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Revision as of 14:10, 3 October 2020
This article is about a function from ApCoCoA2. If you are looking for the ApCoCoA1 version of it, see ApCoCoA:SB.Sagbi. 
SB.SAGBI
Computes a finite SAGBIbasis of a subalgebra if existing.
Syntax
SB.SAGBI(G:LIST of POLY):LIST of POLY
Description
This function computes a finite SAGBIbasis of a subalgebra S generated by the polynomials of the list G, if a finite SAGBIbasis of S is existing. Then a list of polynomials is returned which form a SAGBIbasis of S. Otherwise the computation runs until it is interrupted.
@param G A list of polynomials which generates a subalgebra.
@return A list of polynomials which form a finite SAGBIbasis of the subalgebra generated by G.
Example
Use QQ[x[1..3]]; S := SB.SAGBI([x[1]^2x[3]^2,x[1]*x[2]+x[3]^2,x[2]^22*x[3]^2]); indent(S);  [ x[2]^2 2*x[3]^2, x[1]*x[2] +x[3]^2, x[1]^2 x[3]^2, x[1]^2*x[3]^2 +x[1]*x[2]*x[3]^2 +(1/2)*x[2]^2*x[3]^2 +(1/2)*x[3]^4 ]