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7.10.2.19 crystallographicGroupP31M
Procedure from library fpalgebras.lib (see fpalgebras_lib).
- Usage:
- crystallographicGroupP31M(d); d an integer
- Return:
- ring
- Note:
- - the ring contains the ideal I, which contains the required relations
- p31m group with the following presentation
< x, y, r, t | [x, y] = r^2 = t^2 = (t*r)^3 = 1, r^(-1)*x*r = x, t^(-1)*y*t = y, t^(-1)*x*t = x^(-1)*y, r^(-1)*y*r = x*y^(-1) >
- d gives the degreebound for the Letterplace ring
Example:
| | LIB "fpalgebras.lib";
def R = crystallographicGroupP31M(6); setring R;
I;
==> I[1]=y*x+x*y+1
==> I[2]=y*x+x*y+r*r
==> I[3]=y*x+x*y+t*t
==> I[4]=r*r+1
==> I[5]=t*t+1
==> I[6]=t*r*t*r*t*r+1
==> I[7]=r*r+t*t
==> I[8]=t*r*t*r*t*r+y*x+x*y
==> I[9]=t*r*t*r*t*r+r*r
==> I[10]=t*r*t*r*t*r+t*t
==> I[11]=r*x*r+x
==> I[12]=t*y*t+y
==> I[13]=t*x*t+X*y
==> I[14]=r*y*r+x*Y
==> I[15]=X*x+1
==> I[16]=x*X+1
==> I[17]=Y*y+1
==> I[18]=y*Y+1
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