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Calculize: A Mathematical Scripting Language

72 points by jashkenas 15y ago

jashkenas 15y ago
Direct link to the live demo: http://calculize.com/pickhardt/standard_example http://calculize.com/pickhardt/standard_example
tychonoff 15y ago
Nice.
knowtheory 15y ago
This is pretty awesome! Their contact page 404s unfortunately. There're some visual glitches in their guided tour that i wanted to point out. Seems like an admirable repurposing of what Coffeescript is doing to create a mathematics toolkit. (Last note: too bad they didn't name it Calculon!)
GregBuchholz 15y ago
Others might find the Sage Notebook interesting: http://nb.sagemath.org/ http://nb.sagemath.org/ http://sagenb.com/ http://sagenb.com/ Features •Use Sage, Python, R, Octave, and most other mathematical software with any web browser •Notebook interface that allows you to write and run code, display 2d and 3d plots, and organize and share your work.
j4mie 15y ago
Impressive. They seem to have added operator overloading to CoffeeScript, among other things: # 1. Matrix multiplication m1 = matrix([1, 2, 5], [2, -1, 6], [5, 10, -1]) m2 = matrix([2, 3, 1], [-3, -1, -3], [4, 9, -2]) show m1 * m2 Not sure how this could be used for "serious" number crunching (as it runs in-browser) but I imagine it would be a fantastic teaching tool.
- Vivtek 15y ago
  You could use it as a prototyping tool, then run JS on a server for "serious" crunching, maybe.
- deleted 15y ago
  [deleted]
- jashkenas 15y ago
  One major problem with any JS-based language for number crunching is JS' lack of any numeric types other than a double. I don't know how well the string-based workarounds really work, for arbitrary precision math ... but I'd imagine that they wouldn't be terribly fast or convenient. It's a real shame.
  - mbrubeck 15y ago
    Current versions of Firefox and Chrome have typed arrays, which add more numeric types for performance optimization. Hopefully we will see them in other browsers soon: https://developer.mozilla.org/en/javascript_typed_arrays https://developer.mozilla.org/en/javascript_typed_arrays
- Someone 15y ago
  It would need lots and lots and lots of work before I would call it a fantastic teaching tool. For example, it is spectacularly naive at plotting functions. Even a relatively simple function such as 1/sin(x) already brings it to its knees.
tomp 15y ago
Coffeescript-inspired syntax is nice, but unfortunately Matlab is clearly superior for anything mathematical than most other languages, so drawing some inspiration from it wouldn't hurt... For example: m1 = matrix([1, 2, 5], [2, -1, 6], [5, 10, -1]) why not adapt a simpler syntax for constructing multi-dimensional arrays: m1 = [1 2 5; # commas are optional 2, -1, 6; 5, 10, -1] Also, a special constructor for matrices and vectors is redundant - in a mathematical language, a list/array is the special case, not a matrix/vector. Besides, vectors are just a special case of matrices, no need to treat them differently, especially since the dot product is not overloaded in Calculize. Matlab also wins by having a special syntax for matrix transpose. Now, this depends on the implementation ( AFAIK, Matlab doesn't actually transpose the matrix, it simply uses a different algorithm for further calculations), but would still be nice, since it's often useful (necessary) when trying to multiply matrices.
- sesqu 15y ago
  I don't think you should consider vectors a special case of matrices - that makes tensors difficult to handle. The other way around generalizes better.
  - JadeNB 15y ago
    > I don't think you should consider vectors a special case of matrices - that makes tensors difficult to handle. The other way around generalizes better. I guess (from the first sentence) that you mean to regard matrices as a special case of tensors (which certainly generalises well), rather than of vectors (which is possible but ugly)?
    - sesqu 15y ago
      No, I certainly do mean to regard matrices as a special case of vectors. While it's true that one rarely needs more than 3 dimensions to their array, I see no point in setting an upper limit.
      - 15y ago
benhamner 15y ago
Nice. A good next step would be to add an interactive window, like the main window in Matlab.
autotelicum 15y ago
I like the concept - really nice. It would be cool to see an update of Calculize use a math library instead of JavaScript numbers. In Calculize: a = 1/3 show a+a+a+a+a+a == 6*a # => false show pow 9,18 # => 150094635296999140 # should be: 150094635296999121 show 150094635296999122 - 150094635296999121 # => 0 In Python 2.6.1: >>> p = 1.0/3.0 >>> p+p+p+p+p+p == 6*p False >>> pow(9,18) 150094635296999121 >>> 150094635296999122 - 150094635296999121 1 These minuscule rounding errors are inconsequential for most apps, but for math... Maybe the results will also vary between browsers, because EcmaScript talks of implementation-dependent approximation's. [Edit: Oops, python got me with it's own quirk - division needs to be from the __future__ or it's integer]
abdulhaq 15y ago
I really like the look of this. I developed http://kayali.sf.net http://kayali.sf.net (Maxima/Qt based) and achieving such a clean look is very difficult. Having a web based app makes a lot of sense these days especially for students.

