Lua

math.tau = 2 * math.pi
function math.degree(v)
    return 360 * v / math.tau
end

function math.radian(v)
    return math.tau * v / 360
end
function math.round(num, prec)
    local mult = 10^(prec or 0)
    return ((num * mult + 0.5) / mult):floor()
end
function math.sgn(num)
    return num > 0 and 1 or num < 0 and -1 or 0
end
vector = {}

_meta = _meta or {}
_meta.V = {}
function V(t, n)
    local res = {}
    res.n = n or t.n or #t
    for i = 1, res.n do
        res[i] = t[i]
    end

    return setmetatable(res, _meta.V)
end
function vector.zero(n)
    return vector.fill(n, 0)
end
function vector.fill(n, k)
    local res = {}
    for i = 1, n do
        res[i] = k
    end

    res.n = n
    return setmetatable(res, _meta.V)
end
function vector.unit(n, i)
    local res = {}
    for j = 1, n do
        res[j] = i == j and 1 or 0
    end

    res.n = n
    return setmetatable(res, _meta.V)
end

function vector.length(v)
    local length = 0
    for _, val in ipairs(v) do
        length = length + val^2
    end

    return math.sqrt(length)
end
function vector.cross(v1, v2)
    local res = {}
    res[1] = v1[2]*v2[3] - v1[3]*v2[2]
    res[2] = v1[3]*v2[1] - v1[1]*v2[3]
    res[3] = v1[1]*v2[2] - v1[2]*v2[1]

    res.n = 3
    return setmetatable(res, _meta.V)
end