Singular Manual: crystallographicGroupPM

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