Singular Manual: crystallographicGroupCM

| ##### 7.7.8.0. crystallographicGroupCM Procedure from library `fpalgebras.lib` (see fpalgebras_lib). Usage: crystallographicGroupCM(d); d an integer Return: ring Note: - the ring contains the ideal I, which contains the required relations - cm group with the following presentation < x, y, t | [x, y] = t^2 = 1, t^-1*x*t = x*y, t^-1*y*t = y^-1 > - d gives the degreebound for the Letterplace ring Example:
    LIB "fpalgebras.lib";
    def R = crystallographicGroupCM(5); setring R;
    I;
    ==> I[1]=x(1)*y(2)+y(1)*x(2)+1
    ==> I[2]=x(1)*y(2)+y(1)*x(2)+t(1)*t(2)
    ==> I[3]=t(1)*t(2)+1
    ==> I[4]=t(1)*x(2)*t(3)+x(1)*y(2)
    ==> I[5]=t(1)*y(2)*t(3)+Y(1)
    ==> I[6]=X(1)*x(2)+1
    ==> I[7]=x(1)*X(2)+1
    ==> I[8]=Y(1)*y(2)+1
    ==> I[9]=y(1)*Y(2)+1

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