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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
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