Singular Manual: crystallographicGroupP2GG

| ##### 7.7.8.0. crystallographicGroupP2GG Procedure from library `fpalgebras.lib` (see fpalgebras_lib). Usage: crystallographicGroupP2GG(d); d an integer Return: ring Note: - the ring contains the ideal I, which contains the required relations - p2gg group with the following presentation < x, y, u, v | [x, y] = (u*v)^2 = 1, u^2 = x, v^2 = y, v^-1*x*v = x^-1, u^-1*y*u = y^-1 > - d gives the degreebound for the Letterplace ring Example:
    LIB "fpalgebras.lib";
    def R = crystallographicGroupP2GG(5); setring R;
    I;
    ==> I[1]=x(1)*y(2)+y(1)*x(2)+1
    ==> I[2]=u(1)*v(2)*u(3)*v(4)+x(1)*y(2)+y(1)*x(2)
    ==> I[3]=u(1)*v(2)*u(3)*v(4)+1
    ==> I[4]=u(1)*u(2)+x(1)
    ==> I[5]=v(1)*v(2)+y(1)
    ==> I[6]=V(1)*x(2)*v(3)+X(1)
    ==> I[7]=U(1)*y(2)*u(3)+Y(1)
    ==> I[8]=X(1)*x(2)+1
    ==> I[9]=x(1)*X(2)+1
    ==> I[10]=Y(1)*y(2)+1
    ==> I[11]=y(1)*Y(2)+1
    ==> I[12]=u(1)*U(2)+1
    ==> I[13]=U(1)*u(2)+1
    ==> I[14]=v(1)*V(2)+1
    ==> I[15]=V(1)*v(2)+1

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