#!/usr/bin/ruby
# Liniar ecuations solver - Cramer's rule.
# Example:
# | 2x - 3y +  z =  4
# |  x - 2y - 2z = -6
# | 3x - 4y +  z =  5
func det(a) {
    a = a.map{.map{_}}
    var sign = +1
    var pivot = 1
    for k in ^a {
      var r = (k+1 .. a.end)
      var previous_pivot = pivot
      if ((pivot = a[k][k])==0) {
        a.swap(r.first_by { |i|
            a[i][k] != 0
        } \\ (return 0), k)
        pivot = a[k][k]
        sign = -sign
      }
      for i,j in (r ~X r) {
        a[i][j]              ->
          *= pivot           ->
          -= a[i][k]*a[k][j] ->
          /= previous_pivot
      }
    }
    sign * pivot
}
func cramers_rule(A, terms) {
    gather {
        for i in ^A {
            var Ai = A.map{.map{_}}
            for j in ^terms {
                Ai[j][i] = terms[j]
            }
            take(det(Ai))
        }
    } »/» det(A)
}
var matrix = [
    [2, -3,  1],
    [1, -2, -2],
    [3, -4,  1],
]
var free_terms = [4, -6, 5]
var (x, y, z) = cramers_rule(matrix, free_terms)...
say "x = #{x}"
say "y = #{y}"
say "z = #{z}"
assert_eq(x, 2)
assert_eq(y, 1)
assert_eq(z, 3)
# Another example:
# | 3x +   2y -  z =  1
# | 2x -   2y + 4z = -2
# | -x + 1/2y -  z =  0
var m2 = [
    [3, 2, -1],
    [2, -2, 4],
    [-1, 1/2, -1],
]
var f2 = [1, -2, 0]
assert_eq(cramers_rule(m2, f2), [1, -2, -2])
# Yet another example:
# | 2w -  x + 5y +  z =  -3
# | 3w + 2x + 2y - 6z = -32
# |  w + 3x + 3y -  z = -47
# | 5w - 2x - 3y + 3z =  49
var m3 = [
    [2, -1,  5,  1],
    [3,  2,  2, -6],
    [1,  3,  3, -1],
    [5, -2, -3,  3],
]
var f3 = [-3, -32, -47, 49]
assert_eq(cramers_rule(m3, f3), [2, -12, -4, 1])