Divide

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

Quotient of a numerator and one or more denominators.

✓ checked against that system · ! checked, with disagreements (hover a chip)WikipediaDivision (mathematics)MathWorldDivisionWikidataQ1226939Encyclopedia of MathematicsDivisionBritannicatopic/division-mathematicsWolfram LanguageDivide✓

Divide(complex | infinity, (complex | infinity)+) -> numberQuotient of a numerator and one or more denominators.

Typed signatures

Type	Package	Applies
`(complex \| infinity, (complex \| infinity)+) -> number`	`adeles`replaces `numerals`	on Adele, Idele, ProfiniteNumber
`(complex \| infinity, (complex \| infinity)+) -> number`	`analytic`replaces `compute-engine`	on Around, CenteredInterval, Interval
`(complex \| infinity, (complex \| infinity)+) -> number`	`compute-engine`	always
`(complex \| infinity, (complex \| infinity)+) -> number`	`hypercomplex`replaces `analytic`	for symbols ^(?:i\|j\|epsilon\|e\|f\|theta\|epsilonSymbol\|varepsilon\|thetaSymbol\|vartheta)_\d+$
`(complex \| infinity, (complex \| infinity)+) -> number`	`numerals`replaces `residues`	on AdicNumeral
`(complex \| infinity, (complex \| infinity)+) -> number`	`residues`replaces `hypercomplex`	on ResidueClass

Domain: Compute engine

Plot

the complex plot cannot lower Divide

Applications #

Successive division builds the reciprocals of factorials

\mathrm{FoldList}(\mathrm{Divide}, 1, 1..10)

Out

\bigl\lbrack1, 1, \frac{1}{2}, \frac{1}{6}, \frac{1}{24}, \frac{1}{120}, \frac{1}{720}, \frac{1}{5\,040}, \frac{1}{40\,320}, \frac{1}{362\,880}, \frac{1}{3\,628\,800}\bigr\rbrack

Neat examples #

A table of all ratios $i/j$ , kept as exact fractions

\mathrm{Array}(\mathrm{Divide}, \bigl\lbrack4, 4\bigr\rbrack)

Out

\bigl\lbrack\bigl\lbrack1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}\bigr\rbrack, \bigl\lbrack2, 1, \frac{2}{3}, \frac{1}{2}\bigr\rbrack, \bigl\lbrack3, \frac{3}{2}, 1, \frac{3}{4}\bigr\rbrack, \bigl\lbrack4, 2, \frac{4}{3}, 1\bigr\rbrack\bigr\rbrack

About

Examples	2
Checked against	Wolfram Language 2 agreemathlib4 1 agree
Crosswalk	Wikipedia MathWorld Wikidata Encyclopedia of Mathematics Britannica Wolfram LanguageJulia

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mpmathify keeps an integer quotient at working precision; Python's / would be a double.