The generic Solver

psi 0 0.2 x 1 2.5If

Interval_Solver -F f -R rIn that case the program will call the procedure

Instead of using the `Solve_General_Interval` procedure of `ALIAS` you may use the
`Solve_General_Gradient_Interval`
procedure which requires the gradient of the equations. The gradient
equations are defined in a formula file (e.g. `g`) and you may
then run:

Interval_Solver -F f -G g -R rNote that the equations in the gradient formula file should be ordered with respect to the unknowns using the same ordering than the one used in the range file. Thus for the range file:

x 1 2.5 y 0 0.2and the formula file

eq=y+3*x eq=x^2+x*ydenoted

eq=3 eq=1 eq=2*x+y eq=x

Similarly,
instead of using the `Solve_General_Gradient_Interval` procedure of `ALIAS` you may use the `Solve_General_JH_Interval`
procedure which requires the gradient and hessian of the equations.
The hessian
equations are defined in a formula file (e.g. `h`) and you may
then run:

Interval_Solver -F f -G g -H h -R rNote that the hessian formula file should respect the same ordering than for the gradient formula file. For our previous example the hessian file will be:

eq=0 eq=0 eq=0 eq=0 eq=2 eq=1 eq=1 eq=0Note also that the various formula files may be easily obtained by using the MAPLE procedures described in the next section (12.3).

The result of the computation will be written in a *result
file*. Each line of the result file gives the range for one of the
unknowns, using the same ordering than for the range file (in our
example the range of `x`, followed by the range for `y`). A
range is indicated by two reals separated by a blanc character.
If instead of range the
result file contain the keyword `FAILED`
it means that the solver has been unable to solve the equations. This
keyword is followed by an integer which indicate the reason of the
failure:

- -1: an insufficient storage space has been defined for the solver
- -4: the number of equation in the formula file is incorrect

Whatever the used solving procedure, some
parameters are to be set. The solver
will prompt you to give the values of these parameters. If you want to
avoid this interactive behavior you may define the parameters in a
*configuration file*
and the solver will proceed directly to the
solution. A configuration file consists in a list of keywords followed
by a value. Most of these keywords refers to parameters in the solving
procedure of `ALIAS`, please refer to the corresponding section
for their meaning:

`Result_File name`: the result will be stored in the`name`file instead of the default`.result_IS`file.`Iteration integer`: the maximum number of boxes that may be used by the algorithm`Debug integer`: the debug level for the solving procedure as indicated by`Debug_Level_Solve_General``AccuracyF real`: the`epsilonf`parameter of the solving procedure`AccuracyV real`: the`epsilon`parameter of the solving procedure`Order integer`: the`Order`parameter of the solving procedure`Stop integer`: the`Stop`parameter of the solving procedure`MaxSol integer`: the maximum number of solutions you are looking for`Kanto integer`: the`ApplyKanto`parameter of the solving procedure`DifferenceS real`: the`Dist`parameter of the solving procedure`Machine_Name char`: the name of a computer that will be used during a run of the parallel version of the solver`Single_Bisection`: if you use the solver with the -H or -G option the bisection process will bisect only one variable at a time