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Packages » SubalgebraBases :: forceSB(SAGBIBasis)
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forceSB(SAGBIBasis) -- declare the generators to be a complete subalgebra basis



When forceSB is called on a SAGBIBasis $SB$, the function performs autosubduction on the subalgebra generators of $SB$. 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 the subring generators.

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 = sagbi({x+y,x*y,x*y^2},Limit=>10)

o2 = Partial SAGBIBasis Computation Object with 10 generators, Limit = 10.

o2 : SAGBIBasis
i3 : forceSB S;
i4 : isSAGBI S

o4 = false
i5 : sagbi(S,Recompute=>true)

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

o5 : SAGBIBasis
i6 : isSAGBI S

o6 = false

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.

See also

Ways to use this method: