@ - Maple Help

@

the composition operator

@@

the repeated composition operator

 Calling Sequence f @ g f @@ n

Parameters

 f, g - any functions n - integer

Description

 • $@$ is the function composition operator.
 • $@@$ is the repeated function composition operator.
 • If n is negative, the $\mathrm{invfunc}$ table is checked to see if it has an entry for f.  That is, if $\mathrm{invfunc}\left[f\right]=g$, then $f@@n-->g@@\left(-n\right)$.
 • Composition also applies to procedures.  However, given two procedures f and g, the composition $f@g$ is of type function, not type procedure.  For more information, see type/function and type/procedure.

Composition Examples

 > (sin@cos)(x);
 ${\mathrm{sin}}{}\left({\mathrm{cos}}{}\left({x}\right)\right)$ (1)
 > (sin@arcsin)(x);
 ${x}$ (2)
 > sin@arcsin;
 ${\mathrm{sin}}{@}{\mathrm{arcsin}}$ (3)
 > simplify((3));
 $\left(\right){↦}{\mathrm{args}}$ (4)
 > sin@@0;
 $\left(\right){↦}{\mathrm{args}}$ (5)
 > sin@@1;
 ${\mathrm{sin}}$ (6)
 > (sin@@2)(x);
 ${{\mathrm{sin}}}^{\left({2}\right)}{}\left({x}\right)$ (7)
 > cos@@(-1);
 ${\mathrm{arccos}}$ (8)
 > (D@@2)(ln);
 ${z}{↦}{-}\frac{{1}}{{{z}}^{{2}}}$ (9)