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