72 points by jashkenas 15y ago

Direct link to the live demo: http://calculize.com/pickhardt/standard_example http://calculize.com/pickhardt/standard_example

tychonoff 15y ago

Nice.

knowtheory 15y ago

This is pretty awesome! Their contact page 404s unfortunately. There're some visual glitches in their guided tour that i wanted to point out. Seems like an admirable repurposing of what Coffeescript is doing to create a mathematics toolkit. (Last note: too bad they didn't name it Calculon!)

GregBuchholz 15y ago

Others might find the Sage Notebook interesting: http://nb.sagemath.org/ http://nb.sagemath.org/ http://sagenb.com/ http://sagenb.com/ Features •Use Sage, Python, R, Octave, and most other mathematical software with any web browser •Notebook interface that allows you to write and run code, display 2d and 3d plots, and organize and share your work.

j4mie 15y ago

Impressive. They seem to have added operator overloading to CoffeeScript, among other things: # 1. Matrix multiplication m1 = matrix([1, 2, 5], [2, -1, 6], [5, 10, -1]) m2 = matrix([2, 3, 1], [-3, -1, -3], [4, 9, -2]) show m1 * m2 Not sure how this could be used for "serious" number crunching (as it runs in-browser) but I imagine it would be a fantastic teaching tool.

Vivtek 15y ago
You could use it as a prototyping tool, then run JS on a server for "serious" crunching, maybe.
deleted 15y ago
[deleted]
jashkenas 15y ago
One major problem with any JS-based language for number crunching is JS' lack of any numeric types other than a double. I don't know how well the string-based workarounds really work, for arbitrary precision math ... but I'd imagine that they wouldn't be terribly fast or convenient. It's a real shame.
- mbrubeck 15y ago
  Current versions of Firefox and Chrome have typed arrays, which add more numeric types for performance optimization. Hopefully we will see them in other browsers soon: https://developer.mozilla.org/en/javascript_typed_arrays https://developer.mozilla.org/en/javascript_typed_arrays
Someone 15y ago
It would need lots and lots and lots of work before I would call it a fantastic teaching tool. For example, it is spectacularly naive at plotting functions. Even a relatively simple function such as 1/sin(x) already brings it to its knees.

tomp 15y ago

Coffeescript-inspired syntax is nice, but unfortunately Matlab is clearly superior for anything mathematical than most other languages, so drawing some inspiration from it wouldn't hurt... For example: m1 = matrix([1, 2, 5], [2, -1, 6], [5, 10, -1]) why not adapt a simpler syntax for constructing multi-dimensional arrays: m1 = [1 2 5; # commas are optional 2, -1, 6; 5, 10, -1] Also, a special constructor for matrices and vectors is redundant - in a mathematical language, a list/array is the special case, not a matrix/vector. Besides, vectors are just a special case of matrices, no need to treat them differently, especially since the dot product is not overloaded in Calculize. Matlab also wins by having a special syntax for matrix transpose. Now, this depends on the implementation ( AFAIK, Matlab doesn't actually transpose the matrix, it simply uses a different algorithm for further calculations), but would still be nice, since it's often useful (necessary) when trying to multiply matrices.

sesqu 15y ago
I don't think you should consider vectors a special case of matrices - that makes tensors difficult to handle. The other way around generalizes better.
- JadeNB 15y ago
  > I don't think you should consider vectors a special case of matrices - that makes tensors difficult to handle. The other way around generalizes better. I guess (from the first sentence) that you mean to regard matrices as a special case of tensors (which certainly generalises well), rather than of vectors (which is possible but ugly)?
  - sesqu 15y ago
    No, I certainly do mean to regard matrices as a special case of vectors. While it's true that one rarely needs more than 3 dimensions to their array, I see no point in setting an upper limit.
    - 15y ago

benhamner 15y ago

Nice. A good next step would be to add an interactive window, like the main window in Matlab.

autotelicum 15y ago

I like the concept - really nice. It would be cool to see an update of Calculize use a math library instead of JavaScript numbers. In Calculize: a = 1/3 show a+a+a+a+a+a == 6*a # => false show pow 9,18 # => 150094635296999140 # should be: 150094635296999121 show 150094635296999122 - 150094635296999121 # => 0 In Python 2.6.1: >>> p = 1.0/3.0 >>> p+p+p+p+p+p == 6*p False >>> pow(9,18) 150094635296999121 >>> 150094635296999122 - 150094635296999121 1 These minuscule rounding errors are inconsequential for most apps, but for math... Maybe the results will also vary between browsers, because EcmaScript talks of implementation-dependent approximation's. [Edit: Oops, python got me with it's own quirk - division needs to be from the __future__ or it's integer]

abdulhaq 15y ago

I really like the look of this. I developed http://kayali.sf.net http://kayali.sf.net (Maxima/Qt based) and achieving such a clean look is very difficult. Having a web based app makes a lot of sense these days especially for students.