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subduction -- Subduction against a set elements



Performs subduction on the input with respect to the generating set of the supplied object. The result of subduction of $f$ by $S$ is an element $g$ such that $f-g$ is in $S$. If the generating set is not a subalgebra basis, then the result of subduction may not be a normal form for the input.

i1 : R = QQ[x,y];
i2 : S = subring {x+y, x*y, x*y^2};
i3 : f = x^4;
i4 : subduction(S, f)

           3    4
o4 = - 2x*y  - y

o4 : R
i5 : sagbi S;
i6 : subduction(gens sagbi S, f)

o6 = -y

o6 : R

See also

Ways to use subduction :

For the programmer

The object subduction is a method function with options.