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