LessEqual

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

Less-than-or-equal comparison (less than or equal to).

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

LessEqual(any, any*) -> booleanas compute-engine declares it

SymPyLe(any, any*)Rustless_equal(any, any*)

Typed signatures

Type	Package	Applies
(any, any*) -> boolean	compute-engine	always

Domain: Compute engine

Examples

3 more kept as data, checked against the oracles

Basic #

A chain of non-strict inequalities, resolved exactly

live ↗

In$\frac{2}{17}≤\frac{1}{5}≤\frac{π}{10}$Out$\mathrm{True}$

Scope #

Exact rationals again: $\frac{3}{2} \le \frac{5}{3}$

live ↗

In$\frac{3}{2}≤\frac{5}{3}$Out$\mathrm{True}$

A 20-digit approximation of $\pi$ lies below $\pi$ itself

live ↗

In$N(π, 20)≤π$Out$\mathrm{True}$

Nested radicals compared exactly, with equality in fact: $\sqrt2+\sqrt3 = \sqrt{5+2\sqrt6}$

live ↗

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

live ↗

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

live ↗

In$x≤x$Out$\mathrm{True}$

live ↗

In$π^{e}≤e^{π}$Out$\mathrm{True}$

Properties #

A non-strict assumption $x\le 0$ gives the same $-x$

live ↗

In$\mathrm{Refine}(\sqrt{x^2}, x≤0)$Out$-x$

live ↗

In$\int_{-∞}^{∞}\int_{-∞}^{∞}\!\lbrack1≤x^2+y^2≤2\rbrack x^2\, \mathrm{d}x \mathrm{d}y$Out$\int_{-∞}^{∞}\!\int_{-∞}^{∞}\!\lbrack1≤x^2+y^2≤2\rbrack x^2\, \mathrm{d}y\, \mathrm{d}x$

About

Examples	12
Checked against	Wolfram Language 6 agree5 differSymPy 5 agree5 differmpmath 4 agree4 differRust 5 agree3 differ
Crosswalk	FungrimWolfram LanguageSymPy ×2Rust

Implementation

mappedsympypackages/oracle/src/mappings.ts

mappedsympypackages/oracle/src/mappings.ts

A chain is the conjunction of its neighbors.

mappedmpmathpackages/oracle/src/mappings.ts

mappedrustpackages/oracle/src/mappings.ts