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*h-e; p; ==> e2h2+2e2h+2efh-2ef+f2-h2-e+3h F(p); ==> f2h2-2efh-2f2h+e2-2ef+h2-f-h G(p); ==> e2h2+2e2h+2efh-2ef+f2-h2-e+3h (G(p) == p); // G is the identity ==> 1