## solving a system

### system

• The system to solve must have at most 5 equations or inequalities
• It must be constrained, i.e. its set of solution must consist in a finite number of points.
Hence, the system must have the same number of equations and of unknowns, with optional additional equalities.
ALIAS may deal with other type of systems but not with through this interface.
• By convention the name of the unknowns are `x`, `y`, `z`, `s`, and `t` in this order.
• Expression may involve any usual mathematical functions and may be not algebraic (for example `3 * Sin[x]^2 + Cos[x] - y^2 = 0` is valid). Beware however that restrictions are imposed on some expressions such as division or mathematical functions with a restricted definition domain (see restrictions of use.)
• Numerical constants in expressions are not intervals.

### solutions

Different methods lead to different kind of solutions.

• with General: solutions are intervals
• with Gradient: solutions are either intervals or intervals degenerated to a point. In the first case, we have a singular solution, in the second we have got a box which contains an unique solution, and the box is an approximation of this solution, infinitely refinable.

### equations

• Input syntax for expressions is a linear syntax similar to Maple's or Mathematica's one. Hence are valid:

• mathematical operators: `+`, `-`, `*`, and `/` as well as `^` or `**` for exponentiation, (product operator must be explicit)
• most of the usual mathematical functions: `Sin`, `arccos`, `ArgTanh`, ...
• any parenthesis scheme `()` or `[]`.
• A valid example is:
• ` x*cos(y)+x*y+1=0`
• ` y*sin(y)+x-2 = 0 `

equation 1 : 0

equation 2 : 0

equation 3 : 0

equation 4 : 0

equation 5 : 0

the equations and continue.