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7.7.8.0. 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]=x(1)*y(2)+y(1)*x(2)+1
==> I[2]=x(1)*y(2)+y(1)*x(2)+r(1)*r(2)
==> I[3]=x(1)*y(2)+y(1)*x(2)+t(1)*t(2)
==> I[4]=r(1)*r(2)+1
==> I[5]=t(1)*t(2)+1
==> I[6]=t(1)*r(2)*t(3)*r(4)*t(5)*r(6)+1
==> I[7]=r(1)*r(2)+t(1)*t(2)
==> I[8]=t(1)*r(2)*t(3)*r(4)*t(5)*r(6)+x(1)*y(2)+y(1)*x(2)
==> I[9]=t(1)*r(2)*t(3)*r(4)*t(5)*r(6)+r(1)*r(2)
==> I[10]=t(1)*r(2)*t(3)*r(4)*t(5)*r(6)+t(1)*t(2)
==> I[11]=r(1)*x(2)*r(3)+x(1)
==> I[12]=t(1)*y(2)*t(3)+y(1)
==> I[13]=t(1)*x(2)*t(3)+X(1)*y(2)
==> I[14]=r(1)*y(2)*r(3)+x(1)*Y(2)
==> I[15]=X(1)*x(2)+1
==> I[16]=x(1)*X(2)+1
==> I[17]=Y(1)*y(2)+1
==> I[18]=y(1)*Y(2)+1
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