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



Checks whether the generators of a subring $S$ form a subalgebra basis. The result of the computation is stored in the cache of the ring. Subsequent calls to isSAGBI on $S$ with the same options will look up the cached result unless the option Recompute is set to true. If the option Compute is set to false then isSAGBI attempts to find a previously cached result. If isSAGBI cannot determine a result without computation and the option Compute is set to false, then isSAGBI returns null.

If the generators of $S$ form a subalgebra basis, then the subalgebra generators of the cached partial subalgebra basis are updated to match the ring generators, unless the option ModifySAGBIBasis is set to false. If the option UseSubringGens is set to false, then the generators of a partial subalgebra basis are used instead of the generators of the subring.

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

The options Subduction strategies, SubductionMethod, PrintLevel, and RenewOptions are only used when performing a subalgebra bases computation.

See also

Ways to use this method: