|
7.7.8.0. crystallographicGroupP4GM
Procedure from library fpalgebras.lib (see fpalgebras_lib).
- Usage:
- crystallographicGroupP4GM(d); d an integer
- Return:
- ring
- Note:
- - the ring contains the ideal I, which contains the required relations
- p4gm group with the following presentation
< x, y, r, t | [x, y] = r^4 = t^2 = 1, r^-1*y*r = x^-1, r^-1*x*r = y, t^-1*x*t = y, t^-1*r*t = x^-1*r^-1>
- d gives the degreebound for the Letterplace ring
Example:
| LIB "fpalgebras.lib";
def R = crystallographicGroupP4GM(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]=x(1)*y(2)+y(1)*x(2)+t(1)*t(2)
==> I[5]=t(1)*t(2)+1
==> I[6]=r(1)*r(2)*r(3)*r(4)+t(1)*t(2)
==> I[7]=r(1)*r(2)*r(3)*y(4)*r(5)+X(1)
==> I[8]=r(1)*r(2)*r(3)*x(4)*r(5)+y(1)
==> I[9]=X(1)*r(2)*r(3)*r(4)+t(1)*r(2)*t(3)
==> I[10]=X(1)*x(2)+1
==> I[11]=x(1)*X(2)+1
==> I[12]=Y(1)*y(2)+1
==> I[13]=y(1)*Y(2)+1
|
|