.. status: ok



10.9 Functions Producing Functions
----------------------------------

In `ugUserMake <section-6.14.html#ugUserMake>`__ , you learned how to
use the operation function to create a function from symbolic formulas.
Here we introduce a similar operation which not only creates functions,
but functions from functions.

The facility we need is provided by the package
MakeUnaryCompiledFunction(E,S,T). MakeUnaryCompiledFunction This package
produces a unary (one-argument) compiled function from some symbolic
data generated by a previous computation. MakeBinaryCompiledFunction is
available for binary functions. MakeBinaryCompiledFunction The E tells
where the symbolic data comes from; the S and T give FriCAS the source
and target type of the function, respectively. The compiled function
produced has type S-> T. To produce a compiled function with definition
p(x)==expr, call compiledFunction(expr,x) from this package. The
function you get has no name. You must to assign the function to the
variable p to give it that name.

Do some computation.


.. spadInput
::

	(x+1/3)^5


.. spadMathAnswer
Convert this to an anonymous function of x. Assign it to the variable p
to give the function a name.


.. spadInput
::

	p := compiledFunction(%,x)$MakeUnaryCompiledFunction(POLY FRAC
INT,DFLOAT,DFLOAT)


.. spadMathAnswer
Apply the function.


.. spadInput
::

	p(sin(1.3))


.. spadMathAnswer
For a more sophisticated application, read on.