Singular Manual: lpGkDim

| ##### 7.7.8.0. 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 it is positive infinite Assume: - basering is a Letterplace ring - G is a Groebner basis Example:
    LIB "fpaprops.lib";
    ring r = 0,(x,y,z),dp;
    def R = makeLetterplaceRing(5); // constructs a Letterplace ring
    R;
    ==> // coefficients: QQ
    ==> // number of vars : 15
    ==> //        block   1 : ordering a
    ==> //                  : names    x(1) y(1) z(1) x(2) y(2) z(2) x(3) y(3) z(\
       3) x(4) y(4) z(4) x(5) y(5) z(5)
    ==> //                  : weights     1    1    1    1    1    1    1    1   \
        1    1    1    1    1    1    1
    ==> //        block   2 : ordering dp
    ==> //                  : names    x(1) y(1) z(1)
    ==> //        block   3 : ordering dp
    ==> //                  : names    x(2) y(2) z(2)
    ==> //        block   4 : ordering dp
    ==> //                  : names    x(3) y(3) z(3)
    ==> //        block   5 : ordering dp
    ==> //                  : names    x(4) y(4) z(4)
    ==> //        block   6 : ordering dp
    ==> //                  : names    x(5) y(5) z(5)
    ==> //        block   7 : ordering C
    setring R; // sets basering to Letterplace ring
    ideal I = z(1);//an example of infinite GK dimension
    lpGkDim(I);
    ==> -1
    I = x(1),y(1),z(1); // gkDim = 0
    lpGkDim(I);
    ==> 0
    I = x(1)*y(2), x(1)*z(2), z(1)*y(2), z(1)*z(2);//gkDim = 2
    lpGkDim(I);
    ==> 2

User manual for Singular version 4-1-1, 2018, generated by texi2html.