** Next:** Implementation
** Up:** General purpose solving algorithm
** Previous:** The 3B method
** Contents**

##

Simplification procedure

Most of the procedures in `ALIAS` will accept as optional last
argument
the name of a *simplification procedure*: a user-supplied
procedure that take as input
the current box and proceed to some further reduction of
the width of the box or even determine that there is no
solution for these box, in which case it should return
-1.
Such procedure must be implemented as:

int Simp_Proc(INTERVAL_VECTOR & P)

where `P` is the current box. This procedure must
return either -1 or any other integer. If a reduction of an interval
is done within this procedure, then `P` must be updated
accordingly.
This type of procedure allows the user to add information to the
algorithm without having to add additional equations.
The simplification procedure is applied on a box before
the bisection and is used within the 3B method if this heuristic is applied.

Note that the
Maple package associated to `ALIAS` allows in some cases to
produce automatically the code for such procedure (see the ALIAS-Maple
manual) and that section 2.17 presents a standard
simplification procedure that may be used for almost any system of equations.

** Next:** Implementation
** Up:** General purpose solving algorithm
** Previous:** The 3B method
** Contents**
Jean-Pierre Merlet
2012-12-20