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7.7.8.0. crystallographicGroupP3
Procedure from library fpalgebras.lib (see fpalgebras_lib).
- Usage:
- crystallographicGroupP3(d); d an integer
- Return:
- ring
- Note:
- - the ring contains the ideal I, which contains the required relations
- p3 group with the following presentation
< x, y, r | [x, y] = r^3 = 1, r^-1*x*r = x^-1*y, r^-1*y*r = x^-1>
- d gives the degreebound for the Letterplace ring
Example:
| LIB "fpalgebras.lib";
def R = crystallographicGroupP3(5); setring R;
I;
==> I[1]=x(1)*y(2)+y(1)*x(2)+1
==> I[2]=r(1)*r(2)*r(3)+x(1)*y(2)+y(1)*x(2)
==> I[3]=r(1)*r(2)*r(3)+1
==> I[4]=r(1)*r(2)*x(3)*r(4)+X(1)*y(2)
==> I[5]=r(1)*r(2)*y(3)*r(4)+X(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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