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7.10.2.17 crystallographicGroupP4GM
Procedure from library fpalgebras.lib (see fpalgebras_lib).
- Usage:
- crystallographicGroupP4GM(d); d an integer
- Return:
- ring
- Note:
- - the ring contains the ideal I, which contains the required relations
- p4gm group with the following presentation
< x, y, r, t | [x, y] = r^4 = t^2 = 1, r^(-1)*y*r = x^(-1), r^(-1)*x*r = y, t^(-1)*x*t = y, t^(-1)*r*t = x^(-1)*r^(-1)>
- d gives the degreebound for the Letterplace ring
Example:
| | LIB "fpalgebras.lib";
def R = crystallographicGroupP4GM(5); setring R;
I;
==> I[1]=y*x+x*y+1
==> I[2]=r*r*r*r+y*x+x*y
==> I[3]=r*r*r*r+1
==> I[4]=y*x+x*y+t*t
==> I[5]=t*t+1
==> I[6]=r*r*r*r+t*t
==> I[7]=r*r*r*y*r+X
==> I[8]=r*r*r*x*r+y
==> I[9]=X*r*r*r+t*r*t
==> I[10]=X*x+1
==> I[11]=x*X+1
==> I[12]=Y*y+1
==> I[13]=y*Y+1
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