Homotopy continuation

This document briefly describes how to use numeric homotopy continuation within Mathemagix for solving a polynomial system. 

Mmx]  
use "continewz";
include "continewz/homotopy_solve.mmx"
 
Mmx]  
x1 == coordinate ('x[1]); x2 == coordinate ('x[2]);
 
Mmx]  
f1 == x1 * x2 + x1^2 + x2^2 + x1 - 20
 

Mmx]  
f2 == x1 - x2^2 - x1^2 + x2 - 10
 

Mmx]  
sys == [ f1, f2 ]
 

Mmx]  
sols == homotopy_solve (sys, [ x1, x2 ], 1 :> Ball (Floating, Complex Floating))
 

Mmx]  
[ eval (sys [j], [ x1, x2 ], row (sols, 0)) | j in 0..2 || i in 0..2 ]
 

Mmx]  
bit_precision:= 128;
 
Mmx]  
sols[0,0]
 

Mmx]  
center sols[0,0]
 

Mmx]  
radius sols[0,0]

© 2012 Joris van der Hoeven and Grégoire Lecerf
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU General Public License. If you don't have this file, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.