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Re: DifferenitalD vs CapitalDifferenitalD

  • To: mathgroup at smc.vnet.net
  • Subject: [mg87938] Re: DifferenitalD vs CapitalDifferenitalD
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Mon, 21 Apr 2008 03:22:28 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <fuees1$bds$1@smc.vnet.net>

fizzy wrote:

> After applying Jens correction, I was hoping to be able to use the =
> DifferentialD  with x, etc. and then use the 'dx' , where 'd' here is =
> DifferentialD (just dont know how to add it here in the email),  so it =
> would be a Symbol....but this didnt work....I realize I can use the =
> straight forward   dx , etc.  symbol but I want to highlight the =
> Differential....any way to 'fix' this?....when I type in  DifferentialD =
> , from the Palette, and then add x to it and perform  //Head on it , it =
> just returns DifferentialD

<snip>

Hi Jerry,

The behavior you have noticed is perfectly normal since the built-in 
function *DifferentialD[]*, which can also be entered as |esc|dd|esc| 
(i.e. the escape key followed by the character lowercase d twice 
followed by the escape key again), is a *compound operator with built-in 
meaning*. The full form of a complete expression with *DifferentialD[]* 
is DifferentialD[some_expression] (one argument is required).

For instance, say we enter the expression

     |esc|dd|esc|z

Its full form is

     FullForm[|esc|dd|esc|z] === DifferentialD[z]

And its head is

      Head[|esc|dd|esc|z] === DifferentialD

Thus, one cannot manipulate double struck lowercase d independently.

Now, if you are interested by the above character without built-in 
meaning, you can get it with the following sequence of keys:

     |esc|dsd|dsd|

Note that dsd stands for double struck lowercase d. Similarly, you can 
get a double struck capital C by entering |esc|dsC|esc|

Finally, enter and evaluate the following sequences of keystrokes:

     |esc|int|esc|z |esc|dsd|esc|z

     |esc|int|esc|z |esc|dd|esc|z

They look the same. However, the first expression generates an error 
message, while the second returns the expected definite integral.

Regards,
-- Jean-Marc


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