require "matrix"
local int = require "int"

local function pascal_upper_triangular(n)
    local m = {}
    for i = 1, n do
        m[i] = {}
        for j = 1, n do m[i][j] = (j >= i) ? int.binomial(j - 1, i - 1) : 0 end
    end
    return matrix.from(m)
end

local function pascal_symmetric(n)
    local m = {}
    for i = 1, n do
        m[i] = {}
        for j = 1, n do m[i][j] = int.binomial(i + j - 2, i - 1) end
    end
    return matrix.from(m)
end

local function pascal_lower_triangular(n)
    return pascal_symmetric(n):cholesky()
end

local n = 5
print("Pascal upper-triangular matrix:")
print(pascal_upper_triangular(n))
print("\nPascal lower-triangular matrix:")
print(pascal_lower_triangular(n):format("%d"))
print("\nPascal symmetric matrix:")
print(pascal_symmetric(n))