Package sagbi/SB.IsInSubalgebra SAGBI
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| This article is about a function from ApCoCoA-2. |
SB.IsInSubalgebra_SAGBI
Tests whether a polynomial is in a standard-graded subalgebra using SAGBI bases.
Syntax
SB.IsInSubalgebra_SAGBI(f:POLY, G:LIST of POLY):BOOL
Description
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.
Example
Use QQ[x[1..2]]; G := [x[1]-x[2], x[1]*x[2]-x[2]^2, x[1]*x[2]^2]; SB.IsInSubalgebra_SAGBI(x[1]*x[2]^4-x[2]^5, G); ----------------------------------------------------------------------------- true
Example
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_SAGBI(y[3]^4, G); ----------------------------------------------------------------------------- false
