# [Maxima] solving system of equations

Sat Mar 29 05:39:14 CDT 2008

```Stavros Macrakis pisze:
> On Wed, Mar 26, 2008 at 12:32 PM, Adam Majewski <adammaj1 at o2.pl> wrote:
>>  algsys([2*z=1, z*z+c=z], [c]);
>>  does not work
>
> The meaning of algsys( <equations>, <variables> ) is:
>
> find the constraints on the variables which make the equations true
> for all values of parameters in the equations. So:
>
>        algsys([a*x+y=3,x+b*y=1],[x,y]) =>
>               [[x = (3*b-1)/(a*b-1),y = (a-3)/(a*b-1)]]
> but
>        algsys([a*x+y=3,x+b*y=1],[a,b]) =>
>               [[a = -(y-3)/x,b = -(x-1)/y]]
> and
>        algsys([a*x+y=3,x+b*y=1],[a,b,x,y]) =>
>               [[a = (3*%r1-%r1*%r2)/(%r1*(1-%r1*%r2)),b = %r1,x =
> 1-%r1*%r2,y = %r2]]
> and even
>        algsys([a*x+y=3,x+b*y=1],[x,b]) =>
>               [[x = -(y-3)/a,b = (y+a-3)/(a*y)]]
>        algsys([a*x+y=3,x+b*y=1],[y,a]) =>
>               [[y = -(x-1)/b,a = (x+3*b-1)/(b*x)]]
> etc.
>
> In your equations, if you treat z as a parameter (that is, don't
> include it in the variable list), algsys will find no solutions,
> because there is no value of c which will make 2*z=1 true for all
> values of z.
>
>               -s

Now I know what I have done wrong .
I have changed the way of solution.
Here is the batch file :

The first question  was a case for period=1.
( this code looks for roots points of mandelbrot set )

======== code ============
/* period */
n:7;
/* function */
f(z):=z*z+c;
/* iteration of function */
fn(z,n_max):=block(for n thru n_max do z:f(z),return(z));
/* periodic points  fn(z,n)=z */
F(z,n):=fn(z,n)-z;             /* the same as above */
e1:F(z,n);                     /* e1=0 */
/* */
df(z,n):=diff(fn(z,n),z,1);
e2:df(z,n)-1;                   /* e2=0 it means attracting points */
e3:eliminate([e1,e2],[z]);
solve([e3[1]], [c]);

========== end of code ==============

it works. For periods>=7 maxima has problems.

Regards