Re: Re: ArcCos[]

• To: mathgroup at smc.vnet.net
• Subject: [mg24837] Re: [mg24815] Re: ArcCos[]
• From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
• Date: Tue, 15 Aug 2000 03:04:08 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```I think you solved a differnt problem from the one Gianluca had in mind. In
his case, I think, the correct answer is:

In[1]:=
a=Root[-t + 2*#1 + 2*t^2*#1 + #1^3 & , 1];

In[2]:=
b = Numerator[D[a, t]]
Out[2]=
2        3
1 - 4 t Root[-t + 2 #1 + 2 t  #1 + #1  & , 1]
In[3]:=
FindRoot[Evaluate[b==0],{t,1}]
Out[3]=
{t -> 1.01505}
In[4]:=
FindRoot[Evaluate[b==0],{t,-1}]
Out[4]=
{t -> -1.01505}

--
Andrzej Kozlowski
Toyama International University, JAPAN

For Mathematica related links and resources try:
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on 8/14/00 5:49 AM, John D. Hendrickson at jdh at hend.net wrote:

> I've got Mathematica 4.0.2.0.  Since I'm running Win95 I don't mind
> crashing - thats pretty much a constant, so I tried your dare:)  But mine
> didn't crash - it gave me output.  Also - I have a substitute that might be
> what you want.
>
> In[1]:=
> a = Root[-t + 2*#1 + 2*t^2*#1 + #1^3 & , 1];
>
> In[2]:=
> b = D[a, t];
>
> In[4]:=
> InputForm[ Solve[b == 0, t] ]
>
> Solve::"tdep": "The equations appear to involve the variables to be solved \
> for in an essentially non-algebraic way."
>
> Out[4]//InputForm=
> Solve[(1 - 4*t*Root[-t + 2*#1 + 2*t^2*#1 + #1^3 & , 1])/
> (2 + 2*t^2 + 3*Root[-t + 2*#1 + 2*t^2*#1 + #1^3 & , 1]^
> 2) == 0, t]
>
> ===================================================================
> Would the following be acceptible in your circumstance?
> I assumed by making the unexplicit root object explicit:
> ====================================================================
>
> In[3]:=
> Exit[]
>
> In[1]:=
> a = Root[-t + 2*#1 + 2*t^2*#1 + #1^3 & , 1];
>
> In[2]:=
> ax = First[a][x]
>
> Out[2]=
> \!\(\(-t\) + 2\ x + 2\ t\^2\ x + x\^3\)
>
> In[3]:=
> b = D[ax, t];
>
> In[4]:=
> InputForm[ Solve[b == 0, t] ]
>
> Out[4]//InputForm=
> {{t -> 1/(4*x)}}
>
> ===================================================================
>
> Allan Hayes wrote in message <8mtc0m\$7qb at smc.vnet.net>...
>>
>>
>>
>> "Gianluca Gorni" <gorni at dimi.uniud.it> wrote in message
>> news:8mqvd7\$18j at smc.vnet.net...
>>
>>
>> -----------  Snip -------------
>>> An unrelated problem: the following instructions consistently crash
>>> my Mac Mathematica 4 kernel:
>>>
>>> a = Root[-t + 2*#1 + 2*t^2*#1 + #1^3 & , 1];
>>> b = D[a, t];
>>> Solve[b == 0, t]
>>>
>> --
>> Gianluca ,
>> It crashes Mathematica 4.02  on Windows also.
>>
>> Allan
>> ---------------------
>> Allan Hayes
>> Mathematica Training and Consulting
>> Leicester UK
>> www.haystack.demon.co.uk
>> hay at haystack.demon.co.uk
>> Voice: +44 (0)116 271 4198
>> Fax: +44 (0)870 164 0565
>>
>>
>>
>>
>
>
>
>

```

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