Equal

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

Equality comparison (equal to).

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

Equal(any, any) -> booleanEquality comparison (equal to).

SageMathenumeratio_equal(any, any)SymPyenumeratio_equal(any, any)mpmathalmosteq(any, any, 1e-20)Juliaenumeratio_equal(any, any)Rustequal(any, any)

Typed signatures

Type	Package	Applies
(any, any) -> boolean	adelesreplaces compute-engine	on Adele, Idele, ProfiniteNumber
(any, any) -> boolean	compute-engine	always
(any, any) -> boolean	residuesreplaces compute-engine	on IntegerMod

Domain: Compute engine

Examples

1 more kept as data, checked against the oracles

Basic #

Equal integers

live ↗

In$4=4$Out$\mathrm{True}$

Scope #

A 20-digit approximation compares equal to the exact constant

live ↗

In$N(π, 20)=π$Out$\mathrm{True}$

Two different-looking radicals are proven equal

live ↗

In$\sqrt{2}+\sqrt{3}=\sqrt{5+2\sqrt{6}}$Out$\mathrm{True}$

A symbol equals itself

live ↗

In$x=x$Out$\mathrm{True}$

Chained equality checks every neighbour

live ↗

In$3=3=3$Out$\mathrm{True}$

Lists compare as wholes

live ↗

In$\bigl\lbrack1, 2\bigr\rbrack=\bigl\lbrack1, 2\bigr\rbrack$Out$\mathrm{True}$

live ↗

In$N(π, 20)=π(1+256×(10^{-20}))$Out$\mathrm{True}$

Properties #

Undecidable $x=y$ stays unevaluated while the others resolve

live ↗

In$\begin{cases}x=x\\x=y\\\sqrt{2}+\sqrt{3}=\sqrt{5+2\sqrt{6}}\\π=N(π)\end{cases}$Out$\bigl\lbrack\mathrm{True}, x=y, \mathrm{True}, \mathrm{True}\bigr\rbrack$

live ↗

In$\mathrm{Solve}(ax^2+bx+c=0, x)$Out$\bigl\lbrack\frac{\sqrt{b^2-4ac}-b}{2a}, \frac{-b-\sqrt{b^2-4ac}}{2a}\bigr\rbrack$

Possible issues #

live ↗

In$\mathrm{FullSimplify}((p∨q)=(q∨p))$Out$\mathrm{True}$

About

Examples	11
Checked against	Wolfram Language 8 agree3 differSageMath 7 agree1 differSymPy 6 agree3 differmpmath 3 agree2 differ1 errorJulia 6 agreeRust 6 agree
Crosswalk	FungrimWolfram LanguageSageMathSymPympmathJuliaRust

Implementation

mappedwolframpackages/oracle/src/mappings.ts

The single most valuable row: a large share of documented examples are identities written as Equal.

mappedsympypackages/oracle/src/mappings.ts

The single most valuable row: a large share of documented examples are identities written as Equal.

mappedmpmathpackages/oracle/src/mappings.ts

The single most valuable row: a large share of documented examples are identities written as Equal.

mappedsagepackages/oracle/src/mappings.ts

The single most valuable row: a large share of documented examples are identities written as Equal.

mappedoscarpackages/oracle/src/mappings.ts

The single most valuable row: a large share of documented examples are identities written as Equal.

mappedjuliapackages/oracle/src/mappings.ts

The single most valuable row: a large share of documented examples are identities written as Equal.

mappedmathlib4packages/oracle/src/mappings.ts

The single most valuable row: a large share of documented examples are identities written as Equal.

mappedrustpackages/oracle/src/mappings.ts

The single most valuable row: a large share of documented examples are identities written as Equal.