Singular Manual: lpGkDim

| #### 7.10.3.4 lpGkDim Procedure from library `fpaprops.lib` (see fpaprops_lib). Usage: lpGkDim(G); G an ideal in a letterplace ring Return: int Purpose: Determines the Gelfand Kirillov dimension of A/<G> -1 means positive infinite Assume: - basering is a Letterplace ring - G is a Groebner basis Note: Alias for dim(G) Example:
    LIB "fpaprops.lib";
    ring r = 0,(x,y,z),dp;
    ring R = freeAlgebra(r, 5);
    ideal I = z; // infinite GK dimension (-1)
    lpGkDim(I);
    ==> WARNING: `lpGkDim` is deprecated, you can use `dim` instead.
    ==> -1
    I = x,y,z; I = std(I); // GK dimension 0
    lpGkDim(I);
    ==> WARNING: `lpGkDim` is deprecated, you can use `dim` instead.
    ==> 0
    I = x*y, x*z, z*y, z*z; I = std(I); // GK dimension 2
    lpGkDim(I);
    ==> WARNING: `lpGkDim` is deprecated, you can use `dim` instead.
    ==> 2
    ideal G = y*x - x*y, z*x - x*z, z*y - y*z; G = std(G);
    G;
    ==> G[1]=z*y-y*z
    ==> G[2]=z*x-x*z
    ==> G[3]=y*x-x*y
    lpGkDim(G); // GK dimension 3
    ==> WARNING: `lpGkDim` is deprecated, you can use `dim` instead.
    ==> 3

User manual for Singular version 4.4.1, 2025, generated by texi2html.