
7.2.2.3 map (plural) operations
( )
 composition of maps. If, for example,
f and g are maps,
then f(g) is a map expression giving the composition
of f and g , provided the target ring of g is the basering of f .
 map_expression
[ int_expressions ]
 is a map entry (the image of the corresponding variable)
Example:
 LIB "ncalg.lib";
def Usl2 = makeUsl2(); // this algebra is U(sl_2)
setring Usl2;
map F = Usl2, f, e, h; // involutive endomorphism of U(sl_2)
F;
==> F[1]=f
==> F[2]=e
==> F[3]=h
map G = F(F);
G;
==> G[1]=e
==> G[2]=f
==> G[3]=h
poly p = (f+e*h)^2 + 3*he;
p;
==> e2h2+2e2h+2efh2ef+f2h2e+3h
F(p);
==> f2h22efh2f2h+e22ef+h2fh
G(p);
==> e2h2+2e2h+2efh2ef+f2h2e+3h
(G(p) == p); // G is the identity
==> 1

