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isSAGBI -- Check if the generators are a subalgebra basis

Synopsis

Description

Checks whether the generators of a subring or the subalgebra generators of a SAGBIBasis form a subalgebra basis. If isSAGBI is supplied a matrix or a list A, then the command isSAGBI A is equivalent to isSAGBI subring A. For further details of their respective uses see isSAGBI(Subring) and isSAGBI(SAGBIBasis).

The result of isSagbi is stored in the cache of a subring or the sagbiStatus of a SAGBIBasis. If isSagbi is called again, then the result is looked up, unless the option Recompute is set to true.

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 : isSAGBI sagbi(S, Limit => 5)

o4 = false
 
i5 : S' = subring {x+y,x*y,x*y^2,x*y^4-y};
 
i6 : isSAGBI S'

o6 = false
 
i7 : isSAGBI sagbi(S', Limit => 10)

o7 = true

If isSAGBI is supplied a SAGBIBasis, then the generators of its subring can be checked for being a subalgebra basis by setting UseSubringGens to true. If isSAGBI is supplied a subring, then the generators of a partial subalgebra basis can be checked for being a subalgebra basis by setting UseSubringGens to false.

Optional inputs for specific uses (see isSAGBI(Subring) and isSAGBI(SAGBIBasis)) include the following: Compute, Recompute, Subduction strategies, SubductionMethod, PrintLevel, RenewOptions, UseSubringGens, and ModifySAGBIBasis.

See also

Ways to use isSAGBI:

For the programmer

The object isSAGBI is a method function with options.