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Function: makediff - produce a `diff/...` procedure

Calling sequence:

makediff(g)
makediff(g,vars)

Parameters:

g - a procedure name
vars - set or list of variable names

Description:

This procedure is a work-around for a weakness in the differentiation operator D : when a function f is defined using a second user-defined function g , D(f) doesn't work. What is needed is a procedure named `diff/g` that performs the differentiation of g .

The command makediff(g) produces the procedure `diff/g` , allowing D(f) to work for procedures f defined using g .

If only some of the arguments of g are suitable for differentiation, you can use makediff(g,vars ) where vars is a set or list of arguments of g that are suitable for differentiation. In this case you shouldn't try (directly or indirectly) to differentiate g with respect to one of its arguments not in vars .

See also the command fixD(f) which applies makediff to all user-defined procedures referenced in f , thus allowing D(f) to work.

This works only for global procedures, not local procedures or module exports.

This function is part of the Maple Advisor Database.

Examples:

Defining f using defined function g :

> f:= x -> x*g(x^2);
g:= x -> 1 + x^2;

D(f) does not work:

> D(f);

Using makediff(g) to make this work:

> makediff(g); D(f);

In the following case, it makes no sense to differentiate h with respect to n . Therefore we must use the two-argument form of makediff .

> h:= (x,n) -> sum(1/(1+x^j),j=1..n):
f:= t -> h(t^2,5):
makediff(h,{x});
D(f);

See also:

D , diff , fixD , Problems with D

Maple Advisor Database R. Israel, 2001