magic

import mir.math.sum;
import mir.ndslice: slice, magic, byDim, map, as, repeat, diagonal, antidiagonal;

bool isMagic(S)(S matrix)
{
    auto n = matrix.length;
    auto c = n * (n * n + 1) / 2; // magic number
    return // check shape
        matrix.length!0 > 0 && matrix.length!0 == matrix.length!1
        && // each row sum should equal magic number
        matrix.byDim!0.map!sum == c.repeat(n)
        && // each columns sum should equal magic number
        matrix.byDim!1.map!sum == c.repeat(n)
        && // diagonal sum should equal magic number
        matrix.diagonal.sum == c
        && // antidiagonal sum should equal magic number
        matrix.antidiagonal.sum == c;
}

assert(isMagic(magic(1)));
assert(!isMagic(magic(2))); // 2x2 magic square does not exist
foreach(n; 3 .. 24)
    assert(isMagic(magic(n)));
assert(isMagic(magic(3).as!double.slice));