Singular Manual: crystallographicGroupP2MM

| ##### 7.7.8.0. crystallographicGroupP2MM Procedure from library `fpalgebras.lib` (see fpalgebras_lib). Usage: crystallographicGroupP2MM(d); d an integer Return: ring Note: - the ring contains the ideal I, which contains the required relations - p2mm group with the following presentation < x, y, p, q | [x, y] = [p, q] = p^2 = q^2 = 1, p^-1*x*p = x, q^-1*x*q = x^-1, p^-1*y*p = y^-1, q^-1*y*q = y > - d gives the degreebound for the Letterplace ring Example:
    LIB "fpalgebras.lib";
    def R = crystallographicGroupP2MM(5); setring R;
    I;
    ==> I[1]=x(1)*y(2)+y(1)*x(2)+1
    ==> I[2]=p(1)*q(2)+q(1)*p(2)+1
    ==> I[3]=p(1)*p(2)+1
    ==> I[4]=q(1)*q(2)+1
    ==> I[5]=p(1)*y(2)*p(3)+Y(1)
    ==> I[6]=p(1)*x(2)*p(3)+x(1)
    ==> I[7]=q(1)*y(2)*q(3)+y(1)
    ==> I[8]=q(1)*x(2)*q(3)+X(1)
    ==> I[9]=X(1)*x(2)+1
    ==> I[10]=x(1)*X(2)+1
    ==> I[11]=Y(1)*y(2)+1
    ==> I[12]=y(1)*Y(2)+1
    ==> I[13]=x(1)*y(2)+y(1)*x(2)+p(1)*p(2)
    ==> I[14]=x(1)*y(2)+y(1)*x(2)+q(1)*q(2)
    ==> I[15]=p(1)*p(2)+q(1)*q(2)

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