math-validation

• an api
• a large set of test data
• aims to determine if two mathematical expressions are equal, either having the same form or not
• have a public website where you can add some math and check if it works - also the link should be shareable

demo

yarn demo

Then go to http://localhost:$PORT/demo

Tests

yarn jest

Runs all the tests

There is one test that runs fixture data located here: src/fixtures/latex-equal/*.ts. To filter the fixtures you run here you can use the -t flag:

yarn jest src/__tests__/latex-equal.spec.ts -t src/fixtures/latex-equal/7119.ts --reporters default

Next Steps

• Check that api we expose will support what is needed.
• Do triage on the test failures, add a note to failing test so we can build a picture of the work needed

Test failure triage

theme	notes
latex parsing	seems like we aren't able to parse all the inputs in the test cases
math evaluation	math.js is not seeing things as being equal - need more detail on that
incomplete literal support	we haven't really set up literal options support yet
incorrect test data	sometimes the test data is not quite right

Goals

• we parse from latex -> ast -> mathjs
• clean up symbolic evaluation (in progress)
• avoid the use of string manipulation/regex (in progress)
• more advanced literal validation (todo)
• block input that is clearly too large/unrelated (eg: a user can type in gobbledy-gook - we should just abort if we see that)

Capabilities

It can determine mathematical equivalence between:

• linear equations in one variable
• linear equations in two variables
• quadratic equations
• 2-way inequalities in one or two variables
• compound inequalities in one variable
• trigonometric identities and functions
• inverse trigonometric functions
• similar notation for logarithms and based logarithms

It can also handle degrees, radians and gradians

things that'd be great (but we may have to park until we have more time)

• a faster latex parser
• faster math evaluation

Modes

There are 2 modes - literal and symbolic

Literal: is at its most basic a tuned version of a string validation

By default - ignores spaces and parentheses as long as they do not change the meaning of operations (ex. “a+7 +b” will validate against “ ((a) + (7))+b ”) - ignores leading zeros: “0.1” will validate against “.1” - accepts commas for decimal marks. For example “1,000” will be equivalent with 1000

Literal Validation offers two configuration options that can be used to validate some variety of forms for an expression:

Ignore trailing zeros option; allows the evaluation to accept zeros to the right of the decimal place “4.5” will validate against “4.50000000000000” Ignore order option; makes validation indifferent to the variables order, as long as it does not change operations meaning. In this case “a+7 +b*c” will validate against “7 + a+bc”, but not against “ac+7+b”; without it “a+7 +b” will not validate against “7 + a+b”

Symbolic: attempts to decide if expressions are mathematically equivalent or not

By default, it offers all configurations presented for literal validation, exceeding it by quite a lot In order to check equivalence between 2 expressions, we have to reduce both expressions to the simplest one. Then distribute all coefficients, combine any like terms on each side of the expression, and arrange them in the same order.

Notes

• @babel/runtime is a devDependency if you ever need to link this repo to another package for testing

TODO

• set up api that is compatible w/ ui component options
• derivatives kind of work and kind of not - how to use?

CI

We use circleci - see .circleci/config.yml

debugging tests

vscode

add the following to configurations array in launch.json

    {
      "name": "Attach",
      "port": 9229,
      "request": "attach",
      "skipFiles": [
        "<node_internals>/**"
      ],
      "type": "pwa-node"
    }

node --inspect-brk ./node_modules/.bin/jest --runInBand #and any other flags you want

The launch debug using 'Attach' command above.