Package sagbi/SB.IsInSA SAGBI

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This article is about a function from ApCoCoA-2. If you are looking for the ApCoCoA-1 version of it, see ApCoCoA-1:SB.IsInSubalgebra.


This function tests whether a polynomial is in a given standard-graded subalgebra.


SB.IsInSA(f: RINGELEM,ref S: TAGGED("$apcocoa/sagbi.Subalgebra")): BOOL


This function takes a polynomial f and a subalgebra S and tests whether f is an element of S using truncated SAGBI bases.

  • @param f A polynomial

  • @param S A standard-graded subalgebra, i.e. of type TAGGED("$apcocoa/sagbi.Subalgebra") and the generators of f are homogeneous polynomials with respect to the standard grading.

  • @return true if f is an element of S and false if not.


Use R ::= QQ[x,y,z];
S := SB.Subalgebra(R,[x^2,y+z]);
f := x^4 +2*x^3*y +x^2*y^2 +x^2 +2*x*y +y^2;
SB.IsInSA_SAGBI(f,ref S); -- true

See also

Package sagbi/SB.Subalgebra

Package sagbi/SB.IsInSA

Package sagbi/SB.IsInSubalgebra

Package sagbi/SB.IsInSubalgebra_SAGBI

Package sagbi/SB.IsInToricRing