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.
Example 1:
> 5 / 2;
2.5
Example 2:
> x / 2;
x * 0.5
Example 3:
> x / x;
1
Example 4:
> 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]
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