Conjugate

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

Complex conjugate of a number, or the pointwise conjugate of a function.

✓ checked against that system · ! checked, with disagreements (hover a chip)FungrimConjugate!↗Fungrim entryFindStatMp00041via IntegerComposition↗Mp00202via IntegerPartition↗Wolfram LanguageConjugate✓↗SageMathPartitions(n).map(lambda p: p.conjugate())via IntegerPartition✓↗

Conjugate(T) -> T where T: numberComplex conjugate of a number, or the pointwise conjugate of a function.

SageMathconjugate(T)✓↗SymPyconjugate(T)mpmathconj(T)Juliaenumeratio_ball(conj, T)

Conjugate(x)holds when x isn't known to be a number, so Conjugate(Transpose(m)) stays unevaluated instead of a type error.

SageMathconjugate(x)✓↗SymPyconjugate(x)mpmathconj(x)Juliaenumeratio_ball(conj, x)

Typed signatures

Type	Package	Applies
(T) -> T where T: number	compute-engine	always
(value) -> value	analyticreplaces compute-engine	always
(value) -> value	hypercomplexreplaces analytic	always

Domain: Compute engine

Examples

Properties #

Zero is its own conjugate

live ↗

In$\overline{0}$Out$0$

Known value · Wolfram MathematicalFunctionData, Conjugate

Real numbers are fixed

live ↗

In$\overline{1}$Out$1$

Known value · Wolfram MathematicalFunctionData, Conjugate

A negative real is fixed

live ↗

In$\overline{-1}$Out$-1$

Known value · Wolfram MathematicalFunctionData, Conjugate

Flips $-i$ to $i$

live ↗

In$\overline{-i}$Out$i$

Known value · Wolfram MathematicalFunctionData, Conjugate

$\overline{1+i}=1-i$

live ↗

In$\overline{1+i}$Out$1-i$

Known value · Wolfram MathematicalFunctionData, Conjugate

Real part sign is kept

live ↗

In$\overline{-1+i}$Out$-1-i$

Known value · Wolfram MathematicalFunctionData, Conjugate

Both parts negated, only the imaginary flips

live ↗

In$\overline{-1-i}$Out$-1+i$

Known value · Wolfram MathematicalFunctionData, Conjugate

Conjugation is an involution: $\overline{1-i} = 1+i$

live ↗

In$\overline{1-i}$Out$1+i$

Known value · Wolfram MathematicalFunctionData, Conjugate

Imaginary surd coefficient changes sign

live ↗

In$\overline{1+\sqrt{3}i}$Out$1-\sqrt{3}i$

Known value · Wolfram MathematicalFunctionData, Conjugate

Works with a negative real part

live ↗

In$\overline{\sqrt{3}i-1}$Out$-\sqrt{3}i-1$

Known value · Wolfram MathematicalFunctionData, Conjugate

Both signs flip back to $-\sqrt3 + i$

live ↗

In$\overline{-i-\sqrt{3}}$Out$i-\sqrt{3}$

Known value · Wolfram MathematicalFunctionData, Conjugate

Conjugating twice-negated parts

live ↗

In$\overline{-\sqrt{3}i-1}$Out$\sqrt{3}i-1$

Known value · Wolfram MathematicalFunctionData, Conjugate

Imaginary surd flips from minus to plus

live ↗

In$\overline{1-\sqrt{3}i}$Out$1+\sqrt{3}i$

Known value · Wolfram MathematicalFunctionData, Conjugate

Real surd plus $-i$ flips to $+i$

live ↗

In$\overline{\sqrt{3}-i}$Out$\sqrt{3}+i$

Known value · Wolfram MathematicalFunctionData, Conjugate

Plain integers are real

live ↗

In$\overline{2}$Out$2$

Known value · Wolfram MathematicalFunctionData, Conjugate

live ↗

In$\overline{i}$Out$-i$

Known value · Wolfram MathematicalFunctionData, Conjugate

live ↗

In$\overline{\sqrt{3}+i}$Out$\sqrt{3}-i$

Known value · Wolfram MathematicalFunctionData, Conjugate

live ↗

In$\overline{i-\sqrt{3}}$Out$-i-\sqrt{3}$

Known value · Wolfram MathematicalFunctionData, Conjugate

About

Examples	18
Checked against	Wolfram Language 18 agreeSageMath 18 agreeSymPy 18 agreempmath 18 agreeJulia 18 agree
Crosswalk	FungrimFungrim entry ×30FindStat ×2Wolfram LanguageSageMath ×2SymPympmathJulia

Implementation

mappedsympypackages/oracle/src/mappings.ts

The complex conjugate only; the record's mapOn partition meanings have no SymPy counterpart.

mappedmpmathpackages/oracle/src/mappings.ts

mappedsagepackages/oracle/src/mappings.ts

mappedjuliapackages/oracle/src/mappings.ts