## Name:

/ division function

## Library names:

sollya_obj_t sollya_lib_div(sollya_obj_t, sollya_obj_t) sollya_obj_t sollya_lib_build_function_div(sollya_obj_t, sollya_obj_t) #define SOLLYA_DIV(x,y) sollya_lib_build_function_div((x), (y))

## Usage:

function1 / function2 : (function, function) -> function interval1 / interval2 : (range, range) -> range interval1 / constant : (range, constant) -> range interval1 / constant : (constant, range) -> range

## Parameters:

• function1 and function2 represent functions
• interval1 and interval2 represent intervals (ranges)
• constant represents a constant or constant expression

## Description:

• / represents the division (function) on reals. The expression function1 / function2 stands for the function composed of the division function and the two functions function1 and function2, where function1 is the numerator and function2 the denominator.
• / can be used for interval arithmetic on intervals (ranges). / will evaluate to an interval that safely encompasses all images of the division function with arguments varying in the given intervals. If the intervals given contain points where the division function is not defined, infinities and NaNs will be produced in the output interval. Any combination of intervals with intervals or constants (resp. constant expressions) is supported. However, it is not possible to represent families of functions using an interval as one argument and a function (varying in the free variable) as the other one.

> 5 / 2;
2.5

> x / 2;
x * 0.5

> x / x;
1

> 3 / 0;
NaN

## Example 5:

> diff(sin(x) / exp(x));
(exp(x) * cos(x) - sin(x) * exp(x)) / exp(x)^2

## Example 6:

> [1;2] / [3;4];
[0.25;0.66666666666666666666666666666666666666666666666668]
> [1;2] / 17;
[5.8823529411764705882352941176470588235294117647059e-2;0.11764705882352941176470588235294117647058823529412]
> -13 / [4;17];
[-3.25;-0.76470588235294117647058823529411764705882352941175]