# [Maxima] polynomial equations

Richard Fateman fateman at cs.berkeley.edu
Wed Sep 26 12:16:48 CDT 2007

```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.

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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>
```