Rational

This constructor performs no normalization or validation. Prefer Rational.create for user input and for values that must use Nerdamer's normal reduced-fraction representation.

Fraction strings are reduced and a negative denominator is moved to the numerator. Decimal and scientific-notation strings are converted to the exact rational represented by their finite decimal text. Those forms also set Rational.asDecimal, so later text output normally remains decimal even though the stored arithmetic stays exact.

DivisionByZeroError Thrown when a fraction string has a zero denominator.

Rational and string operands compute exact rational division and return a new Rational. Expression operands promote this rational to an Expression and preserve operand direction, returning this / expression.

DivisionByZeroError Thrown when exact rational division requires inversion of zero.

Rational/string comparisons are exact and use cross multiplication, so decimal-presentation metadata does not affect equality. Expression input delegates to Nerdamer's symbolic comparison semantics.

The operation is folded pairwise and preserves decimal presentation intent when it is present on an operand.

Rational/string comparisons are exact. Expression input delegates to Nerdamer's symbolic ordering rules, including their restrictions on unordered complex values.

The original object is not modified. For normally constructed rationals, the returned denominator remains positive and the sign is carried by the numerator.

DivisionByZeroError Thrown when this rational is exactly zero.

This checks only whether the denominator is exactly 1n. Values built with the raw constructor must therefore be reduced first if equivalent forms such as 8/4 should be recognized as integers.

Nerdamer's normal rational representation keeps the denominator positive, so the numerator carries the sign. Raw constructor values with a negative denominator do not follow that representation.

This is a marker-based guard rather than an instanceof check, which allows compatible Nerdamer rational objects to be recognized where constructor identity is not the useful distinction.

The operation is folded pairwise and preserves decimal presentation intent when it is present on an operand.

Rational/string input is handled with exact rational arithmetic. Expression input is promoted to Nerdamer's symbolic arithmetic. The original operands are not mutated.

The operands are converted to a common denominator, Nerdamer's integer modulo operation is applied to the corresponding numerators, and the resulting fraction is reduced. Decimal presentation is preserved when either operand was marked for decimal output.

A native RangeError when num is zero.

Rational/string input is added exactly and reduced. If either rational operand carries decimal presentation intent, the rational result carries it as well. Expression input is promoted to Nerdamer's symbolic arithmetic.

Expression exponents use Nerdamer's general symbolic power logic. Integer rational exponents use exact bigint exponentiation, with negative exponents handled by first inverting the base. Non-integer rational exponents are evaluated through decimal.js and converted back to a Rational, so that overload is a real numerical approximation rather than symbolic radical or principal-complex evaluation. Decimal presentation from a numerical result is retained, while an exact integer result stays exact unless the base already carried decimal presentation intent.

ZeroToZeroPowerError Thrown for the indeterminate form 0^0.

DivisionByZeroError Thrown when zero is raised to a negative integer power.

Currently only precision is acted upon. Setting it updates the global decimal.js precision, records the value used by Rational.toDecimalString, and recomputes Rational.PI and Rational.E at the new precision.

Scientific formatting is selected when options.scientific supplies an integer significant-digit count from 1 through 1e9. The requested count is preserved in the coefficient, including trailing zeroes. Otherwise decimal formatting is selected when Rational.asDecimal is set or when options.decimal is truthy. Non-integer decimal output uses decimal.js; an optional options.precision temporarily controls its significant-digit precision for this conversion. Integer decimal output includes a .0 suffix. Without decimal formatting, non-integer fractions are emitted from the stored numerator and denominator, and integers as plain text.

Rational/string multiplication is exact and reduced. If either rational operand carries decimal presentation intent, the rational result carries it as well. Expression input is promoted to Nerdamer's symbolic arithmetic.

precision is the maximum number of digits generated after the decimal point. The conversion truncates at that position rather than rounding, then removes trailing zeros and a trailing decimal point. When omitted, the configured Rational precision is used. This method does not depend on Rational.asDecimal; it always requests decimal text.

Strings always produce a new value through Rational.create. An existing Rational is returned by identity unless ensureCopy is true.

This is one of the few mutating methods on Rational; it updates this object and returns the same reference.

This conversion is approximate and subject to the range and precision limits of JavaScript number. Numerator and denominator values that are both safe integers use native division directly; larger values retain the Decimal-backed fallback so finite ratios are not lost merely because an individual component exceeds the native numeric range. Use the rational representation or Rational.toDecimal when native-number limits are unacceptable.