shautvast / matrepl

Inspired by 3Blue1Brown's series on linear algebra

MatRepl

• is a Matrix
• and a repl: Read–Eval–Print Loop, where Print is doing operations on vectors and matrices in a graphic environment
• written in vanilla javascript (ES6)
• see live at https://matrepl.net

The repl has the following syntax (It's work in progress, new capabilities will be added)

• arithmetic expressions:

  • add(+), subtract(-), divide(/), multiply(*) on scalars, vectors and matrices.

• variable declaration eg: a = 1 + 2

• remove(x) removes bindings (when it's an object (eg vector), removes it from the matrix)

• remove(@n) removes an object using it's assigned index (n is a number)

  • By the way, values can be bound to a name (assigned to a variable), but you can always also refer to them using their id, using : @n
  • so a = vector(1,1)

  > vector@0{x0:0, y0: 1, x:1, y:1}

  • and then @0

  > vector@0{x0:0, y0: 1, x:1, y:1}

• method calls: a = vector(12, 1) works as well. The start is now the origin.

  > vector@0{x0:0, y0: 2, x:12, y:1}

  vector(-1 -1) != vector(-1-1) and the latter would mean vector(-2) which is not legal.

• arrays: [i₀, i₁, i₂, ... i_n] creates an array.

  • [i₀, i₁] is special: it is a shorthand for creating a 2-dimensional vector. I'll have to think of another way to create an array of length 2...

• ```id()`` adds a 2d identity matrix, which is also the two basis vectors.

• properties

  • a = [1,2]
  • a.type

  > vector

  • a.x+1

  > 13

• drag vectors using the mouse pointer. You can change the vector arrows visually

• lazy evaluation. The difference between c = a+b and c = "a+b" is that the latter assigns to c a parsed expression that can always be evaluated later. When you apply lazy evaluation and later update a, the value for c will be reevaluated automatically. Combined with vector dragging, this way you can get an intuition for vector addition. Want to do the same for matrix multiplication and basis change.

• Example: enter the following, like in the screenshot:

  a = vector(0.5, 0.5)
  b = vector(-1, 1)
  c = "a + b"
  

• and press enter. Then using the mouse pointer move vector a or b. Or try: a = 2 * a This updates vector a to twice it's size. And, because c is defined lazily, it is updated as well!

To run locally

• make sure you have node/npm
• cmdline: npm run start
• and enter help()