Singular

7.10.2.10 crystallographicGroupP2MM

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

LIB "fpalgebras.lib";
def R = crystallographicGroupP2MM(5); setring R;
I;
==> I[1]=y*x+x*y+1
==> I[2]=q*p+p*q+1
==> I[3]=p*p+1
==> I[4]=q*q+1
==> I[5]=p*y*p+Y
==> I[6]=p*x*p+x
==> I[7]=q*y*q+y
==> I[8]=q*x*q+X
==> I[9]=X*x+1
==> I[10]=x*X+1
==> I[11]=Y*y+1
==> I[12]=y*Y+1
==> I[13]=y*x+x*y+p*p
==> I[14]=y*x+x*y+q*q
==> I[15]=p*p+q*q