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7.10.2.12 crystallographicGroupP2GG
Procedure from library fpalgebras.lib (see fpalgebras_lib).
- Usage:
- crystallographicGroupP2GG(d); d an integer
- Return:
- ring
- Note:
- - the ring contains the ideal I, which contains the required relations
- p2gg group with the following presentation
< x, y, u, v | [x, y] = (u*v)^2 = 1, u^2 = x, v^2 = y, v^(-1)*x*v = x^(-1), u^(-1)*y*u = y^(-1) >
- d gives the degreebound for the Letterplace ring
Example:
| | LIB "fpalgebras.lib";
def R = crystallographicGroupP2GG(5); setring R;
I;
==> I[1]=y*x+x*y+1
==> I[2]=u*v*u*v+y*x+x*y
==> I[3]=u*v*u*v+1
==> I[4]=u*u+x
==> I[5]=v*v+y
==> I[6]=V*x*v+X
==> I[7]=U*y*u+Y
==> I[8]=X*x+1
==> I[9]=x*X+1
==> I[10]=Y*y+1
==> I[11]=y*Y+1
==> I[12]=u*U+1
==> I[13]=U*u+1
==> I[14]=v*V+1
==> I[15]=V*v+1
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