[Maxima] solving system of equations
adammaj1 at o2.pl
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)]]
> algsys([a*x+y=3,x+b*y=1],[a,b]) =>
> [[a = -(y-3)/x,b = -(x-1)/y]]
> 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)]]
> 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.
Thx for answers.
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 */
/* function */
/* 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 */
e2:df(z,n)-1; /* e2=0 it means attracting points */
========== end of code ==============
it works. For periods>=7 maxima has problems.
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