# [Maxima] polynomial equations

Thu Sep 27 10:18:41 CDT 2007

```Richard Fateman pisze:
> Unless n is quite small, like n=2, the system is probably too complicated to
> find any algebraic/symbolic solutions for arbitrary c and z that would be of
> any use.

Yes. It easy for n = 1 or 2. Harder but posiible for 3 but imposible for
n>3 to get explicite formula. But it is possible to get numerical solution.
I thought about something like that :
http://facstaff.unca.edu/mcmcclur/professional/CriticalBifurcationPP.pdf
see page number 9

or

http://departments.ithaca.edu/math/docs/theses/whannahthesis.pdf
see page 12

>
> It is easy to find factors of F, e.g. F[4,c,z] has 3 factors of degree
> (2,1), (2,1), (12,6) in z and c resp.
>
>
>  RJF
>
>
>> -----Original Message-----
>> From: maxima-bounces at math.utexas.edu
>> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of Adam Majewski
>> Sent: Wednesday, September 26, 2007 9:48 AM
>> To: maxima at math.utexas.edu
>> Subject: [Maxima] polynomial equations
>>
>> Hi !
>>
>> I'm trying to solve pair of equations:
>>
>>
>> # 1 definition
>> f[n, c, z] :=
>> if n=0
>>    then z
>>    else (f[n-1, c, z]^2 + c);
>>
>> # 2 def
>>    F[n, c, z] :=f[n, c, z]-z;
>>
>> # 3 def
>>    dF[n,c,z]:=diff(F[n,c,z],z);
>>
>> # pair of equations:
>> # n is constant
>> dF[n,c,z] +1 = exp(angle*%i)
>> F[n, c, z]=0
>>
>> I want to get function
>> c = G(angle)
>> or compute values of c for given angle ( without explicite
>> definition of
>> function G )
>>
>> How can I do it in Maxima ?
>>
>> Any suggestions?
>>
>>
>>
>> PS.
>>
>>
>> Theory of equation : http://xxx.lanl.gov/abs/hep-th/0701234
>>
>>
>>
>>
>>
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>>
```