ReIm

{Re(z), Im(z)} — threads over a list the way Wolfram's Listable ReIm does.

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

ReIm(z)the pair {Re(z), Im(z)}

JuliaAny[enumeratio_ball(real, z), enumeratio_ball(imag, z)]

Typed signatures

Type	Package	Applies
(any) -> list<any>	combinatorics	always

Domain: Collections

Details

• Listable: ReIm({z1, z2}) is {ReIm(z1), ReIm(z2)}, not a single flattened pair.

Examples

Basic #

live ↗

In$\mathrm{ReIm}(3+4i)$Out$\bigl\lbrack3, 4\bigr\rbrack$

The real and imaginary parts of $5+12i$ as a pair

live ↗

In$\mathrm{ReIm}(5+12i)$Out$\bigl\lbrack5, 12\bigr\rbrack$

A real number has imaginary part $0$

live ↗

In$\mathrm{ReIm}(3)$Out$\bigl\lbrack3, 0\bigr\rbrack$

live ↗

In$\mathrm{ReIm}(\bigl\lbrack i, -1, -i, 1\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack0, 1\bigr\rbrack, \bigl\lbrack-1, 0\bigr\rbrack, \bigl\lbrack0, -1\bigr\rbrack, \bigl\lbrack1, 0\bigr\rbrack\bigr\rbrack$

Scope #

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In$\mathrm{ReIm}(\bigl\lbrack1+2i, 3+4i\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack1, 2\bigr\rbrack, \bigl\lbrack3, 4\bigr\rbrack\bigr\rbrack$

Negative reals keep their sign in the real part

live ↗

In$\mathrm{ReIm}(-3)$Out$\bigl\lbrack-3, 0\bigr\rbrack$

Exact rationals stay exact

live ↗

In$\mathrm{ReIm}(\frac{3}{5})$Out$\bigl\lbrack\frac{3}{5}, 0\bigr\rbrack$

Both parts stay unevaluated for a fourth root of a negative number

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In$\mathrm{ReIm}(\sqrt[4]{-17})$Out$\bigl\lbrack\Re(\sqrt[4]{-17}), \Im(\sqrt[4]{-17})\bigr\rbrack$

$\Gamma(-1/2) = -2\sqrt\pi$ is real, so the imaginary part is $0$

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In$\mathrm{ReIm}(Γ(-\frac{1}{2}))$Out$\bigl\lbrack-2\sqrt{π}, 0\bigr\rbrack$

Threads over a ragged nested list, pairing at each leaf

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In$\mathrm{ReIm}(\bigl\lbrack\bigl\lbrack1, -1, 0\bigr\rbrack, \bigl\lbrack0, 1\bigr\rbrack\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack\bigl\lbrack1, 0\bigr\rbrack, \bigl\lbrack-1, 0\bigr\rbrack, \bigl\lbrack0, 0\bigr\rbrack\bigr\rbrack, \bigl\lbrack\bigl\lbrack0, 0\bigr\rbrack, \bigl\lbrack1, 0\bigr\rbrack\bigr\rbrack\bigr\rbrack$

live ↗

In$\mathrm{ReIm}(z)$Out$\bigl\lbrack\Re(z), \Im(z)\bigr\rbrack$

live ↗

In$\mathrm{ReIm}(2z)$Out$\bigl\lbrack\Re(2z), \Im(2z)\bigr\rbrack$

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In$\mathrm{ReIm}(w+z)$Out$\bigl\lbrack\Re(w+z), \Im(w+z)\bigr\rbrack$

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In$\mathrm{ReIm}(\bigl\lbrack a, \bigl\lbrack b, c\bigr\rbrack\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack\Re(a), \Im(a)\bigr\rbrack, \bigl\lbrack\bigl\lbrack\Re(b), \Im(b)\bigr\rbrack, \bigl\lbrack\Re(c), \Im(c)\bigr\rbrack\bigr\rbrack\bigr\rbrack$

live ↗

In$\mathrm{ReIm}(e^{(2/3)i π})$Out$\bigl\lbrack-\frac{1}{2}, \frac{\sqrt{3}}{2}\bigr\rbrack$

Properties #

A symbolic argument gives rank $1$, so it is treated as a single pair

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In$\mathrm{Rank}(\mathrm{ReIm}(\mathrm{mat}))$Out$1$

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In$\mathrm{ReIm}(2x+i)$Out$\bigl\lbrack\Re(2x+i), \Im(2x+i)\bigr\rbrack$

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In$\mathrm{Shape}(\mathrm{ReIm}(\mathrm{mat}))$Out$(2,)$

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In$\mathrm{ReIm}(5e^{(3/4)i π})$Out$\bigl\lbrack-\frac{5\sqrt{2}}{2}, \frac{5\sqrt{2}}{2}\bigr\rbrack$

live ↗

In$\mathrm{ReIm}(i)$Out$\bigl\lbrack0, 1\bigr\rbrack$

Possible issues #

live ↗

In$\mathrm{ReIm}(\bigl\lbrack i, -i, 0\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack0, 1\bigr\rbrack, \bigl\lbrack0, -1\bigr\rbrack, \bigl\lbrack0, 0\bigr\rbrack\bigr\rbrack$

live ↗

In$\mathrm{ReplaceAll}(\mathrm{ReIm}(z), \mathrm{Rule}(z, \bigl\lbrack i, -i, 0\bigr\rbrack))$Out$\bigl\lbrack\bigl\lbrack0, 1\bigr\rbrack, \bigl\lbrack0, -1\bigr\rbrack, \bigl\lbrack0, 0\bigr\rbrack\bigr\rbrack$

About

Examples	22
Checked against	Wolfram Language 21 agree1 differSageMath 18 agree1 errormpmath 14 agreeJulia 14 agree
Crosswalk	Wolfram LanguageJulia

Implementation

mappedmpmathpackages/oracle/src/mappings.ts

mappedsagepackages/oracle/src/mappings.ts

mappedjuliapackages/oracle/src/mappings.ts

See also: NumberQ