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RE: FindRoot problem

• To: mathgroup at smc.vnet.net
• Subject: [mg40040] RE: [mg40032] FindRoot problem
• From: "Pigeon, Robert" <Robert.Pigeon at drdc-rddc.gc.ca>
• Date: Mon, 17 Mar 2003 03:33:16 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Thanks David,
	It works!  But, I would like to understand why Mathematica's
FindRoot is not working when the function has conditions!
BTW, my real equation had, as second condition, x<= 1.535, and when I
applied RootSearch with 1.54 as upper limit, it finds just the first root
(1.4811).  So the conditions apply with the search!  That is great !

Robert


-----Original Message-----
From: David Park [mailto:djmp at earthlink.net]
To: mathgroup at smc.vnet.net
Subject: [mg40040] RE: [mg40032] FindRoot problem


Robert,

Try using Ted Ersek's RootSearch package from MathSource. It even gets both
roots for you.

Needs["Enhancements`RootSearch`"]

f[x_ /; x >= 0 && x <= 1.54] :=
    Module[{}, Sec[x] - 0.0018167 (Sec[x] - 1) - 0.002875 (Sec[x] - 1)^2 -
0.000808 (Sec[x] - 1)^3 ];

RootSearch[f[x] == 10, {x, 0, 1.54}]
{{x -> 1.4811}, {x -> 1.53501}}

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/

From: Pigeon, Robert [mailto:Robert.Pigeon at drdc-rddc.gc.ca]
To: mathgroup at smc.vnet.net

Good day,
	I have a problem with FindRoot that I do not understand, so I am
asking for help!  I have a function defined as a Module.  I use FindRoot to
find a root when the function is given a value.  Everything works fine
except when I put a condition to my function, when I do I get an error
message.  Here what I try to do:

f[x_]:= Module[{}, Sec[x] - 0.0018167 (Sec[x]-1) - 0.002875 (Sec[x]-1)^2 -
0.000808 (Sec[x]-1)^3 ];
f::usage="explanation of f";

If I do
FindRoot[f[x]==10,{x,1.4}]
I get
{x->1.53501}
 All that is correct.

But now if I do
f[x_ /; x>= 0 && x<= 1.54]:= same as above
and I try to find the root the same way, I get an error message
FindRoot[f[x]==10,{x,1.4}]
I get
FindRoot::frjc: Could not symbolically find the Jacobian of {f[x]-10.  Try
giving two starting values for each variable.

I tried putting my conditions inside the Module, after the Module.  I tried
to use Which, If.  But, as soon as I put a condition, I get the same error.

Any idea ???

Thanks,

Robert