Multiply

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

Product of two or more values.

✓ checked against that system · ! checked, with disagreements (hover a chip)WikipediaMultiplication↗MathWorldMultiplication↗WikidataQ40276↗Encyclopedia of MathematicsMultiplication↗Britannicatopic/multiplication↗Wolfram LanguageTimes!↗

Multiply(number*) -> numberProduct of two or more values.

Typed signatures

Type	Package	Applies
(number*) -> number	adelesreplaces numerals	on Adele, Idele, ProfiniteNumber
(number*) -> number	analyticreplaces compute-engine	on Around, CenteredInterval, Interval; for symbols ^ExponentialE$
(number*) -> number	compute-engine	always
(number*) -> number	hypercomplexreplaces analytic	for symbols ^(?:i|j|epsilon|e|f|theta|epsilonSymbol|varepsilon|thetaSymbol|vartheta)_\d+$
(number*) -> number	numeralsreplaces residues	on AdicNumeral
(number*) -> number	residuesreplaces hypercomplex	on IntegerMod

Domain: Compute engine

Examples

Basic #

A scalar threads across a list

live ↗

In$2\bigl\lbrack x, y, z\bigr\rbrack$Out$\bigl\lbrack2x, 2y, 2z\bigr\rbrack$

live ↗

In$\bigl\lbrack\bigl\lbrack a, b\bigr\rbrack, \bigl\lbrack c, d\bigr\rbrack\bigr\rbrack\bigl\lbrack x, y\bigr\rbrack$Out$\bigl\lbrack ax+by, cx+dy\bigr\rbrack$

Scope #

Interval arithmetic takes the extreme products: $[-1,2]\cdot[2,3]=[-3,6]$

live ↗

In$\mathrm{Interval}(-1, 2)\mathrm{Interval}(2, 3)$Out$\mathrm{Interval}(-3, 6)$

live ↗

In$\mathrm{ReplaceAll}(abcd, \mathrm{Rule}(ad, x))$Out$abcd$

Properties #

live ↗

In$\mathrm{NonCommutativeMultiply}(a, b)-\mathrm{NonCommutativeMultiply}(b, a)$Out$\mathrm{NonCommutativeMultiply}(a, b)-\mathrm{NonCommutativeMultiply}(b, a)$

A telescoping product collapses to $\frac{2}{n+2}$

live ↗

In$\prod_{k=1}^{n}\frac{k+1}{k+2}$Out$\frac{2}{n+2}$

About

Examples	6
Checked against	Wolfram Language 5 agree1 differSymPy 2 agree1 unevaluated
Crosswalk	WikipediaMathWorldWikidataEncyclopedia of MathematicsBritannicaWolfram Language

Implementation

mappedsympypackages/oracle/src/mappings.ts

mappedmpmathpackages/oracle/src/mappings.ts

mappedsagepackages/oracle/src/mappings.ts

mappedoscarpackages/oracle/src/mappings.ts

mappedjuliapackages/oracle/src/mappings.ts

mappedmathlib4packages/oracle/src/mappings.ts

mappedrustpackages/oracle/src/mappings.ts