Package sagbi/SB.IsInSubalgebra SAGBI
|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.|
Tests whether a polynomial is in a standard-graded subalgebra using SAGBI bases.
SB.IsInSubalgebra_SAGBI(f:POLY, G:LIST of POLY):BOOL
This function takes a polynomials f and a list of homogeneous polynomials G and checks whether F is in the algebra generated by the polynomials in G using truncated SAGBI bases.
@param f A polynomial.
@param G A list of homogeneous polynomials which generate a subalgebra.
@return true if f is in the subalgebra generated by G, false elsewise.
Use QQ[x[1..2]]; G := [x-x, x*x-x^2, x*x^2]; SB.IsInSubalgebra_SAGBI(x*x^4-x^5, G); -- true
Use QQ[y[1..3]]; G := [y^2-y^2, y*y+y^2, y^2-2*y^2]; SB.IsInSubalgebra_SAGBI(y^4, G); -- false