to "Incremental".
  • SubductionMethod => a string, default value "Top", the name of the method used for subduction either: "Top" or "Engine".
  • Limit => an integer, default value 20, a degree limit for the binomial S-pairs that are computed internally.
  • AutoSubduceOnPartialCompletion => a Boolean value, default value false, a flag that indicates whether autosubduction is applied to the subalgebra generators the first time no new generators are added. Use this only if very few new subalgebra generators are expected.
  • PrintLevel => an integer, default value 0, an option to produce additional output. When this is greater than zero, information is printed about the progress of the computation
  • Recompute => a Boolean value, default value false, a flag that indicates if the computation will resume in subsequent runs, otherwise it starts at the beginning
  • RenewOptions => a Boolean value, default value false, a flag that indicates if the computation will use the options specified, otherwise it will use the previously selected options (except for the following, which may always be specified: PrintLevel, Limit, Recompute, and RenewOptions)
• Outputs:
  • B, a SAGBIBasis, a computation object associated to S

i1 : R = QQ[x,y];

i2 : S = subring{x+y,x*y,x*y^2};

i3 : T = sagbiBasis S

o3 = Partial SAGBIBasis Computation Object with 0 generators, Limit = -1.

o3 : SAGBIBasis

i4 : sagbi(T,Limit=>20)

o4 = Partial SAGBIBasis Computation Object with 20 generators, Limit = 20.

o4 : SAGBIBasis

i5 : subring T

o5 = QQ[p_0..p_2], subring of R

o5 : Subring