Package invarFC0/InvFC0.SAGBI

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This article is about a function from ApCoCoA-2.

InvFC0.SAGBI

This function computes a SAGBI basis of an invariant ring.

Syntax

InvFC0.SAGBI(G:LIST of MAT, opt d:INT):LIST of POLY

Description

This function computes a (d-truncated) SAGBI basis of the invariant ring P^G.

WARNING: May not terminate if P^G does not have a finite SAGBI basis.

  • @param G A list of matrices of size n over a ring P with n indeterminates.

  • @param d (optional) An integer describing the truncation degree.

  • @return A list of polynomials that form a (d-truncated) SAGBI basis.

Example

Use P ::= QQ[x,y,z];
T := matrix(P, [[0,1,0],
                [1,0,0],
                [0,0,1]]);
C := matrix(P, [[0,1,0],
                [0,0,1],
                [1,0,0]]);
S3 := [T*T,T,C,T*C,T*C*C,T*C*T];
InvFC0.SAGBI(S3);

Example

A := Mat(P, [[0,1,0],
             [0,0,1],
             [1,0,0]]);
G := [A,A^2,A^3]; // cyclic group generated by A
TruncG := InvFC0.SAGBI(G,7); // has no finite DegRevLex-SAGBI basis

See also

Package invarFC0

Package invarFC0/InvFC0.MinGens