forceSB(Subring) -- declare the generators to be a complete subalgebra basis

Synopsis

Function: forceSB
Usage:

forceSB S
Inputs:
- S, a subring,
Optional inputs:
- AutoSubduce => a Boolean value, default value true, a flag indicating whether to autosubduce the generators of $S$.
- Limit => an integer, default value 20, a degree limit for the binomial S-pairs that are computed internally.
- PrintLevel => an integer, default value 0, indicating how much additional information should be printed. When this is greater than zero, information is printed about the progress of the computation.
- RenewOptions => a Boolean value, default value false, if true then 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)
- Strategy => a string, default value "Master", the update strategy used for updating the SAGBIBasis: "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".
- UseSubringGens => a Boolean value, default value true, a flag indicating whether to use the generators of the subring. If false then the method uses the subalgebra generators of the partial subalgebra basis.
- SubductionMethod => a string, default value "Engine", the name of the method used for subduction either: "Top" or "Engine".

Description

When forceSB is called on a subring $S$, the function performs autosubduction on the generators of $S$. The completion flag is then set to complete without checking whether the generators form a subalgebra basis.

The option UseSubringGens can be toggled between true and false to operate on any partial subalgebra basis created for $S$.

If the generators supplied to forceSB do not form a subalgebra basis, then the resulting behavior may be unexpected.

i1 : R = QQ[x,y];

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

o2 = QQ[p_0..p_2], subring of R

o2 : Subring

i3 : forceSB S;

i4 : isSAGBI S

o4 = true

i5 : sagbi(S,Recompute=>true)

o5 = Partial SAGBIBasis Computation Object with 20 generators, Limit = 20.

o5 : SAGBIBasis

i6 : isSAGBI S

o6 = true

In this example, forceSB causes isSAGBI to return true even though the generators of $S$ do not form a subalgebra basis. Recomputing the subalgebra basis exposes that the generators do not form a subalgebra basis.

Ways to use this method: