Difference between revisions of "Package sagbi/SB.SAGBI"
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| + | | This article is about the function in [[ApCoCoA:Downloads#ApCoCoA-2.0 Beta|ApCoCoA-2.0]]. If you are looking for the [[ApCoCoA:What is ApCoCoA|ApCoCoA-1.0]] version of it, see [[ApCoCoA:SB.Sagbi]]. | ||
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<title>SB.SAGBI</title> | <title>SB.SAGBI</title> | ||
Revision as of 09:44, 27 September 2020
| This article is about the function in ApCoCoA-2.0. If you are looking for the ApCoCoA-1.0 version of it, see ApCoCoA:SB.Sagbi. |
SB.SAGBI
Computes a finite SAGBI-basis of a subalgebra if existing.
Syntax
SB.SAGBI(G:LIST of POLY):LIST of POLY
Description
This function computes a finite SAGBI-basis of a subalgebra S generated by the polynomials of the list G, if a finite SAGBI-basis of S is existing. Then a list of polynomials is returned which form a SAGBI-basis 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 SAGBI-basis of the subalgebra generated by G.
Example
Use QQ[x[1..3]]; S := SB.SAGBI([x[1]^2-x[3]^2,x[1]*x[2]+x[3]^2,x[2]^2-2*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 ]
