Singular Manual: crystallographicGroupP6

| #### 7.10.2.21 crystallographicGroupP6 Procedure from library `fpalgebras.lib` (see fpalgebras_lib). Usage: crystallographicGroupP6(d); d an integer Return: ring Note: - the ring contains the ideal I, which contains the required relations - p6 group with the following presentation < x, y, r | [x, y] = r^6 = 1, r^(-1)*x*r = y, r^(-1)*y*r = x^(-1)*y> - d gives the degreebound for the Letterplace ring Example:
    LIB "fpalgebras.lib";
    def R = crystallographicGroupP6(7); setring R;
    I;
    ==> I[1]=y*x+x*y+1
    ==> I[2]=r*r*r*r*r*r+y*x+x*y
    ==> I[3]=r*r*r*r*r*r+1
    ==> I[4]=r*r*r*r*r*x*r+y
    ==> I[5]=r*r*r*r*r*y*r+X*y
    ==> I[6]=X*x+1
    ==> I[7]=x*X+1
    ==> I[8]=Y*y+1
    ==> I[9]=y*Y+1

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