Singular Manual: crystallographicGroupP2

| ##### 7.7.8.0. crystallographicGroupP2 Procedure from library `fpalgebras.lib` (see fpalgebras_lib). Usage: crystallographicGroupP2(d); d an integer Return: ring Note: - the ring contains the ideal I, which contains the required relations - p2 group with the following presentation < x, y, m, t | [x, y] = t^2 = 1, m^2 = y, t^-1*x*t = x, m^-1*x*m = x^-1, t^-1*y*t = y^-1, t^-1*m*t = m^-1 > - d gives the degreebound for the Letterplace ring Example:
    LIB "fpalgebras.lib";
    def R = crystallographicGroupP2(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)+t(1)*t(2)
    ==> I[3]=m(1)*m(2)+y(1)
    ==> I[4]=t(1)*t(2)+1
    ==> I[5]=t(1)*x(2)*t(3)+x(1)
    ==> I[6]=M(1)*x(2)*m(3)+X(1)
    ==> I[7]=t(1)*y(2)*t(3)+Y(1)
    ==> I[8]=t(1)*m(2)*t(3)+M(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]=m(1)*M(2)+1
    ==> I[14]=M(1)*m(2)+1

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