How to rewrite the halve function in J?

Question

in the J programming language,

-: i. 5 

the above function computes the halves of all integers in [0,4]. Now let's say I'd like to re-write the -: function, just for the fun of it. My best guess so far was

]&%.2

but that doesn't seem to cut it. How do you do it?

Answer 1

%&2    NB. divide by two
0.5&*  NB. multiply by one half

Answer 2

Note that ] % 2: would also work, but to ensure proper grammar you would either want to use that as the definition of a name, or you would want to put the expression in parenthesis.

Answer 3

I saw you were using %. probably because you were dividing a matrix and thought you needed to do a "matrix divide".

The matrix divide and matrix inverse they are talking about there is for matrix algebra, where you have a list of, well, essentially polynomials, and you want to do transformations on the polynomials all at once, so as to solve the equations. One of the things you can do really easily in J is matrix algebra, there are builtins for matrix divide and for inverting a matrix (as you have seen) and in the phrases section, there are short phrases for doing all of the typical matrix transformations. Taking the determinant, for example.

But when you are simply dividing a vector by a scalar to get a vector, or you are dividing a matrix by the corresponding elements of another matrix, well, that is just the % division symbol.

If you want to try and understand this, look at euler problem 101 (http://projecteuler.net/problem=101) and then google curve fitting on the Jsoftware.com site. Creating the matrixes from the observations, and the basic matrixes as shown allow you to solve for ax^2+bx+c = y where you have x and y and you want to determine a, b, and c. Just remember to use extended arithmetic for everything, as the resultant equations are very good but not perfect unless you do, and to solve the equation you need perfect equations.

Just a thought, unless you want to play with Matrix Algebra, you might not care.