RealAbs

The absolute value of a real number x, as a function defined only on the reals.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageRealAbs✓↗

RealAbs(x)the absolute value of the real number x.

Juliaenumeratio_ball(abs, x)

Typed signatures

Type	Package	Applies
(number) -> number	analytic	always

Domain: Elementary functions

Details

• Agrees with native Abs on every real x -- RealAbs exists so a plot or a domain check can say "real only" and mean it, the way Wolfram's does.
• A concretely complex argument is outside RealAbs's domain and is left unevaluated -- unlike Abs, which is complex-valued (the modulus).

Plot

Examples

Basic #

The absolute value of a real number

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In$\mathrm{RealAbs}(-2.5)$Out$2.5$

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In$\mathrm{RealAbs}(-\frac{7}{2})$Out$\frac{7}{2}$

A positive number is unchanged

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In$\mathrm{RealAbs}(2)$Out$2$

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In$\frac{\mathrm{d}\mathrm{RealAbs}(x)}{\mathrm{d}x}$Out$\mathrm{sgn}(x)$

Scope #

Threads element-wise over a list

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In$\mathrm{RealAbs}(\bigl\lbrack-1, 2, -3\bigr\rbrack)$Out$\bigl\lbrack1, 2, 3\bigr\rbrack$

Exact numeric arguments

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In$\mathrm{RealAbs}(-π)$Out$π$

A 50-digit value of $|\pi - G|$, with $G$ Catalan's constant

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In$N(\mathrm{RealAbs}(π-\operatorname{G}), 50)$Out$2.225\,627\,059\,412\,574\,223\,408\,039\,868\,347\,118\,773\,423\,020\,025\,093\,4$

Applied entrywise to a matrix

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In$\mathrm{RealAbs}(\bigl\lbrack\bigl\lbrack\frac{1}{2}, -1\bigr\rbrack, \bigl\lbrack0, -\frac{1}{2}\bigr\rbrack\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack\frac{1}{2}, 1\bigr\rbrack, \bigl\lbrack0, \frac{1}{2}\bigr\rbrack\bigr\rbrack$

As a matrix function it acts on eigenvalues, not entries, so the off-diagonal becomes 0

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In$\mathrm{MatrixFunction}(\mathrm{RealAbs}, \bigl\lbrack\bigl\lbrack\frac{1}{2}, -1\bigr\rbrack, \bigl\lbrack0, -\frac{1}{2}\bigr\rbrack\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack\frac{1}{2}, 0\bigr\rbrack, \bigl\lbrack0, \frac{1}{2}\bigr\rbrack\bigr\rbrack$

Interval arithmetic gives $[0,5]$ from $[-5,3]$

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In$\mathrm{RealAbs}(\mathrm{Interval}(-5, 3))$Out$\mathrm{Interval}(0, 5)$

Zero stays zero

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In$\mathrm{RealAbs}(0)$Out$0$

Infinity maps to infinity

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In$\mathrm{RealAbs}(∞)$Out$∞$

Negative infinity also gives positive infinity

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In$\mathrm{RealAbs}(-∞)$Out$∞$

Rewrites to the ordinary absolute value

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In$\mathrm{PiecewiseExpand}(\mathrm{RealAbs}(x))$Out$\vert x\vert$

Properties #

Agrees with Abs on the reals

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In$\mathrm{RealAbs}(-5)=\vert-5\vert$Out$\mathrm{True}$

About

Examples	15
Checked against	Wolfram Language 15 agreeJulia 8 agree2 error
Crosswalk	Wolfram LanguageJulia

Implementation

mappedjuliapackages/oracle/src/mappings.ts