Singular Manual: crystallographicGroupP6MM

| #### 7.7.2.22 crystallographicGroupP6MM Procedure from library `fpalgebras.lib` (see fpalgebras_lib). Usage: crystallographicGroupP6MM(d); d an integer Return: ring Note: - the ring contains the ideal I, which contains the required relations - p6mm group with the following presentation < x, y, r, m | [x, y] = r^6 = m^2 = 1, r^(-1)*y*r = x^(-1)*y, r^(-1)*x*r = y, m^(-1)*x*m = x^(-1), m^(-1)*y*m = x^(-1)*y, m^(-1)*r*m = r^(-1)*y> - d gives the degreebound for the Letterplace ring Example:
    LIB "fpalgebras.lib";
    def R = crystallographicGroupP6MM(7); setring R;
    I;
    ==> I[1]=x*y+y*x+1
    ==> I[2]=r*r*r*r*r*r+x*y+y*x
    ==> I[3]=r*r*r*r*r*r+1
    ==> I[4]=x*y+y*x+m*m
    ==> I[5]=r*r*r*r*r*r+m*m
    ==> I[6]=m*m+1
    ==> I[7]=m*x*m+X
    ==> I[8]=m*y*m+X*y
    ==> I[9]=r*r*r*r*r*x*r+y
    ==> I[10]=r*r*r*r*r*y*r+X*y
    ==> I[11]=r*r*r*r*r*y+m*r*m
    ==> I[12]=X*x+1
    ==> I[13]=x*X+1
    ==> I[14]=Y*y+1
    ==> I[15]=y*Y+1

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