News for hackers. Stuff that matters.

A comment on Calculize: A Mathematical Scripting Language.

Re:Calculize: A Mathematical Scripting Language by tomp on Tuesday August 09, 2011 @12:35PM (#2864636)
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.

[ Parent | on HN ]
Re:Calculize: A Mathematical Scripting Language by sesqu on Tuesday August 09, 2011 @03:41PM (#2865315)
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.
[ Parent | on HN ]
Re:Calculize: A Mathematical Scripting Language by JadeNB on Wednesday August 10, 2011 @08:41AM (#2867901)
> 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)?

[ Parent | on HN ]
Re:Calculize: A Mathematical Scripting Language by sesqu on Wednesday August 10, 2011 @10:22AM (#2868309)
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.
[ Parent | on HN ]
Re:Calculize: A Mathematical Scripting Language by tomp on Thursday August 11, 2011 @04:27AM (#2871986)
Probably this is just a lapsus lingue, but what you are saying makes no sense.

Vectors are a special case of matrices, which are a special case of tensors (finally, scalars, which is just a fancy name for plain numbers, are a special case of vectors). Although there are many mathematical representation of all these objects (geometrical, functional, etc.), they can be written as multidimensional arrays (after selecting for a base).

Thus, scalars are 1x1 matrices, and a vector of size n is actually a nx1 matrix. Although a common high-school notation of a vector is x = (1, 2, 3), a vector is actually

  x = [ 1
        2
        3 ]
Tensors are the extension of matrices to further dimensions.
[ Parent | on HN ]
Re:Calculize: A Mathematical Scripting Language by sesqu on Thursday August 11, 2011 @07:17PM (#2875259)
Right. And how would you characterize the 4-dimensional extension, in terms of the first three?

Or do you simply draw the line at two dimensions, figuring that's as much as anyone will ever need?

[ Parent | on HN ]
Re:Calculize: A Mathematical Scripting Language by JadeNB on Tuesday August 23, 2011 @04:29PM (#2918244)
What are the two dimensions of which you speak here? The 'row' and 'column' dimensions of a matrix? If so, that's exactly what tensors do: A matrix is a 2-tensor (better, a (1, 1)-tensor, but let's not get into that). If you want an m-dimensional generalisation, just use an m-tensor.
[ Parent | on HN ]