Element

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

Test whether a value is an element of a collection. Optional third argument is a boolean expression (condition) for filtered iteration in Sum/Product. Element supports two modes of operation: 1. Set membership: Element(3, [List, 1, 2, 3]) checks if 3 is in the list 2. Type-style membership: Element(x, integer) checks if x has type integer Type-style membership works with: - Mathematical sets: Integers, RealNumbers, ComplexNumbers, etc. - Type names: integer, rational, real, number, positive_integer, etc. - Invalid type names remain unevaluated (e.g., Element(2, "Booleans"))

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

Element(any, any, boolean?) -> booleanTest whether a value is an element of a collection. Optional third argument is a boolean expression (condition) for filtered iteration in Sum/Product. Element supports two modes of operation: 1. Set membership: Element(3, [List, 1, 2, 3]) checks if 3 is in the list 2. Type-style membership: Element(x, integer) checks if x has type integer Type-style membership works with: - Mathematical sets: Integers, RealNumbers, ComplexNumbers, etc. - Type names: integer, rational, real, number, positive_integer, etc. - Invalid type names remain unevaluated (e.g., Element(2, "Booleans"))

Typed signatures

Type	Package	Applies
(any, any, boolean?) -> boolean	combinatoricsreplaces number-theory	always
(any, any, boolean?) -> boolean	compute-engine	always
(any, any, boolean?) -> boolean	frontendreplaces combinatorics	always
(any, any, boolean?) -> boolean	hypercomplexreplaces structures	always
(any, any, boolean?) -> boolean	number-theoryreplaces numerals	always
(any, any, boolean?) -> boolean	numeralsreplaces residues	always
(any, any, boolean?) -> boolean	residuesreplaces hypercomplex	always
(any, any, boolean?) -> boolean	structuresreplaces compute-engine	always

Domain: Compute engine

Examples

Basic #

live ↗

In$3∈ℤ$Out$\mathrm{True}$

live ↗

In$\frac{1}{2}∈ℤ$Out$\mathrm{False}$

live ↗

In$π∈ℝ$Out$\mathrm{True}$

Scope #

live ↗

In$\mathrm{Refine}(\sin(πx), x∈ℤ)$Out$0$

live ↗

In$\mathrm{Refine}(\sqrt{(x+y-2)^2}, \bigl\lbrack x, y\bigr\rbrack∈\mathrm{Disk}())$Out$\vert x+y-2\vert$

live ↗

In$\mathrm{Refine}(x^{y}+\ln(x+y)∈ℝ, x\gt0∧y\gt0)$Out$\mathrm{True}$

live ↗

In$\mathrm{Refine}(\bigl\lbrack x, y\bigr\rbrack∈\mathrm{Rectangle}(\bigl\lbrack-1, -1\bigr\rbrack, \bigl\lbrack1, 1\bigr\rbrack), x^2+y^2≤1)$Out$\bigl\lbrack x, y\bigr\rbrack∈\mathrm{Rectangle}(\bigl\lbrack-1, -1\bigr\rbrack, \bigl\lbrack1, 1\bigr\rbrack)$

About

Examples	7
Checked against	Wolfram Language 6 agree1 differ
Crosswalk	FungrimWolfram LanguageSageMath

Implementation

mappedwolframpackages/oracle/src/mappings.ts

Only a real match for a Wolfram domain symbol as the second operand (Element[7, Primes], kernel-verified True); against a literal list or one of our own collections (a diagram algebra's basis, PolygonalNumbers(k), …) real Element stays unevaluated instead of erroring, so the scan will record those as disagreements rather than a wrong-but-silent answer.

mappedsagepackages/oracle/src/mappings.ts