Singular Manual: crystallographicGroupP4MM

| #### 7.7.2.16 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*y+y*x+1
    ==> I[2]=r*r*r*r+x*y+y*x
    ==> I[3]=r*r*r*r+1
    ==> I[4]=r*r*r*x*r+X
    ==> I[5]=r*r*r*x*r+y
    ==> I[6]=X*x+1
    ==> I[7]=x*X+1
    ==> I[8]=Y*y+1
    ==> I[9]=y*Y+1

User manual for Singular version 4-1-1p4, 2018, generated by texi2html.