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+--- Thread: What's the function of a function variable's function? (/thread-2354.html)
What's the function of a function variable's function? - DrD - 10-29-2014 12:24 PM
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-
RE: What's the function of a function variable's function? - Han - 10-29-2014 02:18 PM
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).
RE: What's the function of a function variable's function? - DrD - 10-29-2014 03:22 PM
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-