Simplify

A simpler equivalent of an expression, optionally under assumptions such as $x > 0$.

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

Simplify(expr, options?)Runs compute-engine's own simplifier and then folds a quotient of same-argument $\sin/\cos$ or $\sinh/\cosh$ into $\tan$/$\cot$/$\tanh$/$\coth$, and applies $\cosh^2 - \sinh^2 = 1$, identities Wolfram's Simplify recognizes but compute-engine's does not. An expression in GoldenRatio and rationals that is rational folds to it ($1 + 1/\varphi - \varphi = 0$).

Typed signatures

Type	Package	Applies
(any, any?) -> expression	analyticreplaces compute-engine	always
(any, any?) -> expression	compute-engine	always
(any, any?) -> expression	residuesreplaces analytic	always

Domain: Compute engine

Examples

Basic #

$\sin x / \cos x = \tan x$

live ↗

In$\mathrm{Simplify}(\frac{\sin(x)}{\cos(x)})$Out$\tan(x)$

$\sinh x / \cosh x = \tanh x$

live ↗

In$\mathrm{Simplify}(\frac{\sinh(x)}{\cosh(x)})$Out$\tanh(x)$

Scope #

$\cosh^2 x - \sinh^2 x = 1$

live ↗

In$\mathrm{Simplify}(\cosh(x)^2-\sinh(x)^2)$Out$1$

About

Examples	3
Checked against	Wolfram Language 3 agreeSageMath 3 agreeSymPy 3 agree
Crosswalk	Wolfram LanguageSageMathSymPy

Implementation

mappedsympypackages/oracle/src/mappings.ts

SymPy has one simplifier, so FullSimplify maps to it too. The scan compares what each answers by value (the difference simplifies to zero, or agrees at sample points), not by form; an answer ours leaves as written is no agreement unless SymPy leaves it too. Assumptions (a second operand) are not mapped.

mappedsagepackages/oracle/src/mappings.ts