HERA-0.2

Synopsis

# Documentation

A wrapper around Ball allowing the results of operations like division by interval containing zero to be represented and do not cause errors.

Nothing represents undefined interval.

Make an interval from a ball and normalize it to specified precision.

Just make an interval from a ball.

Make an interval from two endpoints so that no precision is lost.

Arguments

 :: Precision precision of the interval's center -> Dyadic left endpoint -> Dyadic right endpoint -> Interval

Make an interval from two endpoints.

Checks if second interval is inside the first. _|_ is above all.

Checks if interval contains dyadic. _|_ contains everything.

includes :: Interval -> Interval -> InclusionSource

Returns Below if second interval is inside first, Above if converse, NoInclusion otherwise.

Return the intersection of two intervals. The resulting interval's center has specified precision.

If one of the intervals is _|_ then just return the other (even if it is _|_).

Return the intersection of two intervals so that no precision is lost.

Negate the interval. neg _|_ = _|_.

Addition. If one of the arguments is _|_, so is the result.

Multiplication. If one of the arguments is _|_, so is the result

Subtraction. If one of the arguments is _|_, so is the result

Division. If one of the arguments is _|_ or divisor contains 0 then result is _|_.

Square root. If one argument is _|_ or interval contains 0 then result is _|_.

` e ^ i ` If argument is _|_ so is the result.

Natural logarithm. If one argument is _|_ or interval contains 0 then result is _|_.

Compare two intervals. If one of them is _|_ the result is incomparable, otherwise result is comparison of balls.

Maximum of intervals. If one interval is _|_ so is the result.

Similar to maxI.

Center of interval. Center on _|_ will result in fail.

Lower endpoint of interval with precision of the center. Lower on _|_ will result in fail.

Upper endpoint of interval with precision of the center. Upper on _|_ will result in fail.