@ - Maple Help

# Online Help

###### All Products    Maple    MapleSim

type/composition

test for a composition

type/@

test for the composition operator

type/@@

test for the repeated composition operator

 Calling Sequence type(expr, composition) type(expr, @) type(expr, @@)

Parameters

 expr - expression

Description

 • These commands test expr for various forms of function composition.
 • The type(expr, @) calling sequence returns true if expr is a composition of functions.  It is equivalent to type(expr, specfunc(anything, @)).
 • The type(expr, @@) calling sequence returns true if expr is a repeated composition.  It is equivalent to type(expr, specfunc(anything, @@)).
 • The type(expr, composition) calling sequence returns true if expr is either of type @ or @@.
 • For more information about function composition, see compose.

Examples

 > $\mathrm{type}\left(\mathrm{sin}@\mathrm{cos},\mathrm{@}\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{type}\left(\mathrm{sin}@\mathrm{cos}@\mathrm{csc},\mathrm{@}\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{type}\left({\mathrm{csc}}^{\left(2\right)},\mathrm{@@}\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{type}\left({\left(\mathrm{cos}@\mathrm{sin}\right)}^{\left(2\right)},\mathrm{@@}\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{type}\left(\mathrm{sin}@\mathrm{cos},\mathrm{composition}\right)$
 ${\mathrm{true}}$ (5)
 > $\mathrm{type}\left({\mathrm{sin}}^{\left(2\right)}@{\mathrm{cos}}^{\left(2\right)},\mathrm{composition}\right)$
 ${\mathrm{true}}$ (6)
 > $\mathrm{type}\left(\mathrm{sin},\mathrm{@@}\right)$
 ${\mathrm{false}}$ (7)
 > $\mathrm{type}\left({\mathrm{sin}}^{\left(0\right)},\mathrm{@@}\right)$
 ${\mathrm{false}}$ (8)
 > $\mathrm{type}\left(\mathrm{sin}\left(\mathrm{cos}\left(x\right)\right),\mathrm{composition}\right)$
 ${\mathrm{false}}$ (9)

 See Also