Developer documentation

Multivariate Bernstein subdivision solver

The solver solver_mv_sbd computes the real solutions of a multivariate polynomial system in a box by subdivision methods. It can be used as command with a file name argument:

solver_mv_sbd_double ex2d

The file system should be described in a file with the following format:

n0
f1;
f2;
...
a1 b1 ... an bn

where

  • n0 is the number of equations,
  • f1, f2, ... are the polynomials expressed in the monomial basis,
  • a1, b1, ..., an, bn are the lower and upper bound of the interval for the first, ..., nth coordinates of the solutions.

Here is an example:

2
x0^2+x1^2-1;
x0*x1-0.25;
-2 2 -2 2

The output of

Equations:
x0^2+x1^2-1.000000
x0*x1-0.250000
Box: [-2,2] [-2,2]
Strategy: 7
Solutions:
[0.965926, 0.258819], [0.258819, 0.965926], [-0.258819, -0.965926], [-0.965926, -0.258819]
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