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