Rational methods
Rational represents a reduced exact fraction. An Integer receiver uses the Integer surface; write a fraction such as 7/1 or convert to :Rational when Rational-only methods are required.
Method reference
| Full syntax | Result | Meaning |
|---|---|---|
rational.Numerator() |
Integer |
Return the reduced numerator. |
rational.Denominator() |
Integer |
Return the positive reduced denominator. |
rational.Negate() |
Rational |
Return the additive inverse. |
rational.Reciprocal() |
Rational |
Exchange numerator and denominator. |
rational.Abs() |
Rational |
Return the non-negative magnitude. |
rational.Floor() |
Integer |
Round toward negative infinity. |
rational.Ceil() |
Integer |
Round toward positive infinity. |
rational.Trunc() |
Integer |
Round toward zero. |
rational.Round(mode?) |
Integer |
Round with half-even by default; modes are half-even, half-up, toward-zero, floor, and ceil. |
rational.RoundTo(places, mode?) |
Rational |
Round to an exact number of decimal places. Negative places round left of the decimal point. |
rational.E(exponent) |
Rational |
Multiply exactly by 10^exponent. |
rational.ToMixedString() |
String |
Format as a mixed number. |
rational.ToDecimal() |
String |
Format an exact terminating or repeating decimal representation. |
rational.ToDecimalApproximation(options) |
exact or CertifiedApproximation |
Use {= fractionalDigits=n } to return a parseable certified decimal prefix. |
rational.ToRepeatingDecimal(options?) |
String \| null |
Format a repeat, with map options limit, onLimit, and useRepeatNotation. |
rational.ToRepeatingDecimalInfo(options?) |
Map |
Return the decimal, period length, and truncation status. |
rational.ToLocaleString(options) |
String |
Display with exact locale separators and grouping; source grammar is unchanged. |
rational.ToContinuedFraction(options?) |
Array |
Return terms; map options include maxTerms and long. |
rational.ToContinuedFractionString(options?) |
String |
Format the continued fraction; long=1 selects the alternate finite form. |
rational.ToContinuedFractionApproximation(options) |
exact or CertifiedApproximation |
Use {= maxTerms=n } to return a certified cylinder. |
rational.Convergents(maxCount?) |
Array |
Return successive continued-fraction convergents. |
rational.Convergent(index) |
Rational |
Return a one-based convergent. |
rational.ApproximationError(other) |
Rational |
Return the absolute error from another exact rational. |
rational.BestApproximation(maxDenominator) |
Rational |
Find the closest rational with a bounded denominator. |
rational.BestConvergent(maxDenominator) |
Rational |
Find the best continued-fraction convergent under the bound. |
rational.BitLength() |
Integer |
Return the combined exact storage bit length. |
rational.ToString() |
String |
Return the reduced fraction spelling. |
rational.CheckTraits() |
1 \| null |
Validate attached semantic traits. |
Structure, signs, and rounding
q := -7/3;
q.Numerator() ##@ == -7;
q.Denominator() ##@ == 3;
q.Negate() ##@ == 7/3;
q.Reciprocal() ##@ == -3/7;
q.Abs() ##@ == 7/3;
q.Floor() ##@ == -3;
q.Ceil() ##@ == -2;
q.Trunc() ##@ == -2;
(7/2).Round() ##@ == 4;
(5/2).Round("half-even") ##@ == 2;
(1/3).RoundTo(2) ##@ == 33/100;
(123/10).RoundTo(-1).Numerator() ##@ == 10;
(3/4).E(2).Numerator() ##@ == 75;Colon strings such as :half-even are ordinary RiX strings, so quoted spellings also work.
Formatting and continued fractions
q := 355/113;
(7/3).ToMixedString() ##@ == "2..1/3";
(1/8).ToDecimal() ##@ == "0.125";
cf := q.ToContinuedFraction();
cf.Len() ##@ == 3;
cf.Get(3) ##@ == 16;
q.ToContinuedFraction(2).Len() ##@ == 2;
q.ToContinuedFractionString().Len() ##@ > 0;
q.Convergents().Len() ##@ == 3;
q.Convergents(2).Len() ##@ == 2;
q.Convergent(2) ##@ == 22/7;
q.ApproximationError(22/7) ##@ == 1/791;
q.BestApproximation(100) ##@ == 311/99;
q.BestConvergent(100) ##@ == 22/7;
q.BitLength() ##@ > 0;
q.ToString() ##@ == "355/113";
q.CheckTraits() ##@ == 1;
(1/7).ToDecimalApproximation({= fractionalDigits=5 }).ToString() ##@ == "0.14285?";
(103993/33102).ToContinuedFractionApproximation({= maxTerms=3 }).ToString() ##@ == "3.~7~15?";
(3/2).ToContinuedFractionString({= long=1 }) ##@ == "1.~1~1";BestApproximation searches all denominators under the bound; BestConvergent restricts the result to continued-fraction convergents, so the answers can differ.