Square

The second power of x: $x^2$.

WikipediaSquare function↗WikidataQ3075175↗

Square(x)the second power $x^2$.

Juliaenumeratio_pow(x, 2)Rustpower(x, n(2))

Typed signatures

Type	Package	Applies
(number) -> number	compute-engine	always

Domain: Arithmetic

Details

• Canonicalizes to $x^2$: $\mathrm{Square}(x)$ and $\mathrm{Power}(x, 2)$ are the same expression. See Sqrt.
• Even function: $(-x)^2 = x^2$, so the sign of the input is lost.
• Always non-negative for real x; for a complex number it need not be, e.g. $(1+i)^2 = 2i$.
• Threads element-wise over a list.
• Square is purely a convenience head: it canonicalizes away to $x^2$ (Power).

Plot

Examples

Basic #

live ↗

In$5^2$Out$25$

Same result for x and -x

live ↗

In$(-5)^2$Out$25$

live ↗

In$(\frac{2}{3})^2$Out$\frac{4}{9}$

Canonicalizes to $x^2$

live ↗

In$x^2$Out$x^2$

Threads element-wise over a list

live ↗

In$\bigl\lbrack2, 3, -4\bigr\rbrack^2$Out$\bigl\lbrack4, 9, 16\bigr\rbrack$

Applications #

The area of a 3×3 square tile

live ↗

In$3^2$Out$9$

Properties #

Even function: $(-x)^2 = x^2$

live ↗

In$(-5)^2=5^2$Out$\mathrm{True}$

$(1+i)^2 = 2i$ -- squaring a complex number needn't stay real

live ↗

In$(1+i)^2=2i$Out$\mathrm{True}$

Possible issues #

Infinity squared stays infinite rather than erroring

live ↗

In$∞^2$Out$∞$

About

Examples	9
Checked against	Wolfram Language 9 agreeSageMath 8 agree1 errorSymPy 8 agree1 errormpmath 6 agree1 errorJulia 7 agree1 errorRust 6 agree
Crosswalk	WikipediaWikidataJuliaRust

Implementation

mappedwolframpackages/oracle/src/mappings.ts

mappedsympypackages/oracle/src/mappings.ts

mappedmpmathpackages/oracle/src/mappings.ts

mappedsagepackages/oracle/src/mappings.ts

mappedjuliapackages/oracle/src/mappings.ts

mappedrustpackages/oracle/src/mappings.ts

See also: Sqrt, Root