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7.10.2.14 crystallographicGroupC2MM
Procedure from library fpalgebras.lib (see fpalgebras_lib).
- Usage:
- crystallographicGroupC2MM(d); d an integer
- Return:
- ring
- Note:
- - the ring contains the ideal I, which contains the required relations
- c2mm group with the following presentation
< x, y, m, r | [x, y] = m^2 = r^2 = 1, m^(-1)*y*m = y^(-1), m^(-1)*x*m = x*y, r^(-1)*y*r = y^(-1), r^(-1)*x*r = x^(-1), m^(-1)*r*m = r^(-1) >
- d gives the degreebound for the Letterplace ring
Example:
| | LIB "fpalgebras.lib";
def R = crystallographicGroupC2MM(5); setring R;
I;
==> I[1]=y*x+x*y+1
==> I[2]=y*x+x*y+m*m
==> I[3]=y*x+x*y+r*r
==> I[4]=m*m+1
==> I[5]=r*r+1
==> I[6]=m*m+r*r
==> I[7]=m*y*m+Y
==> I[8]=m*x*m+x*y
==> I[9]=r*y*r+Y
==> I[10]=r*x*r+X
==> I[11]=m*r*m+r
==> I[12]=X*x+1
==> I[13]=x*X+1
==> I[14]=Y*y+1
==> I[15]=y*Y+1
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