Package sagbi/SB.IsInSubalgebra

From ApCoCoAWiki
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 subalgebra.


SB.IsInSubalgebra(f:POLY, G:LIST of POLY):BOOL


This function takes a polynomials f and a list of polynomials G and checks whether F is in the algebra generated by the polynomials in G.

  • @param f A polynomial.

  • @param G A list of 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[1]-x[2], x[1]*x[2]-x[2]^2, x[1]*x[2]^2];
SB.IsInSubalgebra(x[1]*x[2]^4-x[2]^5, G);
-- true


Use QQ[y[1..3]];
G := [y[1]^2-y[3]^2, y[1]*y[2]+y[3]^2, y[2]^2-2*y[3]^2];
SB.IsInSubalgebra(y[3]^4, G);
-- false

See also

Package sagbi/SB.IsInSubalgebra_SAGBI

Package sagbi/SB.IsInSA

Package sagbi/SB.IsInSA_SAGBI

Package sagbi/SB.IsInToricRing