Singular Manual: crystallographicGroupP4MM

| ##### 7.7.8.0. crystallographicGroupP4MM Procedure from library `fpalgebras.lib` (see fpalgebras_lib). Usage: crystallographicGroupP4MM(d); d an integer Return: ring Note: - the ring contains the ideal I, which contains the required relations - p4mm group with the following presentation < x, y, r, m | [x, y] = r^4 = m^2 = 1, r^-1*y*r = x^-1, r^-1*x*r = y, m^-1*x*m = y, m^-1*r*m = r^-1 > - d gives the degreebound for the Letterplace ring Example:
    LIB "fpalgebras.lib";
    def R = crystallographicGroupP4MM(5); setring R;
    I;
    ==> I[1]=x(1)*y(2)+y(1)*x(2)+1
    ==> I[2]=r(1)*r(2)*r(3)*r(4)+x(1)*y(2)+y(1)*x(2)
    ==> I[3]=r(1)*r(2)*r(3)*r(4)+1
    ==> I[4]=r(1)*r(2)*r(3)*x(4)*r(5)+X(1)
    ==> I[5]=r(1)*r(2)*r(3)*x(4)*r(5)+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

User manual for Singular version 4-1-1p3, 2018, generated by texi2html.