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