isSAGBI(Subring) -- Check if the generators are a subalgebra basis

Synopsis

• Function: isSAGBI

• Usage:

  result = isSAGBI S

• Inputs:
  • S, a subring,
• Optional inputs:
  • Compute => a Boolean value, default value true, a flag indicating whether to perform computation.
  • Recompute => a Boolean value, default value false, if true then cached results are ignored and a computation is performed to verify if the generators are a subalgebra basis.
  • 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".
  • SubductionMethod => a string, default value "Top", the method used for subduction either: "Top" or "Engine".
  • PrintLevel => an integer, default value 0, 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)
  • 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.
  • ModifySAGBIBasis => a Boolean value, default value true, a flag indicating whether to replace the partial subalgebra basis cached in the subring.
• Outputs:
  • result, a Boolean value, if true, then the generators or subalgebra generators form a subalgebra basis.

Description

i1 : R = QQ[x,y,z];

i2 : S = subring {x+y+z,x*y+x*z+y*z, x*y*z, (x-y)*(x-z)*(y-z)};

i3 : isSAGBI S

o3 = false

i4 : S' = subring {x+y+z,x*y+x*z+y*z, x*y*z};

i5 : isSAGBI S'

o5 = true

See also

• isSAGBI -- Check if the generators are a subalgebra basis
• isSAGBI(SAGBIBasis) -- Check if the generators are a subalgebra basis
• Subring -- The type of all subrings
• sagbi -- Compute a subalgebra basis (sagbi basis)
• Compute -- Flag for performing computations while checking the completeness of a subalgebra basis
• Recompute -- Flag for restarting a sagbi or isSAGBI computation
• Subduction strategies -- Update procedure for the Sagbi algorithm
• SubductionMethod -- Subduction method for the Sagbi algorithm
• PrintLevel -- Levels of information displayed during Sagbi algorithm
• RenewOptions -- Flag for reselecting the options for a subalgebra bases computation
• UseSubringGens -- Flag for using the subring generators when checking a subalgebra basis
• ModifySAGBIBasis -- Flag for allowing the cached computation object to be modified