Everett (Demo)

Artwork by K_0313_heaseong on X

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Everett is a Math Expression List Evaluator. Inspired by taking my Physics II course at NAU.
This application was built with React, TypeScript, TailwindCSS, Tauri and WASM. In terms of Web Assembly, this application uses another library I built called Nero, a C++ LaTeX parser, evaluator and formula finder.

Installation

Prebuilt Release (Recommended)

git clone https://github.com/Illusion137/Everett.git
cd Everett
wget -P public/wasm http://github.com/Illusion137/Nero/releases/latest/download/Nero.wasm
yarn install

Build Nero from Source

NOTE: Building from source should only be done for quickly iterating through changes if you are directly developing Nero.

git clone https://github.com/Illusion137/Nero.git # Nero for building the WASM library from source
git clone https://github.com/Illusion137/Everett.git
cd Nero
sed -E -i '.bak' 's/(EVERETT_PATH)=.*/\1="PATH_TO_EVERETT"/g' build.sh # replace PATH_TO_EVERETT with your Everett path with escaped slashes
npm i
sh build.sh
cd ../Everett
yarn install

Usage

Running / Building

Run Development Server (Web)

yarn dev

Run Development Server (Tauri)

yarn tauri dev

Build as Application (Tauri)

yarn tauri build

Application Usage

Each Math Expression Box is divided into 2 sections.
$\bigg| \mathrm{Math Expression} \bigg| \mathrm{Unit Expression} \bigg|$

Combined Expressions

The math and unit expressions are then combined before evaluation.

Combined Expression Examples

Ex 1: Implicit 1 Unit

$\bigg| x = 25.0 \bigg| \space \bigg|$

$\rightarrow x = ( 25.0 ) \cdot 1 = 25.0$

If a unit is not provided, then the expression will just parse without it and treat the unit as if multiplying by 1.

Ex 2: numeric Unit

$\bigg| \frac{2}{9} + 1 \bigg| 9 \bigg|$

$\rightarrow (\frac{2}{9} + 1) \cdot 9 = 11$

The Units Section can take in any mathematical expression.

Ex 3: derived Unit

$\bigg| 5^2 + 2 \bigg| \mathrm{\mu V} \bigg|$

$\rightarrow (5^2 + 2) \cdot \mathrm{\mu V} = 2.7 \cdot 10^{-5}\mathrm{V}$

Besides working with the 7 base SI units [m, s, kg, A, K, mol, cd], Everett also supports the derived SI units.

Ex 4: unit expression Unit

$\bigg| \ln(e \sin(\frac{\pi}{2})) \bigg| \mathrm{kg\frac{m}{s^2}} \bigg|$

$\rightarrow (\ln(e \sin(\frac{\pi}{2}))) \cdot \mathrm{kg\frac{m}{s^2}} = 1\mathrm{N}$

Note the support for functions, moreover complex units get simplified to what they really mean.

Ex 5: bad math Expression

$\bigg| 5\mathrm{mm} \bigg| 1 \bigg|$

$\rightarrow \mathrm{error}$: Undefined variable 'm'

Note that units ONLY work in the Unit Section, this is because the Units Section, tokenizes units and the Math Section does not.

Support

Special Operators

$?=\mathrm{Unit}$ Formula query; finds all formulas to obtain a target from units in the expression list
$\mathrm{Var}:=$ Solve-for; solves the expression for the given variable
@ $=\mathrm{Var}_1,\mathrm{Var}_2,\ldots$ Solve system; solves a system of equations for the listed variables
$\pm$ Plus-minus; evaluates an expression as both its positive and negative form

Constants

Constant	Description	Value
$\mathrm{g}$	Gravitational acceleration	$9.8 \ \frac{m}{s^2}$
$\mathrm{G}$	Gravitational constant	$6.6743 \cdot 10^{-11} \ \frac{Nm^2}{kg^2}$
$\mathrm{e}$	Euler's number	$2.718281828459$
$\mathrm{e_c}$	Elementary charge	$1.602 \cdot 10^{-19} \ C$
$\mathrm{e_0}$	Electric constant (permittivity of free space)	$8.854187817 \cdot 10^{-12} \ \frac{F}{m}$
$\epsilon_0$	Vacuum permittivity (alias for e_0)	$8.854187817 \cdot 10^{-12} \ \frac{F}{m}$
$\mathrm{k}$	Coulomb constant	$8.99 \cdot 10^9 \ \frac{Nm^2}{C^2}$
$\mu_0$	Vacuum permeability	$4\pi \cdot 10^{-7} \ \frac{H}{m}$
$\mathrm{c}$	Speed of light in vacuum	$2.99792458 \cdot 10^8 \ \frac{m}{s}$
$\mathrm{m_e}$	Electron mass	$9.1093837 \cdot 10^{-31} \ kg$
$\mathrm{m_p}$	Proton mass	$1.67262192 \cdot 10^{-27} \ kg$
$\mathrm{m_n}$	Neutron mass	$1.674927 \cdot 10^{-27} \ kg$
$\mathrm{R_g}$	Ideal gas constant	$8.31446 \ JK^{-1}mol^{-1}$
$\mathrm{R_a}$	Ideal gas constant (atm units)	$0.0821 \ \atmLK^{-1}mol^{-1}$
$\mathrm{C_K}$	Celsius->Kelvin offset	$273.15 \ K$
$\mathrm{h}$	Planck constant	$6.62607015 \cdot 10^{-34} \ Js$
$\mathrm{a_0}$	Bohr radius	$5.291772 \cdot 10^{-11} \ m$
$\mathrm{N_A}$	Avogadro constant	$6.022 \cdot 10^{23} \ mol^{-1}$
$\alpha$	Fine-structure constant	$7.2973525693 \cdot 10^{-3}$

Functions

Basic Math

sqrt ceil floor round abs

Trigonometric

sin cos tan sec csc cot

Inverse Trigonometric

arcsin arccos arctan arcsec arccsc arccot

Hyperbolic

sinh cosh tanh sech csch coth

Inverse Hyperbolic

arcsinh arccosh arctanh

Logarithmic

log ln

Statistical

mean std var median

Combinatorics

nCr nPr

Aggregates

sum prod min max

Number Theory

gcd lcm

Linear Algebra

det trace

Complex Numbers

conj Re Im

Utility

fact sig val unit clamp lerp norm dot cross

Integration

int

Temperature Conversion

FahrC FahrK CelK CelF

Angle Conversion

rad deg

Other

sin^{-1} cos^{-1} tan^{-1} sec^{-1} csc^{-1} cot^{-1} tr

Footnotes

The name of both this application, Everett, as well as the backing library, Nero, are based off of Secrets of the Silent Witch. Everett, because Monic Everett is known for her mathematical genius and memorization of formulas, and Nero just because he is her familar.