RationalInterval methods
RationalInterval stores exact rational endpoints. Bounds are available both in source order (Start, End) and sorted order (Low, High).
Method reference
| Full syntax | Result | Meaning |
|---|---|---|
interval.Start() |
Rational |
Return the first stored endpoint. |
interval.End() |
Rational |
Return the second stored endpoint. |
interval.Low() |
Rational |
Return the lesser bound. |
interval.High() |
Rational |
Return the greater bound. |
interval.Width() |
Rational |
Return High() - Low(). |
interval.IsAscending() |
1 \| null |
Test whether source order is ascending. |
interval.Midpoint() |
Rational |
Return the arithmetic midpoint. |
interval.Mediant() |
Rational |
Return the endpoint mediant. |
interval.Negate() |
RationalInterval |
Negate the interval. |
interval.Reciprocal() |
RationalInterval |
Return the reciprocal interval; zero-containing intervals are invalid. |
interval.Overlaps(other) |
1 \| null |
Test whether two intervals overlap. |
interval.Contains(other) |
1 \| null |
Test whether the whole other interval is contained. |
interval.ContainsValue(value) |
1 \| null |
Test exact rational membership. |
interval.ContainsZero() |
1 \| null |
Test whether zero lies in the interval. |
interval.Intersection(other) |
RationalInterval \| null |
Return the shared interval. |
interval.Union(other) |
RationalInterval |
Return the covering interval. |
interval.ShortestDecimal(base?) |
Rational \| null |
Find the contained rational with the smallest power-of-base denominator. |
interval.DenominatorInterval(denominator?, onEmpty?) |
RationalInterval \| null |
Restrict to a fixed denominator grid. onEmpty is error, null, or mid. |
interval.Random(parameters?) |
Rational \| Array |
Sample exact points using the current .RNG; parameters are {: count, denominator?, tolerance? }. |
interval.RandomPartition(parameters?) |
Array |
Split at distinct random exact points using the same parameter tuple. |
interval.E(exponent) |
RationalInterval |
Multiply both bounds exactly by 10^exponent. |
interval.BitLength() |
Integer |
Return the combined exact storage bit length. |
interval.ToMixedString() |
String |
Format both endpoints as mixed numbers. |
interval.ToRepeatingDecimal(options?) |
String \| null |
Format both endpoints as repeating decimals with an optional limit policy. |
interval.ToCompactDecimal() |
String |
Compact a shared decimal prefix and endpoint suffixes. |
interval.ToRelativeMidDecimal() |
String |
Format exact offsets around the midpoint. |
interval.ToRelativeDecimal() |
String |
Format exact offsets around a short contained decimal. |
interval.ToString() |
String |
Return the exact interval spelling. |
interval.CheckTraits() |
1 \| null |
Validate attached semantic traits. |
Bounds and interval operations
i := 1/4:3/4;
j := 1/2:1;
i.Start() ##@ == 1/4;
i.End() ##@ == 3/4;
i.Low() ##@ == 1/4;
i.High() ##@ == 3/4;
i.Width() ##@ == 1/2;
i.IsAscending() ##@ == 1;
i.Midpoint() ##@ == 1/2;
i.Mediant() ##@ == 1/2;
i.Negate() ##@ == (-3/4):(-1/4);
(1:2).Reciprocal() ##@ == 1/2:1;
i.Overlaps(j) ##@ == 1;
(0:1).Contains(i) ##@ == 1;
i.ContainsValue(1/2) ##@ == 1;
(-1:2).ContainsZero() ##@ == 1;
i.Intersection(j) ##@ == 1/2:3/4;
i.Union(j) ##@ == 1/4:1;Grids, random sampling, and formatting
i := 1/10:4/10;
i.ShortestDecimal() ##@ == 1/10;
i.ShortestDecimal(2) ##@ == 1/4;
i.DenominatorInterval(10) ##@ == 1/10:2/5;
(1/3:2/3).DenominatorInterval(2) ##@ == 1/2:1/2;
.RNG(:default, {= seed=456 });
point := (0:1).Random({: 1, 1000 });
(0:1).ContainsValue(point) ##@ == 1;
parts := (0:1).RandomPartition({: 4, 1000 });
parts.Len() ##@ == 4;
(1/4:3/4).E(2) ##@ == 25:75;
i.BitLength() ##@ > 0;
(7/3:8/3).ToMixedString().Len() ##@ > 0;
i.ToRepeatingDecimal().Len() ##@ > 0;
i.ToCompactDecimal().Len() ##@ > 0;
i.ToRelativeMidDecimal().Len() ##@ > 0;
i.ToRelativeDecimal().Len() ##@ > 0;
i.ToString() ##@ == "1/10:2/5";
i.CheckTraits() ##@ == 1;Seeding .RNG makes examples and simulations repeatable. Without an explicit seed, the host’s configured random source is used.