> <\body> This document contains simple examples using analytic functions within . Basic calculations are shown in . The following sample of code shows how to constuct simple analytic functions operating on balls: <\cpp-code> #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; } The following session shows basic operations available for constructing and studing log>: <\session|mathemagix|default> <\input> <|input> use "continewz"; type_mode? := true; <\unfolded-io> <|unfolded-io> z == analytic (ball 0.0, ball 1.0) <|unfolded-io> +1.000000000000000000*z+|)>*z+|)>*z+|)>*z+|)>*z+|)>*z+|)>*z+|)>*z+|)>*z+O|)>>: ,Ball|)>|)>> <\unfolded-io> <|unfolded-io> l == log (1 - z) <|unfolded-io> -1.0000000000000000*z-0.50000000000000000*z-0.3333333333333333*z-0.25000000000000000*z-0.20000000000000000*z-0.1666666666666667*z-0.1428571428571429*z-0.12500000000000000*z-0.11111111111111111*z+O|)>>: ,Ball|)>|)>> <\unfolded-io> <|unfolded-io> l[20] <|unfolded-io> : |)>> <\unfolded-io> <|unfolded-io> radius_bound l <|unfolded-io> : > <\unfolded-io> <|unfolded-io> upper_bound (l, 0.8) <|unfolded-io> : > <\unfolded-io> <|unfolded-io> lower_bound (l, 0.8) <|unfolded-io> : > <\unfolded-io> <|unfolded-io> tail_bound (l, 0.8, 20) <|unfolded-io> : > <\unfolded-io> <|unfolded-io> l # (complex ( 1.0, \ 1.0)) # (complex ( 1.0, -1.0)) \ \ # (complex (-1.0, -1.0)) # (complex (-1.0, \ 1.0)) <|unfolded-io> -1.000000000000000*z-0.500000000000000*z-0.33333333333333*z-0.250000000000000*z-0.200000000000000*z-0.16666666666667*z-0.142857142857143*z-0.125000000000000*z-0.111111111111111*z+O|)>>: ,Ball|)>|)>> The latter computation corresponds to the evaluation of log> along the following loop around the pole: \; <\with|par-mode|center> |gr-frame|>|gr-geometry||gr-grid||1>|gr-grid-old||1>|gr-edit-grid-aspect|||>|gr-edit-grid||1>|gr-edit-grid-old||1>|arrow-length|10ln|arrow-height|6ln|gr-arrow-end|\|magnify|2.66666666666667|||magnify|0.666666666666667||>>||magnify|0.666666666666667||>>||magnify|0.666666666666667||>>||magnify|0.666666666666667||>>>> . If you don't have this file, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.> <\initial> <\collection>