Singular Manual: map operations (plural)

| #### 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

User manual for Singular version 4.3.0p1, 2022, generated by texi2html.