The SimplexConsistency procedure

This simplification procedure may be used to solve systems of equations as soon as the system has at least two equations with polynomial terms in at least one variable. The principle used for this simplification procedure is explained in the ALIAS-C++ manual section of Solve_Simplex.

The syntax of this procedure is:

 
\SimplexConsistency(EQ,VAR,"Simp"):

where EQ is a list of equation, VAR a list of variable name and Simp is the name of the simplification procedure that will be written in the file Simp.C.

The behavior of this simplification procedure may be modified by using the following variables:

• `ALIAS/full_simplex`: an integer n. The simplification procedure will try to improve the width of the n largest variable ranges. If n is -1 (the default value for this variable) the procedure will just return -1 if there is no solution to the system but no improvement on the range of the variable will be obtained. n may be larger than the number of variables.
• `ALIAS/diam_simplex`: a floating point number f (default value: 0.1). The procedure will not improve the range of variable whose width is lower than f
• `ALIAS/min_diam_simplex`: a floating point number f (default value: 1e7). The procedure will not try to improve the range of variables whose width is greater than f
• `ALIAS/mid_simplex`: by default the procedure uses a linearization at the lower bound of the variables. If you set this flag to 1, then the linearization point will be the mid point of the range

Two remarks about this procedure:

1. it is usually very effective
2. it may be computer intensive for large systems: hence its use should in general be avoided within the 3B method (see section 4.5)
3. it is not numerically safe with the current implementation of the simplex i.e. in some cases it may lead to miss some solutions