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## [Help-gsl] multiroot and complex

 From: sholman Subject: [Help-gsl] multiroot and complex Date: Mon, 4 Apr 2016 15:13:26 -0600 User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:38.0) Gecko/20100101 Thunderbird/38.6.0

```Hello All, I have successfully ran examples in GSL from my IDE (eclipse
mars) and in the terminal "by hand", but I want to ask before I start
this new project, a question.

I have polynomials, and/or systems of such, that are nonlinear and
complex, something like,

0 = fn1(a1,#,I)*z  + fn2(a2,#,I)*z^2 + fn3(a3,#,I)*z^3 + ...

where "#" are just numbers (complex), and "I" is sqrt{-1},

and I want to solve for the unknowns a1, a2, a3, ... by setting each
coefficient equal to zero. This is similar to solving differential
equations by the power series method.

Anyway, the coefficient/equations are long and so I thought I'd ask
first. As I notice things like gsl_vector_complex_real and
gsl_complex_vector_imag, but not "complex" versions of gsl_vector or
gsl_vector_get, can I change the example code;

https://www.gnu.org/software/gsl/manual/html_node/Example-programs-for-Multidimensional-Root-finding.html#Example-programs-for-Multidimensional-Root-finding

to one for (a) polynomial(s) in a ring C[z]..?

*********

I also noticed;

https://www.gnu.org/software/gsl/manual/html_node/Roots-of-Polynomials-Examples.html#Roots-of-Polynomials-Examples

but again it looks like the coefficients might not be able to be
complex....?

If there is an example somewhere of something like solving for the roots
of P(z) = z^6 + 3*I*z^4 + ln(3)*I*z = 0, then I can adapt it as necessary.

Also, is there a way to implement support right away for very large or
small numbers beyond just declaring doubles?