The

- a file, called
a
*formula file*, in which is written the analytical form of the equation - name and ranges for the variables

eq=(y^2-1)*z+(2*y*t-2)*x eq=2+(-10*t+(-10+2*y*t)*y)*y+((4+4*y^2)*z+(4+4*y*t-x*z)*x)*x eq=(2*y*t-2)*z+(t^2-1)*x eq=2+(4*x+(4-x*z)*z)*z+((-10+4*z^2)*y+(-10+4*x*z+2*y*t)*t)*tis a valid formula file in

The parser may handle almost any complex analytical equation based on the most classical mathematical functions, using MAPLE notation. Currently you may use the following operators:

- arithmetic operator: "+","-","/","*"," " or "**" (power)
- trigonometric and inverse trigonometric functions:
`sin`,`cos`,`tan`,`arcsin`,`arccos`,`arctan`(which may be used with the syntax`arctan`(x) or`arctan`(y,x)) - hyperbolic functions:
`sinh`,`cosh`,`tanh`,`arcsinh`,`arccosh`,`arctanh` - mathematical functions:
`abs`(absolute value),`log`,`log10`,`exp`,`sqrt` - integer functions:
`ceil`(returns an interval which bounds are the smallest integer greater than or equal to each bound of the box,`floor`(returns an interval which bounds are the greatest integer less than or equal to each bound of the box),`round`(returns an interval which bounds are the nearest integer of each bound of the box)

`Min`: this operator takes as input a list of mathematical expression and will return an interval reduced to the minimum value of all the lower bound of the interval evaluation of each term in the list. For example:Min(3,3*x1,3*x2+x3,4*(x2+x1))

for`x1`in [-1,1],`x2`in [0,2],`x3`in [3,10] will return the interval [-4,-4]`Max`: this operator is similar to`Min`except it returns the maximal value of the upper bound on the interval evaluation. For the previous example`Max`will return the interval [16,16]`MinMax`: this operator applied on the list will return the interval [`Min`(),`Max`()]. In the previous example the interval will be [-4,16]

The parser may also handle intervals. For example you may evaluate an equation in which some coefficients are intervals. In the equation these coefficients should be indicated using the MAPLE notation as in the following example:

INTERVAL(0.1 .. sin(1))