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7.10.2.11 crystallographicGroupP2
Procedure from library fpalgebras.lib (see fpalgebras_lib).
- Usage:
- crystallographicGroupP2(d); d an integer
- Return:
- ring
- Note:
- - the ring contains the ideal I, which contains the required relations
- p2 group with the following presentation
< x, y, m, t | [x, y] = t^2 = 1, m^2 = y, t^(-1)*x*t = x, m^(-1)*x*m = x^(-1), t^(-1)*y*t = y^(-1), t^(-1)*m*t = m^(-1) >
- d gives the degreebound for the Letterplace ring
Example:
| | LIB "fpalgebras.lib";
def R = crystallographicGroupP2(5); setring R;
I;
==> I[1]=y*x+x*y+1
==> I[2]=y*x+x*y+t*t
==> I[3]=m*m+y
==> I[4]=t*t+1
==> I[5]=t*x*t+x
==> I[6]=M*x*m+X
==> I[7]=t*y*t+Y
==> I[8]=t*m*t+M
==> I[9]=X*x+1
==> I[10]=x*X+1
==> I[11]=Y*y+1
==> I[12]=y*Y+1
==> I[13]=m*M+1
==> I[14]=M*m+1
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