Or

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

Logical disjunction (OR): true when at least one operand is true. Short-circuits: operands are evaluated left to right and evaluation stops at the first True.

✓ checked against that system · ! checked, with disagreements (hover a chip)WikipediaLogical disjunction↗MathWorldDisjunction↗WikidataQ1651704↗Encyclopedia of MathematicsDisjunction↗FungrimOr↗Wolfram LanguageOr!↗SymPyOr($*,)

Or(boolean+) -> booleanas compute-engine declares it

Typed signatures

Type	Package	Applies
(boolean+) -> boolean	compute-engine	always

Domain: Compute engine

Examples

Basic #

One true branch is enough, even with an irrational bound

live ↗

In$2\lt1∨3\lt π$Out$\mathrm{True}$

Scope #

A True anywhere makes the whole Or True, whatever the unknowns

live ↗

In$x∨\mathrm{True}∨z$Out$\mathrm{True}$

live ↗

In$\mathrm{ReplaceAll}(x=0∨y=\frac{1}{x}, \mathrm{Rule}(x, 0))$Out$\mathrm{True}$

live ↗

In$\mathrm{ReplaceAll}(y=\frac{1}{x}∨x=0, \mathrm{Rule}(x, 0))$Out$\mathrm{True}$

Applications #

The assumption makes $\sqrt{(x^2-1)^2}$ equal $|x^2-1|$

live ↗

In$\mathrm{Refine}(\sqrt{(x^2-1)^2}, x≤-1∨x≥1)$Out$\vert x^2-1\vert$

live ↗

In$\int_{-∞}^{∞}\int_{-∞}^{∞}\!\lbrack x^2+y^2\lt1∨(x-1)^2+y^2\lt2\rbrack\, \mathrm{d}x \mathrm{d}y$Out$\int_{-∞}^{∞}\!\int_{-∞}^{∞}\!\lbrack x^2+y^2\lt1∨(x-1)^2+y^2\lt2\rbrack\, \mathrm{d}y\, \mathrm{d}x$

Properties #

De Morgan applied to a negated three-way Or

live ↗

In$\mathrm{BooleanConvert}(¬(a∨b∨c))$Out$¬{{a}}∧¬{{b}}∧¬{{c}}$

About

Examples	7
Checked against	Wolfram Language 6 agree1 differSymPy 2 agree1 differ
Crosswalk	WikipediaMathWorldWikidataEncyclopedia of MathematicsFungrimWolfram LanguageSymPy

Implementation

mappedsympypackages/oracle/src/mappings.ts