Argument

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

Complex argument (phase angle) of a number.

✓ checked against that system · ! checked, with disagreements (hover a chip)FungrimArg✓↗Fungrim entryWolfram LanguageArg!↗

Argument(complex | infinity) -> numberAs native, and keeps its digits past a double's for a complex number (N(Argument(e + i pi), 20)).

SageMatharg(complex | infinity)SymPyarg(complex | infinity)mpmatharg(complex | infinity)Juliaenumeratio_ball(angle, complex | infinity)

Typed signatures

Type	Package	Applies
(complex | infinity) -> number	compute-engine	always
(complex | infinity) -> number	evaluationreplaces compute-engine	always

Domain: Compute engine

Plot

ComplexPlot

real slice

Examples

1 more kept as data, checked against the oracles

Basic #

$\arg(i) = \pi/2$

live ↗

In$\arg(i)$Out$\frac{π}{2}$

live ↗

In$\arg(1+i)$Out$\frac{π}{4}$

live ↗

In$\arg(-1)$Out$π$

Scope #

live ↗

In$N(\arg(e+i π), 20)$Out$0.857\,511\,786\,355\,846\,265\,01$

live ↗

In$\arg(-123)$Out$π$

live ↗

In$\arg(123-456i)$Out$\arctan(-\frac{152}{41})$

live ↗

In$\arg(\bigl\lbrack\bigl\lbrack\frac{1}{2}, -1\bigr\rbrack, \bigl\lbrack-\frac{5}{3}, \frac{1}{2}\bigr\rbrack\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack0, π\bigr\rbrack, \bigl\lbrack π, 0\bigr\rbrack\bigr\rbrack$

live ↗

In$\mathrm{FullSimplify}(\mathrm{MatrixFunction}(\mathrm{Argument}, \bigl\lbrack\bigl\lbrack1/2, -1\bigr\rbrack, \bigl\lbrack-5/3, 1/2\bigr\rbrack\bigr\rbrack))$Out$\bigl\lbrack\bigl\lbrack\frac{π}{2}, \frac{\sqrt{15}π}{10}\bigr\rbrack, \bigl\lbrack\frac{\sqrt{15}π}{6}, \frac{π}{2}\bigr\rbrack\bigr\rbrack$

live ↗

In$\arg(0)$Out$0$

live ↗

In$\arg(∞)$Out$0$

live ↗

In$\arg(-∞)$Out$π$

live ↗

In$\arg(∞i)$Out$\operatorname{Indeterminate}$

About

Examples	13
Checked against	Wolfram Language 12 agree1 differSageMath 11 agree1 differSymPy 9 agree1 differ2 unevaluatedmpmath 11 agree1 unevaluatedJulia 9 agree3 error
Crosswalk	FungrimFungrim entry ×18Wolfram LanguageSageMathSymPympmathJulia

Implementation

mappedsympypackages/oracle/src/mappings.ts

mappedmpmathpackages/oracle/src/mappings.ts

mappedsagepackages/oracle/src/mappings.ts

mappedjuliapackages/oracle/src/mappings.ts