Singular Manual: crystallographicGroupP3

| ##### 7.7.8.0. crystallographicGroupP3 Procedure from library `fpalgebras.lib` (see fpalgebras_lib). Usage: crystallographicGroupP3(d); d an integer Return: ring Note: - the ring contains the ideal I, which contains the required relations - p3 group with the following presentation < x, y, r | [x, y] = r^3 = 1, r^-1*x*r = x^-1*y, r^-1*y*r = x^-1> - d gives the degreebound for the Letterplace ring Example:
    LIB "fpalgebras.lib";
    def R = crystallographicGroupP3(5); setring R;
    I;
    ==> I[1]=x(1)*y(2)+y(1)*x(2)+1
    ==> I[2]=r(1)*r(2)*r(3)+x(1)*y(2)+y(1)*x(2)
    ==> I[3]=r(1)*r(2)*r(3)+1
    ==> I[4]=r(1)*r(2)*x(3)*r(4)+X(1)*y(2)
    ==> I[5]=r(1)*r(2)*y(3)*r(4)+X(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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