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Jun 3, 2024
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Add documentation about boolean/set functions #669

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20 changes: 19 additions & 1 deletion docs/src/manual/usage.md
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Expand Up @@ -93,7 +93,7 @@ sin(Y)

## Comparisons and set operations

All comparisons and set operations for `Real` have been purposely disallowed to prevent silent errors.
All comparisons and set operations for `Real` have been purposely disallowed to prevent silent errors. For instance, `x == y` does not implies `x - y == 0` for non-singleton intervals.

```@repl usage
interval(1) < interval(2)
Expand All @@ -104,6 +104,24 @@ intersect(interval(1, 2), interval(2))
intersect_interval(interval(1, 2), interval(2))
```

In particular, `if ... else ... end` statements used for floating-points will generally break with intervals.

One can refer to the following:
- `<`: cannot be used with intervals. See instead [`isstrictless`](@ref) or [`strictprecedes`](@ref).
- `==`: allowed if the arguments are singleton intervals, or if at least one argument is not an interval (equivalent to [`isthin`](@ref)). Otherwise, see [`isequal_interval`](@ref).
- `iszero`, `isone`: allowed (equivalent to [`isthinzero`](@ref) and [`isthinone`](@ref) respectively).
- `isinteger`: cannot be used with intervals. See instead [`isthininteger`](ref).
- `isfinite`: cannot be used with intervals. See instead [`isbounded`](@ref).
- `isnan`: cannot be used with intervals. See instead [`isnai`](@ref).
- `in`: allowed if at least one argument is not an interval and the interval argument is a singleton. Otherwise, see [`in_interval`](@ref).
- `issubset`: cannot be used with intervals. See instead [`issubset_interval`](@ref).
- `isdisjoint`: cannot be used with intervals. See instead [`isdisjoint_interval`](@ref).
- `issetequal`: cannot be used with intervals.
- `isempty`: cannot be used with intervals. See instead [`isempty_interval`](@ref).
- `union`: cannot be used with intervals. See instead [`hull`](@ref).
- `intersect`: cannot be used with intervals. See instead [`intersect_interval`](@ref).
- `setdiff`: cannot be used with intervals. See instead [`interiordiff`](@ref).



## Custom interval bounds type
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