Numerator

Generated from the engine's own definition: compute-engine's symbol, which we neither extend nor document by hand.

Numerator of an expression

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageNumerator!↗

Numerator(number) -> nothing | numberNumerator of an expression

Julianumerator(number)Rustnumerator(number)

Typed signatures

Type	Package	Applies
(number) -> nothing | number	compute-engine	always
(number, any*) -> nothing | number	number-theoryreplaces residues	always
(number, any*) -> nothing | number	residuesreplaces compute-engine	always
(value) -> value	adelesreplaces number-theory	on ProfiniteNumber

Domain: Compute engine

Details

• Over -> QuotientRing(Integers, p) (Wolfram's Modulus -> p, p prime) reads the expression over the field $\mathbb{Z}/p$ (@enumeratio/residues): a quotient in lowest terms over $\mathbb{Q}$ with integer coefficients, then its coefficients mod p. A constant denominator, and a monomial one when no polynomial divides anywhere, moves its unit into the numerator ($x/(2y) \to 4x/y$ mod 7). It stays unevaluated where Wolfram has no answer, as for a denominator that vanishes mod p. It threads over a list. The unit of a denominator of several terms follows Wolfram's convention for a single unknown; with several unknowns the result may differ from Wolfram's by a unit (the same function). Over -> Integers is the ordinary numerator.

Examples

1 more kept as data, checked against the oracles

Basic #

live ↗

In$\mathrm{Numerator}(\frac{3}{4})$Out$3$

An integer is its own numerator

live ↗

In$\mathrm{Numerator}(5)$Out$5$

live ↗

In$\mathrm{Numerator}(\frac{2}{3})$Out$2$

live ↗

In$\mathrm{Numerator}(\frac{(x-2)(x-1)}{(x-3)^2})$Out$(x-2)(x-1)$

live ↗

In$\mathrm{Numerator}(\frac{\sin(x)^{a}}{(\sin(x)-2)^{b}})$Out$\frac{\sin(x)^{a}}{(\sin(x)-2)^{b}}$

Scope #

live ↗

In$\mathrm{Numerator}(\frac{3}{7})$Out$3$

live ↗

In$\mathrm{Numerator}(\frac{3}{7}+\frac{1}{11}i)$Out$33+7i$

live ↗

In$\mathrm{Numerator}(\frac{(x-1)^2}{(x-3)(x-2)})$Out$(x-1)^2$

live ↗

In$\mathrm{Numerator}(\frac{1}{xa^{b}})$Out$a^{-b}$

live ↗

In$\mathrm{Numerator}(2b^2x^{y})$Out$2b^2x^{y}$

live ↗

In$\mathrm{Numerator}(\frac{24x^{y}}{(3b)^3}, (\mathrm{Over},ℤ/5ℤ))$Out$2x^{y}$

live ↗

In$\mathrm{Numerator}(\frac{\frac{x}{3}+\frac{3y}{4}}{\frac{3x}{5}-\frac{y}{2}}, (\mathrm{Over},ℤ/7ℤ))$Out$6x+3y$

About

Examples	13
Checked against	Wolfram Language 10 agree2 differSageMath 8 agree3 differJulia 4 agree1 differ1 errorRust 4 agree1 differ
Crosswalk	Wolfram LanguageJuliaRust

Implementation

mappedsagepackages/oracle/src/mappings.ts

Generic -- works for a plain rational/integer and for a ProfiniteNumber's Sage counterpart (Qhat) alike.

mappedjuliapackages/oracle/src/mappings.ts

mappedrustpackages/oracle/src/mappings.ts