Divides

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

Divides(a, b) returns True if a divides b (i.e. b is an integer multiple of a), corresponding to the notation a ∣ b. Both operands are integers; a symbolic operand keeps the relation unevaluated.

✓ checked against that system · ! checked, with disagreements (hover a chip)FungrimDivides↗Fungrim entry4ec333↗805c7a↗ed65c8↗Wolfram LanguageDivisible!↗

Divides(integer, integer) -> booleanas compute-engine declares it

Juliaiszero(mod(ZZ(integer), ZZ(integer)))Rustdivides(integer, integer)

Typed signatures

Type	Package	Applies
(integer, integer) -> boolean	compute-engine	always

Domain: Compute engine

Examples

Basic #

2 divides 10

live ↗

In$2\mid10$Out$\mathrm{True}$

2 does not divide 5

live ↗

In$2\mid5$Out$\mathrm{False}$

Scope #

Exact multiples divide

live ↗

In$3\mid6$Out$\mathrm{True}$

Decided exactly even for a 3000-digit number

live ↗

In$16\,001\mid1+10^{3\,000}$Out$\mathrm{True}$

Applications #

Digit sum of 2895 is 24, a multiple of 3

live ↗

In$3\mid2\,895$Out$\mathrm{True}$

Alternating digit sum is a multiple of 11

live ↗

In$11\mid918\,082$Out$\mathrm{True}$

Properties #

Predicates evaluate inside a list

live ↗

In$\bigl\lbrack\mathrm{IsInteger}(5), 2\mid10\bigr\rbrack$Out$\bigl\lbrack\mathrm{True}, \mathrm{True}\bigr\rbrack$

$48 = 8\cdot 6$

live ↗

In$8\mid48$Out$\mathrm{True}$

12 does not divide 25

live ↗

In$12\mid25$Out$\mathrm{False}$

live ↗

In$\mathrm{Simplify}(a\mid ba, \bigl\lbrack a, b\bigr\rbrack∈ℤ)$Out$a\mid ab$

About

Examples	10
Checked against	Wolfram Language 9 agree1 differmathlib4 8 agreeJulia 8 agreeRust 8 agree
Crosswalk	FungrimFungrim entry ×3Wolfram LanguageJuliaRust

Implementation

mappedmathlib4packages/oracle/src/mappings.ts

Divisibility over the integers, zero included (0 divides only 0); a rational operand fails to elaborate.

mappedjuliapackages/oracle/src/mappings.ts

mappedrustpackages/oracle/src/mappings.ts