|
7.5.5.0. makeUg2
Procedure from library ncalg.lib (see ncalg_lib).
- Usage:
- makeUg2([p]), p an optional int (field characteristic)
- Return:
- ring
- Purpose:
- set up the U(g_2) in variables (x(i),y(i),Ha,Hb) for i=1..6 over the field of char p
- Note:
- activate this ring with the
setring command
the variables are ordered as x(1),...x(6),y(1),...,y(6),Ha,Hb.
Example:
| LIB "ncalg.lib";
def a = makeUg2();
setring a; a;
==> // characteristic : 0
==> // number of vars : 14
==> // block 1 : ordering dp
==> // : names x(1) x(2) x(3) x(4) x(5) x(6) y(1) y(2) y(\
3) y(4) y(5) y(6) Ha Hb
==> // block 2 : ordering C
==> // noncommutative relations:
==> // x(2)x(1)=x(1)*x(2)-x(3)
==> // x(3)x(1)=x(1)*x(3)-2*x(4)
==> // x(4)x(1)=x(1)*x(4)+3*x(5)
==> // y(1)x(1)=x(1)*y(1)-Ha
==> // y(3)x(1)=x(1)*y(3)+3*y(2)
==> // y(4)x(1)=x(1)*y(4)+2*y(3)
==> // y(5)x(1)=x(1)*y(5)-y(4)
==> // Hax(1)=x(1)*Ha+2*x(1)
==> // Hbx(1)=x(1)*Hb-x(1)
==> // x(5)x(2)=x(2)*x(5)+x(6)
==> // y(2)x(2)=x(2)*y(2)-Hb
==> // y(3)x(2)=x(2)*y(3)-y(1)
==> // y(6)x(2)=x(2)*y(6)-y(5)
==> // Hax(2)=x(2)*Ha-3*x(2)
==> // Hbx(2)=x(2)*Hb+2*x(2)
==> // x(4)x(3)=x(3)*x(4)+3*x(6)
==> // y(1)x(3)=x(3)*y(1)+3*x(2)
==> // y(2)x(3)=x(3)*y(2)-x(1)
==> // y(3)x(3)=x(3)*y(3)-Ha-3*Hb
==> // y(4)x(3)=x(3)*y(4)-2*y(1)
==> // y(6)x(3)=x(3)*y(6)-y(4)
==> // Hax(3)=x(3)*Ha-x(3)
==> // Hbx(3)=x(3)*Hb+x(3)
==> // y(1)x(4)=x(4)*y(1)+2*x(3)
==> // y(3)x(4)=x(4)*y(3)-2*x(1)
==> // y(4)x(4)=x(4)*y(4)-2*Ha-3*Hb
==> // y(5)x(4)=x(4)*y(5)+y(1)
==> // y(6)x(4)=x(4)*y(6)+y(3)
==> // Hax(4)=x(4)*Ha+x(4)
==> // y(1)x(5)=x(5)*y(1)-x(4)
==> // y(4)x(5)=x(5)*y(4)+x(1)
==> // y(5)x(5)=x(5)*y(5)-Ha-Hb
==> // y(6)x(5)=x(5)*y(6)+y(2)
==> // Hax(5)=x(5)*Ha+3*x(5)
==> // Hbx(5)=x(5)*Hb-x(5)
==> // y(2)x(6)=x(6)*y(2)-x(5)
==> // y(3)x(6)=x(6)*y(3)-x(4)
==> // y(4)x(6)=x(6)*y(4)+x(3)
==> // y(5)x(6)=x(6)*y(5)+x(2)
==> // y(6)x(6)=x(6)*y(6)-Ha-2*Hb
==> // Hbx(6)=x(6)*Hb+x(6)
==> // y(2)y(1)=y(1)*y(2)+y(3)
==> // y(3)y(1)=y(1)*y(3)+2*y(4)
==> // y(4)y(1)=y(1)*y(4)-3*y(5)
==> // Hay(1)=y(1)*Ha-2*y(1)
==> // Hby(1)=y(1)*Hb+y(1)
==> // y(5)y(2)=y(2)*y(5)-y(6)
==> // Hay(2)=y(2)*Ha+3*y(2)
==> // Hby(2)=y(2)*Hb-2*y(2)
==> // y(4)y(3)=y(3)*y(4)-3*y(6)
==> // Hay(3)=y(3)*Ha+y(3)
==> // Hby(3)=y(3)*Hb-y(3)
==> // Hay(4)=y(4)*Ha-y(4)
==> // Hay(5)=y(5)*Ha-3*y(5)
==> // Hby(5)=y(5)*Hb+y(5)
==> // Hby(6)=y(6)*Hb-y(6)
| makeUsl, makeUgl
|