What's the function of a function variable's function?

[DrD]

Interestingly, I found nothing in the user guide regarding this usage of a function variable:

CAS enter:
r(t):=[t-sin(t) 1-cos(t)]

Produces:
r:=(t)->BEGIN [t-sin(t),1-cos(t)]; END;
(t)->BEGIN [t-sin(t),1-cos(t)]; END;

Example:
A revolving cycloid at t=0 (rest), position r(0) => [0,0] rotates to pi radians, r(π) => [π,2], completes a full cycle at r(2*π) => [2*π,0].

Is there any further information on this?

-Dale-

[Han]

You can find more info by looking at the documentation for xcas/giac.

There isn't anything special about a variable whose content is a function. It's supposed to reflect a mathematical function. So you can create functions by simply using the form:

function_name(var_name):= <expression in terms of var_name>;

This is typical for any CAS. The CAS also knows how to handle functional algebra. So you can define two functions f(x) and g(t) and ask the CAS to compute h:=f+g, and then use compute, say, h(3).

[DrD]

The fact that it created the function in much the same way as 'Define' might, was new to me. The 'BEGIN and END' surround wasn't something I expected, but now that I have learned of that behavior, I imagine it will become quite useful.

Thanks for the xcas/giac reference.

-Dale-