functionx 1.2.0

A powerful equation parser and solver for Dart. Parse expressions, extract variables, evaluate, solve equations, and perform symbolic calculus with a comprehensive physics constants library.

functionx

A powerful equation parser and solver for Dart — f(x) for your code.

Features

• 🧮 Expression Parsing - Strictly explicit parsing (e.g. 2*x, m*a) for maximum predictability
• 📊 Variable Extraction - Intelligently extract variables while filtering constants
• 🔢 Expression Evaluation - Multi-mode evaluation (Real, Complex, and Mixed)
• ⚡ Equation Solving - High-precision algebraic and numerical solvers
• 📈 Symbolic Calculus - Fast differentiation and integration
• 🔬 Auto-resolve Constants - Automatic identification of symbols like $c$, $h$, and $k_B$
• 🇬🇷 LaTeX Support - Seamless parsing of Greek letters and complex subscripts

Installation

Add to your pubspec.yaml:

dependencies:
  functionx: ^1.2.0

Quick Start

import 'package:functionx/functionx.dart';

void main() {
  // Extract variables from an equation
  final vars = ExpressionParser.extractVariables('y = m*x + b');
  print(vars); // ['b', 'm', 'x', 'y']

  // Evaluate an expression
  final result = Evaluator.evaluate('x^2 + 2*x + 1', {'x': 3});
  print(result); // 16.0

  // Solve an equation
  final solution = Solver.solve(
    'F = m*a',
    {'F': 10, 'm': 2},
    solveFor: 'a',
  );
  print(solution.value); // 5.0

  // Use physical constants
  final c = Constants.speedOfLight;
  print('${c.name}: ${c.value} ${c.unit}'); // Speed of Light: 299792458 m/s

  // Symbolic differentiation
  final derivative = Cas.differentiate('x^2', 'x');
  print(derivative); // '2.0 * x'
}

Expression Syntax

This parser is designed to be ergonomic but strictly explicit:

✅ Notation	📝 Example
Explicit	2*x + 3*y
Parentheses	3*(x+1)*(x-1)
Complex	(1+i)i
Greek	\Delta E = h*\nu
Subscripts	x_1 + x_2

Supported Operators

Operator	Description
+	Addition
-	Subtraction
*	Multiplication
/	Division
^	Exponentiation

Supported Functions

Function	Description
sin(x)	Sine
cos(x)	Cosine
tan(x)	Tangent
asin(x)	Arc sine
acos(x)	Arc cosine
atan(x)	Arc tangent
sqrt(x)	Square root
abs(x)	Absolute value
log(x)	Natural logarithm
ln(x)	Natural logarithm
exp(x)	Exponential
pow(x, n)	Power

Mathematical Constants

Constant	Value
PI	3.14159...
EN	2.71828...
INF	∞
IN	i (√-1)

Reserved Words & Aliases

To avoid ambiguity (like $c$ for the speed of light vs $c$ for a variable), functionx uses Strict Constant Lookup. You MUST use these specific keys if you want the parser to auto-resolve constants. Common symbols like c, g, h are treated as plain variables.

• Functions: sin, cos, tan, asin, acos, atan, sqrt, abs, log, ln, exp, pow
• Math Constants: PI, EN, INF, IN
• Natural Constants (Keys): SOL (Speed of Light), GC (Gravitational), PC (Planck), SG (Standard Gravity), NA (Avogadro), etc.

Note: You must explicitly use SOL (or speed_of_light) to get the constant $c$. Uses of c will just be the variable $c$.

API Reference

ExpressionParser

// Parse expression or equation
final result = ExpressionParser.parse('y = m*x + b');
print(result.isEquation); // true

// Extract variables
final vars = ExpressionParser.extractVariables('F = m*a');
print(vars); // ['F', 'a', 'm']

Evaluator

// Evaluate with variables
final result = Evaluator.evaluate('x^2 + y', {'x': 3, 'y': 5});
print(result); // 14.0

// Evaluate numeric expression (no variables)
final result = Evaluator.evaluateNumeric('2 + 3 * 4');
print(result); // 14.0

Solver

// Solve for unknown variable
final result = Solver.solve(
  '2*x + 5 = 11',
  {'x': null},
);
print(result.value); // 3.0
print(result.steps); // ['...solution steps...']

// Solve physics equation
final result = Solver.solve(
  'F = m*a',
  {'F': 10, 'm': 2},
  solveFor: 'a',
);
print(result.value); // 5.0

Cas (Computer Algebra System)

// Differentiation
final deriv = Cas.differentiate('x^3', 'x');
print(deriv); // '3.0 * x ^ 2.0'

// Integration
final integral = Cas.integrate('x', 'x');
print(integral); // '0.5*x^2'

// Simplification
final simplified = Cas.simplify('x + x');
print(simplified); // '2.0 * x'

Constants

A comprehensive collection of physical and mathematical constants.

// Access by property
final c = Constants.speedOfLight;
print(c.value);  // 299792458
print(c.symbol); // c
print(c.unit);   // m/s
print(c.name);   // Speed of Light

// Get by key
final g = Constants.get('GC');
print(g?.value); // 6.6743e-11

// List all constants in a category
final fundamental = Constants.byCategory('fundamental');

// Search constants
final results = Constants.search('mass');

Available Categories

Category	Examples
mathematical	π, e, φ (golden ratio), √2, i
fundamental	Speed of light, Planck constant, Gravitational constant
electromagnetic	Elementary charge, Vacuum permittivity, Coulomb constant
atomic	Electron/Proton mass, Bohr radius, Fine structure, Rydberg
thermodynamic	Boltzmann const, Gas constant, Radiation constants
quantum	Magnetic Flux Quantum, Conductance Quantum, Josephson
electrochemical	Faraday constant
earth	Standard gravity, Earth mass, Earth radius
celestial	Sun mass, Astronomical unit, Light year

Common Constants

Property	Key	Symbol	Value
Constants.speedOfLight	SOL	c	299792458 m/s
Constants.planck	PC	h	6.626e-34 J⋅s
Constants.gravitationalConstant	GC	G	6.674e-11 N⋅m²/kg²
Constants.boltzmann	BC	kB	1.381e-23 J/K
Constants.avogadro	AN	NA	6.022e23 1/mol
Constants.faraday	FC	F	96485 C/mol
Constants.rydberg	RYD	R∞	1.097e7 1/m
Constants.standardGravity	SG	g	9.807 m/s²
Constants.elementaryCharge	EC	e	1.602e-19 C
Constants.coulomb	CC	k	8.988e9 N⋅m²/C²
Constants.pi	PI	π	3.14159...
Constants.e	EN	e	2.71828...
Constants.imaginaryUnit	IN	i	√-1

License

MIT License - see LICENSE for details.