|
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
|
|