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7.10.2.20 crystallographicGroupP3M1
Procedure from library fpalgebras.lib (see fpalgebras_lib).
- Usage:
- crystallographicGroupP3M1(d); d an integer
- Return:
- ring
- Note:
- - the ring contains the ideal I, which contains the required relations
- p3m1 group with the following presentation
< x, y, r, m | [x, y] = r^3 = m^2 = 1, m^(-1)*r*m = r^2, r^(-1)*x*r = x^(-1)*y, r^(-1)*y*r = x^(-1), m^(-1)*x*m = x^(-1), m^(-1)*y*m = x^(-1)*y >
- d gives the degreebound for the Letterplace ring
Example:
| | LIB "fpalgebras.lib";
def R = crystallographicGroupP3M1(5); setring R;
I;
==> I[1]=y*x+x*y+1
==> I[2]=r*r*r+y*x+x*y
==> I[3]=y*x+x*y+m*m
==> I[4]=r*r*r+1
==> I[5]=m*m+1
==> I[6]=r*r*r+m*m
==> I[7]=m*r*m+r*r
==> I[8]=r*r*x*r+X*y
==> I[9]=r*r*y*r+X
==> I[10]=m*x*m+X
==> I[11]=m*y*m+X*y
==> I[12]=X*x+1
==> I[13]=x*X+1
==> I[14]=Y*y+1
==> I[15]=y*Y+1
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