And

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

Logical conjunction (AND): true when all operands are true. Short-circuits: operands are evaluated left to right and evaluation stops at the first False.

✓ checked against that system · ! checked, with disagreements (hover a chip)WikipediaLogical conjunction↗MathWorldConjunction↗WikidataQ191081↗Encyclopedia of MathematicsConjunction↗nLablogical conjunction↗Britannicatopic/conjunction-logic↗FungrimAnd↗Wolfram LanguageAnd!↗SymPyAnd($*,)

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

Typed signatures

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

Domain: Compute engine

Examples

Basic #

Every conjunct is decided, so the whole conjunction is True

live ↗

In$1\lt2∧3\lt π$Out$\mathrm{True}$

Scope #

live ↗

In$\mathrm{ReplaceAll}(x≠0∧y=\frac{1}{x}, \mathrm{Rule}(x, 0))$Out$\mathrm{False}$

live ↗

In$\mathrm{ReplaceAll}(y=\frac{1}{x}∧x≠0, \mathrm{Rule}(x, 0))$Out$\mathrm{False}$

Applications #

Assumptions on $a$ and $b$ license $(a^b)^c = a^{bc}$

live ↗

In$\mathrm{Refine}((a^{b})^{c}, a≥0∧b∈ℝ)$Out$a^{bc}$

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: $\neg(a\wedge b) = \neg a \vee \neg b$

live ↗

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

About

Examples	6
Checked against	Wolfram Language 5 agree1 differSymPy 1 agree1 differ
Crosswalk	WikipediaMathWorldWikidataEncyclopedia of MathematicsnLabBritannicaFungrimWolfram LanguageSymPy

Implementation

mappedsympypackages/oracle/src/mappings.ts