Complex Function Integral

mathjs is a powerful library for mathematical operations, including support for complex numbers. Unfortunately, it does not yet provide a built-in function for computing integrals, and in particular it lacks support for complex function integrals.

This library fills that gap by providing a simple interface to compute the integral of a complex function over the interval [0, 1]. The integral is computed using a simple midpoint Riemann sum with a default of 1000 subdivisions.

Note: It uses the Complex type and related utilities exported by mathjs for complex number operations

Usage

import type { ComplexFunction } from 'complex-function-integral'
import { complex, computeComplexIntegral } from 'complex-function-integral'

// Example complex function: f(t) = cos(t) + isin(t) = e^(it)
const complexFunction: ComplexFunction = t => complex(Math.cos(t), Math.sin(t))

computeComplexIntegral({ complexFunction })

Run this project locally

Prerequisites

To ensure compatibility and reproducibility, this project requires pnpm version 10.28.2 or higher.

{
  "engines": {
    "pnpm": ">=10.28.2"
  }
}

Install the dependencies

pnpm install --frozen-lockfile

Improvements

Potential future improvements to this library include:

• The current implementation uses a simple numerical integration method (midpoint Riemann sum). Future improvements could include other simple implementations (e.g., left and right Riemann sums, trapezoidal rule).
• computeComplexIntegral currently does not round the result, which may lead to very small real or imaginary parts due to numerical precision issues. Adding an option to round the result to a specified number of decimal places if desired could be beneficial.
• The library could be extended to support integration over different intervals or even along complex paths in the complex plane.

Misc

Supply chain security

To reduce the risk of installing compromised packages, this project enforces a 7-day delay before installing newly published package versions. The policy is configured in pnpm-workspace.yaml with:

minimumReleaseAge: 10080 # minutes (= 7 days)

License

This project is licensed under the MIT License. See the LICENSE file for details.