Re: Re: Help with Root function
- To: mathgroup at smc.vnet.net
- Subject: [mg79506] Re: [mg79439] Re: Help with Root function
- From: DrMajorBob <drmajorbob at bigfoot.com>
- Date: Sat, 28 Jul 2007 05:29:58 -0400 (EDT)
- References: <f89q55$5nu$1@smc.vnet.net> <24667963.1185542703257.JavaMail.root@m35>
- Reply-to: drmajorbob at bigfoot.com
In the v6 documentation for Root, ToRadicals is linked after "See Also".
Below that, there's also a link to the tutorial "Algebraic Numbers", which
describes ToRadicals.
Even so, ToRadicals should be mentioned more prominently in the Root
article, I think, since it exists only to operate on Root objects.
Bobby
On Fri, 27 Jul 2007 04:41:13 -0500, jeremito <jeremit0 at gmail.com> wrote:
> Thank you all who offered the solution to this problem. The answer
> is:
>
> Eigenvalues[B]//ToRadicals
>
> How simple, if you know how to do it. My follow-up question is:
>
> How could I (or anyone) have found that on their own? I searched in
> the documentation, but couldn't find it until I knew what to search
> for.
>
> Thanks again,
> Jeremy
>
> On Jul 26, 5:39 am, jeremito <jerem... at gmail.com> wrote:
>> I am trying to find the eigenvalues of a 3x3 matrix with non-numeric
>> elements. This requires finding the roots of cubic polynomials.
>> Mathematica can do this, but I know how to interpret its output. For
>> example
>>
>> In[1]:= B = {{a, 1, 1}, {1, b, 1}, {1, 1, c}}
>>
>> Out[1]= {{a, 1, 1}, {1, b, 1}, {1, 1, c}}
>>
>> In[2]:= Eigenvalues[B]
>>
>> Out[2]= {Root[-2 + a + b + c -
>> a b c + (-3 + a b + a c + b c) #1 + (-a - b - c) #1^2 + #1^3 &,
>> 1], Root[-2 + a + b + c -
>> a b c + (-3 + a b + a c + b c) #1 + (-a - b - c) #1^2 + #1^3 &,
>> 2], Root[-2 + a + b + c -
>> a b c + (-3 + a b + a c + b c) #1 + (-a - b - c) #1^2 + #1^3 &,
>> 3]}
>>
>> How can I get Mathematica to give me the full answer? I know it is
>> long and ugly, but at least I can do something with it. I can't do
>> anything with what it gives me now. Does that make sense?
>> Thanks,
>> Jeremy
>
>
>
>
--
DrMajorBob at bigfoot.com