Home Online Manual
Top
Back: crystallographicGroupP6MM
Forward: dyckGroup2
FastBack:
FastForward:
Up: fpalgebras_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

7.10.2.23 dyckGroup1

Procedure from library fpalgebras.lib (see fpalgebras_lib).

Usage:
dyckGroup1(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 - x_(i+1)^p_(i+1)
- d gives the degreebound for the Letterplace ring
- varying n and P produces a family of examples

Example:
 
LIB "fpalgebras.lib";
intvec P = 1,2,3;
def R = dyckGroup1(3,5,P); setring R;
I;
==> I[1]=x(2)*x(2)+x(1)
==> I[2]=x(3)*x(3)*x(3)+x(2)*x(2)
==> I[3]=x(1)*x(2)*x(3)+x(3)*x(3)*x(3)
==> I[4]=x(1)*x(2)*x(3)+1