Singular Manual: dyckGroup1

| #### 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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