Singular Manual: crystallographicGroupPG

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

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