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7.10.2.8 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]=y*x+x*y+1
==> I[2]=y*x+x*y+m*m
==> I[3]=m*m+1
==> I[4]=m*x*m+x
==> I[5]=m*y*m+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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