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Is this a BUG of D[f, var1, ..., NonConstants -> {u1, ...}] ?

• To: mathgroup at smc.vnet.net
• Subject: [mg65186] Is this a BUG of D[f, var1, ..., NonConstants -> {u1, ...}] ?
• From: "wyelen at gmail.com" <wyelen at gmail.com>
• Date: Fri, 17 Mar 2006 00:13:29 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

As we all know, when Evaluating the following command:

     D[f[x], t, NonConstants -> {x}]

we should got something like this:

     D[x, t, NonConstants -> {x}] f ' [x]

But there seems to be some particular names in Mathematica, which will
cause strange things when using as variables.

eg. We expect a result as

     D[g, t, NonConstants -> {g}] f ' [g]

when Evaluate

     D[f[g], t, NonConstants -> {g}]

but in fact Mathematica gives 0.

And let's go further, to run the following code to see more instances.

   (*define a arbitrary function fn's derivative*)
     Clear[tpf]
     tpf[mvr_, vr_] := D[fn[mvr], vr, NonConstants -> {mvr}]

   (*we'll calculate derivatives using variables named over this List*)
     stl = ToExpression[CharacterRange["a", "z"]];

   (*the result-table. you'll find some unexpected and regular zeros.*)
     dchn = Table[tpf[stl[[lp1]], stl[[lp2]]], {lp1, 26}, {lp2, 26}];
     TableForm[dchn]

   (*for clear vision*)
     TableForm[dchn /. D :> (Subscript[#1, #2] & )]

In order to paste the result here, I replaced all of the nonzero
elements in it with ".", so you can see clearly.

	  a b c d e f g h i j k l m n o p q r s t u v w x y z
	a . . . . . 0 . . . . . . . 0 . . . . 0 . . . . . . .
	b . . . . . 0 . . . . . . . . 0 . . . 0 . . . . . . .
	c . . . . . 0 . . . . . . . . . 0 . . 0 . . . . . . .
	d . . . . . 0 . . . . . . . . . . 0 . 0 . . . . . . .
	e . . . . . 0 . . . . . . . . . . . 0 0 . . . . . . .
	f . . . . . . . . . . . . . . . . . . 0 . . . . . . .
	g . . . . . 0 . . . . . . . . . . . . 0 0 . . . . . .
	h . . . . . 0 . . . . . . . . . . . . 0 . 0 . . . . .
	i . . . . . 0 . . . . . . . . . . . . 0 . . 0 . . . .
	j . . . . . 0 . . . . . . . . . . . . 0 . . . 0 . . .
	k . . . . . 0 . . . . . . . . . . . . 0 . . . . 0 . .
	l . . . . . 0 . . . . . . . . . . . . 0 . . . . . 0 .
	m . . . . . 0 . . . . . . . . . . . . 0 . . . . . . 0
	n 0 . . . . 0 . . . . . . . . . . . . 0 . . . . . . .
	o . 0 . . . 0 . . . . . . . . . . . . 0 . . . . . . .
	p . . 0 . . 0 . . . . . . . . . . . . 0 . . . . . . .
	q . . . 0 . 0 . . . . . . . . . . . . 0 . . . . . . .
	r . . . . 0 0 . . . . . . . . . . . . 0 . . . . . . .
	s . . . . . 0 . . . . . . . . . . . . . . . . . . . .
	t . . . . . 0 0 . . . . . . . . . . . 0 . . . . . . .
	u . . . . . 0 . 0 . . . . . . . . . . 0 . . . . . . .
	v . . . . . 0 . . 0 . . . . . . . . . 0 . . . . . . .
	w . . . . . 0 . . . 0 . . . . . . . . 0 . . . . . . .
	x . . . . . 0 . . . . 0 . . . . . . . 0 . . . . . . .
	y . . . . . 0 . . . . . 0 . . . . . . 0 . . . . . . .
	z . . . . . 0 . . . . . . 0 . . . . . 0 . . . . . . .

• Follow-Ups:
  • Re: Is this a BUG of D[f, var1, ..., NonConstants -> {u1, ...}] ?
    • From: Bruce Miller <brucem@wolfram.com>