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SubalgebraBases :: isSAGBI

isSAGBI -- Check if the generators are a sagbi basis

Synopsis

Description

After running sagbi on a subring, the result of the computation is stored in that subring. If new sagbi generators need to be added to S to make it a sagbi basis then isSAGBI will return false. If isSAGBI is run on a ring for which no sagbi computation has been peformed, then isSAGBI will return null. In this case it is recommended to use verifySagbi to check whether the generators are a sagbi basis.

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
i4 : sagbi(S, Limit => 5)

o4 = Partial SAGBIBasis Computation Object with 6 generators, Limit = 5.

o4 : SAGBIBasis
i5 : isSAGBI S

o5 = false
i6 : S' = subring {x+y+z,x*y+x*z+y*z, x*y*z};
i7 : isSAGBI S'
i8 : sagbi(S', Limit => 5)

o8 = SAGBIBasis Computation Object with 3 generators, Limit = 5.

o8 : SAGBIBasis
i9 : isSAGBI S'

o9 = true

See also

Ways to use isSAGBI :

For the programmer

The object isSAGBI is a method function.