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