Package sagbi/SB.IsInSubalgebra SAGBI

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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