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7.10.2.13 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]=y*x+x*y+1
==> I[2]=y*x+x*y+t*t
==> I[3]=t*t+1
==> I[4]=t*x*t+x*y
==> I[5]=t*y*t+Y
==> I[6]=X*x+1
==> I[7]=x*X+1
==> I[8]=Y*y+1
==> I[9]=y*Y+1
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