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MathGroup Archive 2000

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Derivative of Root objects

  • To: mathgroup at smc.vnet.net
  • Subject: [mg23831] Derivative of Root objects
  • From: Gianluca Gorni <gorni at dimi.uniud.it>
  • Date: Sat, 10 Jun 2000 03:00:57 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello!

It seems that the derivative in the form f'[x] and in the form D[f[x] ,x]
behave differently when f[x] contains Root objects.

My version is 4.0 for PowerMac.

Example:

f[x_] = Root[#^3 - x &, 1];

f'[x]  gives  0  (wrong, of course)

D[f[x], x]  gives  1/(3*Root[-x + #1^3 & , 1]^2)  (right)

%%%%%%%%%%%

I take the opportunity to submit a shortcoming of FullSimplify that
I have just found, for developer use:

expr = y*Root[-3*y*#1 + 2*#1^3 & , 3]^2;

The third derivative of expr is zero:

D[expr, {y, 3}]//FullSimplify  gives  0.

Still, FullSimplify does not realize that the second derivative is
constant:

D[expr, {y,2}]//FullSimplify  gives a complicated expression.

Developer`ZeroQ fails too, because

Developer`ZeroQ[D[expr, {y,2}]-(D[expr, {y,2}] /. y->1)]

gives False.

Best regards,

                 Gianluca Gorni

-- 


 +---------------------------------+
 | Gianluca Gorni                  |
 | Universita` di Udine            |
 | Dipartimento di Matematica      |
 |   e Informatica                 |
 | via delle Scienze 208           |
 | I-33100 Udine UD                |
 | Italy                           |
 +---------------------------------+
 | Ph.: (39) 0432-558422           |
 | Fax: (39) 0432-558499           |
 | mailto:gorni at dimi.uniud.it      |
 | http://www.dimi.uniud.it/~gorni |
 +---------------------------------+




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