These examples are from the web page "A very short introduction in Matlab", and from some other sources. Let us switch to Matlab mode. Matlab uses a very short display by default.
>matlab on; shortestformat;
Matrices can now have blanks between elements. Note: For negative elements, use the comma, since [1 -1 1] would yield [0 1] in Euler.
>A=[16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1]
16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1
Matrix elements can be accessed with round brackets.
>A(1,1)+A(2,1)+A(3,1)+A(4,1)
34
The sum operator now works columns vectors diffently.
>sum(A(1:4,1)) // use sum(A[1:4,1]') in Euler
34
>sum(A) //
[ 34 34 34 34 ]
>diag(A,0)
16 10 7 1
fliplr works like flipx, and flipud like flipy.
>sum(diag(fliplr(A)))
34
Functions like fliplr are declared in matlab.e and loaded into each Euler session.
>rot(A,2)
1 14 15 4 12 7 6 9 8 11 10 5 13 2 3 16
Euler does also have an algorithm for magic triangles.
>magic(4)
16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1
Euler used the matrix language consistently for all operators. Matlab uses .* for the elementwise multiplication.
>v=1:10; v.*v
[ 1 4 9 16 25 36 49 64 81 100 ]
And it uses * for the matrix product.
>v*v'
[ 385 ]
The power operator now uses the matrix power function.
>A=[1,2;3,4]; A^2
7 10 15 22
This works for the invers too.
>A^-1*A
1 0 0 1
The division uses "divide into" now. I.e. b/A = (A'\b')'
>sum(A)/A
[ 1 1 ]
The \ operator now uses fit.
>A=[1,2;3,4;5,6]; b=[1;2;3]; A\b
0 0.5
The same in Euler.
>fit(A,b)
0 0.5
In Matlab mode, you can use Matlab's syntax for functions. A proper "return y" statement will be added. If the function is the last or the only function in a file, "endfunction" can be omitted.
>function y=f(x)
y=x^2; endfunction
>f(5)
25