Add

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

Sum of two or more values.

✓ checked against that system · ! checked, with disagreements (hover a chip)WikipediaAddition↗MathWorldAddition↗WikidataQ32043↗Encyclopedia of MathematicsAddition↗Britannicatopic/addition↗FungrimAdd↗Wolfram LanguagePlus✓↗

Add(value+) -> valueSum of two or more values.

Typed signatures

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

Domain: Compute engine

Examples

Basic #

Lists add element by element

live ↗

In$\bigl\lbrack10, 20, 30\bigr\rbrack+\bigl\lbrack1, 2, 3\bigr\rbrack$Out$\bigl\lbrack11, 22, 33\bigr\rbrack$

live ↗

In$x+\bigl\lbrack1, 2, 3\bigr\rbrack$Out$\bigl\lbrack x+1, x+2, x+3\bigr\rbrack$

Scope #

Symbolic lists add element-wise too

live ↗

In$\bigl\lbrack a, b\bigr\rbrack+\bigl\lbrack c, d\bigr\rbrack$Out$\bigl\lbrack a+c, b+d\bigr\rbrack$

A scalar is added to every element

live ↗

In$x+\bigl\lbrack a, b, c\bigr\rbrack$Out$\bigl\lbrack a+x, b+x, c+x\bigr\rbrack$

The scalar reaches every entry of a nested list

live ↗

In$x+\bigl\lbrack\bigl\lbrack a, b\bigr\rbrack, \bigl\lbrack c, d\bigr\rbrack\bigr\rbrack$Out$\bigl\lbrack\bigl\lbrack a+x, b+x\bigr\rbrack, \bigl\lbrack c+x, d+x\bigr\rbrack\bigr\rbrack$

Interval endpoints add: $[0,1]+[-1,1]=[-1,2]$

live ↗

In$\mathrm{Interval}(0, 1)+\mathrm{Interval}(-1, 1)$Out$\mathrm{Interval}(-1, 2)$

live ↗

In$\bigl\lbrack\bigl\lbrack a, b\bigr\rbrack, \bigl\lbrack c, d\bigr\rbrack\bigr\rbrack+\bigl\lbrack\bigl\lbrack1, 2\bigr\rbrack, \bigl\lbrack3, 4\bigr\rbrack\bigr\rbrack$Out$\bigl\lbrack\bigl\lbrack a+1, b+2\bigr\rbrack, \bigl\lbrack c+3, d+4\bigr\rbrack\bigr\rbrack$

Properties #

A sum is flat: four terms, one Add of length 4

live ↗

In$\mathrm{Length}(a+b+c+d)$Out$4$

Folding Add gives the running partial sums

live ↗

In$\mathrm{FoldList}(\mathrm{Add}, 0, \bigl\lbrack a, b, c\bigr\rbrack)$Out$\bigl\lbrack0, a, a+b, a+b+c\bigr\rbrack$

live ↗

In$\mathrm{ReplaceAll}(a+b+c+d, \mathrm{Rule}(a+d, x))$Out$a+b+c+d$

live ↗

In$f+g\lhd x$Out$f+g\lhd x$

live ↗

In$\mathrm{Through}((f+g\lhd x))$Out$g(x)+f(x)$

About

Examples	12
Checked against	Wolfram Language 12 agreeSageMath 7 agreeSymPy 8 agreeJulia 1 agreeRust 1 error
Crosswalk	WikipediaMathWorldWikidataEncyclopedia of MathematicsBritannicaFungrimWolfram 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