Singular

7.10.2.24 dyckGroup2

Usage:

dyckGroup2(n,d,P); n an integer, d an integer, P an intvec

Return:

ring

Note:

- the ring contains the ideal I, which contains the required relations - The Dyck group with the following presentation
< x_1, x_2, ... , x_n | (x_1)^p1 = (x_2)^p2 = ... = (x_n)^pn = x_1 * x_2 * ... * x_n = 1 > - negative exponents are allowed
- representation in the form x_i^p_i - 1
- d gives the degreebound for the Letterplace ring
- varying n and P produces a family of examples

LIB "fpalgebras.lib";
intvec P = 1,2,3;
def R = dyckGroup2(3,5,P); setring R;
I;
==> I[1]=x(1)+1
==> I[2]=x(2)*x(2)+1
==> I[3]=x(3)*x(3)*x(3)+1
==> I[4]=x(1)*x(2)*x(3)+1