Package sagbi/SB.IsInSubalgebra SAGBI
From ApCoCoAWiki
< Package sagbi
Revision as of 10:51, 27 September 2020 by Andraschko (talk | contribs) (Created page with "{| cellspacing="8" cellpadding="0" style="background-color:#eeeeff; width:100%; font-size:95%; border-bottom: 2px solid blue; border-top: 2px solid blue; position:top; clear:b...")
| This article is about a function in ApCoCoA-2.0. |
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
