Singular Manual: crystallographicGroupC2MM

| ##### 7.7.8.0. crystallographicGroupC2MM Procedure from library `fpalgebras.lib` (see fpalgebras_lib). Usage: crystallographicGroupC2MM(d); d an integer Return: ring Note: - the ring contains the ideal I, which contains the required relations - c2mm group with the following presentation < x, y, m, r | [x, y] = m^2 = r^2 = 1, m^-1*y*m = y^-1, m^-1*x*m = x*y, r^-1*y*r = y^-1, r^-1*x*r = x^-1, m^-1*r*m = r^-1 > - d gives the degreebound for the Letterplace ring Example:
    LIB "fpalgebras.lib";
    def R = crystallographicGroupC2MM(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]=x(1)*y(2)+y(1)*x(2)+r(1)*r(2)
    ==> I[4]=m(1)*m(2)+1
    ==> I[5]=r(1)*r(2)+1
    ==> I[6]=m(1)*m(2)+r(1)*r(2)
    ==> I[7]=m(1)*y(2)*m(3)+Y(1)
    ==> I[8]=m(1)*x(2)*m(3)+x(1)*y(2)
    ==> I[9]=y(2)*r(3)+Y(1)
    ==> I[10]=r(1)*x(2)*r(3)+X(1)
    ==> I[11]=m(1)*r(2)*m(3)+r(1)
    ==> I[12]=X(1)*x(2)+1
    ==> I[13]=x(1)*X(2)+1
    ==> I[14]=Y(1)*y(2)+1
    ==> I[15]=y(1)*Y(2)+1

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