This document contains simple examples using analytic functions within Mathemagix.

1.Use from C++

Basic calculations are shown in continewz/test/analytic_test.cpp. The following sample of code shows how to constuct simple analytic functions operating on balls:

#include <numerix/ball_complex.hpp>
#include <continewz/analytic_matrix.hpp>
using namespace mmx;

#define R          ball<floating<> >
#define C          ball<complex<floating<> > >
#define Polynomial polynomial<C>
#define Analytic   analytic<C>

int
main () {
  Polynomial P= seq (C (1), C (-2), C (3));
  Analytic f (1);
  Analytic g (P);

  mmout << "f= " << f << lf;
  mmout << "g= " << g << lf;
  mmout << "f + g= " << f + g << lf;
}

2.Use from the interpreter

The following session shows basic operations available for constructing and studing :

Mmx]  

use "continewz";
type_mode? := true;

Mmx]  

z == analytic (ball 0.0, ball 1.0)

Mmx]  

l == log (1 - z)

Mmx]  

l[20]

Mmx]  

radius_bound l

Mmx]  

upper_bound (l, 0.8)

Mmx]  

lower_bound (l, 0.8)

Mmx]  

tail_bound (l, 0.8, 20)

Mmx]  

l # (complex ( 1.0,  1.0)) # (complex ( 1.0, -1.0))
  # (complex (-1.0, -1.0)) # (complex (-1.0,  1.0))

The latter computation corresponds to the evaluation of along the following loop around the pole :