math

Web app that helps to perform some math computation, and tries to provide the intermediate steps taken.

Very basic, matrix related stuff here and logic related stuff here

Where is this hosted?

This project has simple CI/CD, and semantic versioning. I manage my deployments with the master and develop branches.

master branch is hosted here. It is also the link on the right side of panel of the Github page of this repo. This contains the production build, so it is the latest stable release. For every update to this branch, the semantic version changes.

develop branch is hosted here. This contains the staging build, so it contains the very latest code, being usually ahead of master. For every update to this branch, the semantic version might not change.

Vercel provides a preview deployment for every push to a branch. As a result the code can get tested online in each PR, prior to merging into develop. This usually means that develop is as stable as master. Thus, more often than not, you can just use the develop version.

Functions

This app currently supports the following functions:

Determinant of a square matrix

Frontend page: /matrix

Frontend usage: det [[1,2],[3,4]] or determinant [[1,2],[3,4]]

API: /api/matrix/determinant?matrix=[[1,2],[3,4]]

Description: Calculates the determinant of a square matrix. Currently does not show the intermediate steps taken. The algorithm used is Laplace expansion which is O(N!), so this could be slow for larger matrices.

RREF of a matrix

Frontend page: /matrix

Frontend usage: rref [[1,2],[3,4]]

API: /api/matrix/rref?matrix=[[1,2],[3,4]]

Description: Reduces a matrix to RREF. The algorithm used first reduces the matrix to a REF form, then to RREF form.

Inverse of a square matrix

Frontend page: /matrix

Frontend usage: inv [[1,2],[3,4]] or inverse [[1,2],[3,4]]

API: /api/matrix/inverse?matrix=[[1,2],[3,4]]

Description: Obtains the inverse of a matrix. The algorithm used reduces the original matrix to RREF while playing the same row operations onto an identity matrix of the same dimensions.

"Echelon status" of a matrix

Frontend page: /matrix

Frontend usage: status [[1,2],[3,4]]

API: /api/matrix/status?matrix=[[1,2],[3,4]]

Description: Returns a string, either "Neither", "Row echelon form", or "Reduced row echelon form". Determines the form of the matrix.

Generate a truth table, given a mathematical logic expression

Frontend page: /logic

Frontend usage: !(p | q)

API: /api/logic/truthTable?expression=!(p | q)

Description: An abstract syntax tree is built, and variables are detected. Every combinations of true and false is substituted into the variables in the logic expression, and the expression is evaluated for each combination, resulting in the truth table for the expression.

Caveats

• Does not support fraction input
• Supports RREF calculations where you have non-terminating decimals, such as the decimal representation of 1/3. The output might contain somewhat long decimal representations but the idea is there.
• Comes with usual floating point errors

Purpose

This project is primarily for exploring and learning web development, and CI/CD. This project features the following:

Web development

• Javascript frontend + Typescript backend
• Using Vercel's serverless functions to host the backend

Testing

• API and unit testing with Mocha
• Mocking a server to perform API tests on Vercel serverless functions, with vercel-node-server

Automated tasks

• Automated testing with Github Workflow
• Automated changelog with auto-changelog