Re: Function of N variable

• To: mathgroup at smc.vnet.net
• Subject: [mg121101] Re: Function of N variable
• From: Sam Takoy <sam.takoy at yahoo.com>
• Date: Sun, 28 Aug 2011 04:05:18 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• Reply-to: Sam Takoy <sam.takoy at yahoo.com>

```E.G, the following?

1, {Derivative[1][f][x]},
2, {Derivative[1, 0][f][x], Derivative[0, 1][f][x]},
3, {Derivative[1, 0, 0][f][x], Derivative[0, 1, 0][f][x],
Derivative[0, 0, 1][f][x]},
4, {Derivative[1, 0, 0, 0][f][x], Derivative[0, 1, 0, 0][f][x],
Derivative[0, 0, 1, 0][f][x], Derivative[0, 0, 0, 1][f][x]}]

f[x_, y_] = x^2 + y^2;

Thanks!

________________________________
From: Ethan Dyer <ethansdyer at gmail.com>
To: Sam Takoy <sam.takoy at yahoo.com>
Cc: "mathgroup at smc.vnet.net" <mathgroup at smc.vnet.net>
Sent: Saturday, August 27, 2011 9:24 AM
Subject: [mg121101] Re: Function of N variable

Sam,

Mathematica allows one to define functions that take an arbitrary number of arguments using double underscore (BlankSequence) or triple underscore (BlankNullSequence)

For instance F[args__]:={args} takes in any number of arguments except zero.

A function defined with three underscores can take any number including zero.

Ethan

On Aug 27, 2011, at 8:17 AM, Sam Takoy <sam.takoy at yahoo.com> wrote:

> Hi,
>
> I have put together a few function for differential geometry in 3D.
> All my functions were of the kind F(z1_, z2_, z3_). Now I want to
> generalize to 4D, then 5D, etc. Is there a good way to represent a
> function of N variables? For example, I want to be able to say grad[F]
> [???] to obtain a list of N function (partial derivatives) of N
> variables. I understand these are vague questions, but I am only
> looking for some keywords.
>