RE: Functions with multiple groups of arguments? [David Park?]

• To: mathgroup at smc.vnet.net
• Subject: [mg40039] RE: [mg40031] Functions with multiple groups of arguments? [David Park?]
• From: "David Park" <djmp at earthlink.net>
• Date: Mon, 17 Mar 2003 03:33:12 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Tony,

I picked up that form from reading Alfred Gray's Modern Differential
Geometry book. For example, he writes the parametrization of a general
ellipse as

ellipse[a_, b_][t_] := {a Cos[t], b Sin[t]}

This separates the "parametrization" variable t from the shape parameters a
and b. To me, this is conceptually valuable, but there is also a Mathematica
advantage. We can easily calculate the velocity of a point on the curve
using the prime notation.

ellipse[a, b]'[t]
{-a Sin[t], b Cos[t]}

In other words, ellipse[a,b] is a function name.

ellipse2[a_, b_, t_] := {a Cos[t], b Sin[t]}

we would have to use the more complicated statement

D[ellipse2[a, b, t], t]
{-a Sin[t], b Cos[t]}

or

Derivative[0, 0, 1][ellipse2][a, b, t]
{-a Sin[t], b Cos[t]}

to obtain the velocity.

?? ellipse
Global`ellipse
ellipse[a_,b_][t_]:={a Cos[t], b Sin[t]}

but where is this stored? It's stored in...

SubValues[ellipse]
{HoldPattern[ellipse[a_, b_][t_]] :> {a Cos[t], b Sin[t]}}

David Park

From: AES/newspost [mailto:siegman at stanford.edu]
To: mathgroup at smc.vnet.net

In a recent message on Mathematica programming, David Park included a
sample function definition in a form I've never encountered before,
namely

f[a_,b_,c_][x_]  := a + Sin[b x + c]

What is this?  How does it work?  (I can guess, but don't seem to find

Given the same values of a, b, c and x, does this form work differently
in *any* way from

f[a_,b_,c_, x_]  := a + Sin[b x + c]

If not, why do it this way? Or is the only reason for doing it this way
one of cosmetics?

???

--
"Power tends to corrupt.  Absolute power corrupts absolutely."
Lord Acton (1834-1902)
"Dependence on advertising tends to corrupt.  Total dependence on