Complex Expression Parser

Complex Expression Parser parses mathematical expression strings over the field of complex numbers.

Installation

If you want to use it in a browser:

• Just include es5/expression.js or es5/expression.min.js before your scripts.
• Include a shim such as es6-shim if your target browser does not support common ES6 features such as extra methods on Array or Number.

For node.js just run

npm install complex-expression-parser

If you are running in an environment that supports ES6 then you may begin using Expression in your code using

import Complex from './es6/complex.js';
import Expression from './es6/expression.js';

ES6 environments can use the Complex and ComplexMath classes directly by importing their respective files.

Usage

Expression has a single method: evaluate.

Construction

Expression takes a single string as an argument to its constructor. This string should be a valid mathematical expression. Any symbol which is not known to the parser is interpreted as a variable. If the expression is not syntactically valid then the constructor throws an exception.

// Create an expression for the equation 2x^2 + 3x - i where i is the
// imaginary constant
const expression = new Expression('2x * x + 3x - i');

evaluate

evaluate takes a single, optional dictionary of symbols and their values and returns the value of the expression as a Complex. If the expression has any unset variables then this method throws an exception.

const expression = new Expression('2x + i');

const valueA = expression.evaluate({'x': new Complex(2, 4)}); // valueA is 6 + 9i
const valueB = expression.evaluate({'x': 2}); // valueB is 4 + i
const noValue = expression.evaluate(); // throws exception

Naming Symbols

Symbols can be any number of alphabetic characters followed by any number of digits or can be a single Unicode character.

Example symbols:

• x
• yy
• M104
• ☃
• \uD83D\uDE80

Example non-symbols:

• i - Known constant
• 2x - Interpreted as 2 * x
• M104M - Interpreted as M104 * M
• ☃☃ - Interpreted as ☃ * ☃
• \uD83D\uDE80\uD83D\uDE80 - Interpreted as \uD83D\uDE80 * \uD83D\uDE80

Supported Functions and Constants

Constants

• e: Euler's constant
• i: The imaginary unit
• pi: The ratio of a circle's circumference to its diameter

Functions

Arithmetic

• + (unary): The identity function
• + (binary): Addition
• - (unary): Negation
• - (binary): Subtraction
• *: Multiplication
• /: Division

Algebraic

• abs(x): The magnitude of x
• arg(x): The phase of x
• ceil(x): The ceiling of x
• conj(x): The conjugate of x
• exp(x): The exponential of x
• floor(x): The floor of x
• frac(x): The fractional part of x
• imag(x): The imaginary part of x
• ℑ(x): The imaginary part of x
• lg(x): The log base 2 of x
• ln(x): The natural log of x
• log(base, x): The log base base of x
• log10(x): The log base 10 of x
• mod(x, y): x mod y
• nint(x): The nearest integer of x
• norm(x): The norm of x
• pow(base, power): base raised to the power of power
• real(x): The real part of x
• ℜ(x): The real part of x
• sqrt(x): The square root of x

Trigonometric

• arccos(x): The inverse cosine of x
• arccosh(x): The inverse hyperbolic cosine of x
• arccot(x): The inverse cotangent of x
• arccoth(x): The inverse hyperbolic cotangent of x
• arccsc(x): The inverse cosecant of x
• arccsch(x): The inverse hyperbolic cosecant of x
• arcsec(x): The inverse secant of x
• arcsech(x): The inverse hyperbolic secant of x
• arcsin(x): The inverse sine of x
• arcsinh(x): The inverse hyperbolic sine of x
• arctan(x): The inverse tangent of x
• arctanh(x): The inverse hyperbolic tangent of x
• cos(x): The cosine of x
• cosh(x): The hyperbolic cosine of x
• cot(x): The cotangent of x
• coth(x): The hyperbolic cotangent of x
• csc(x): The cosecant of x
• csch(x): The hyperbolic cosecant of x
• sec(x): The secant of x
• sech(x): The hyperbolic secant of x
• sin(x): The sine of x
• sinh(x): The hyperbolic sine of x
• tan(x): The tangent of x
• tanh(x): The hyperbolic tangent of x

Special

• gamma(x): The gamma of x
• Γ(x): The gamma of x

Contributing

Submit a pull request and mail [email protected].

Development should occur against the ES6 files. Build and test using

npm run prepare

All changes must include appropriate tests.

License

Complex Expression Parser is open-sourced software licensed under the MIT license