Negate

The additive inverse of x: $-x$.

✓ checked against that system · ! checked, with disagreements (hover a chip)WikipediaAdditive inverse↗MathWorldAdditiveInverse↗WikidataQ715358↗Wolfram LanguageMinus✓↗

Negate(x)the additive inverse $-x$.

Typed signatures

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

Domain: Arithmetic

Details

• The additive inverse: $\operatorname{Negate}(x) = -x$.
• Double negation cancels: $-(-x) = x$.
• Distributes over a sum: $-(a+b) = -a - b$.
• Threads element-wise over a list.
• compute-engine keeps Negate as its own head rather than rewriting to $\mathrm{Multiply}(-1, x)$.

Plot

ComplexPlot

real slice

Examples

Basic #

live ↗

In$-5$Out$-5$

live ↗

In$5$Out$5$

Its own negation

live ↗

In$0$Out$0$

live ↗

In$-\frac{3}{4}$Out$-\frac{3}{4}$

Threads element-wise over a list

live ↗

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

Stays symbolic

live ↗

In$-x$Out$-x$

Scope #

live ↗

In$-(1+2i)$Out$-1-2i$

Threads over a matrix, entry by entry

live ↗

In$-\bigl\lbrack\bigl\lbrack1, -2\bigr\rbrack, \bigl\lbrack3, 4\bigr\rbrack\bigr\rbrack$Out$\bigl\lbrack\bigl\lbrack-1, 2\bigr\rbrack, \bigl\lbrack-3, -4\bigr\rbrack\bigr\rbrack$

Folds into a numeric coefficient

live ↗

In$-(2x)$Out$-2x$

Applications #

Recording a $42.50 charge as a negative balance adjustment

live ↗

In$-42.5$Out$-42.5$

Properties #

Double negation cancels: $-(-x) = x$

live ↗

In$--x$Out$x$

Distributes over a sum: $-(a+b) = -a - b$

live ↗

In$-(a+b)=-a-b$Out$\mathrm{True}$

$-(a-b) = b-a$

live ↗

In$-(a-b)$Out$b-a$

The additive inverse: $x + (-x) = 0$

live ↗

In$x-x$Out$0$

Possible issues #

Flips signed infinities too

live ↗

In$-∞$Out$-∞$

About

Examples	15
Checked against	Wolfram Language 15 agreeSageMath 15 agreeSymPy 15 agreempmath 8 agreemathlib4 6 agree1 errorOscar 8 agreeJulia 9 agreeRust 7 agree
Crosswalk	WikipediaMathWorldWikidataWolfram 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

See also: Abs, Sign