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
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| Gianluca Gorni |
| Universita` di Udine |
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