#!/usr/local/bin/lua -i

Vector={}


function Vector.new(x,y) 
	local v={x,y}
	setmetatable (v, Vektorrechnung)
	return v
end

function Vector.add(a,b) return Vector.new(a[1]+b[1], a[2]+b[2]) end

function Vector.length(v) return (v[1]^2+v[2]^2)^0.5 end

function Vector.prettyprint(v) return "("..v[1]..", "..v[2]..")" end

function Vector.mul(a,b)
	if (type(a)=="number")
	then return Vector.new(a*b[1], a*b[2])	-- skalare Multiplikation
	else return a[1]*b[1]+a[2]*b[2]		-- Skalarprodukt
	end
end

Vektorrechnung={
		__add=Vector.add,
		__mul=Vector.mul,
		__tostring=Vector.prettyprint,
		__len=Vector.length
}

a=Vector.new(1,1)
b=Vector.new(0,-1)
print(a)
print(b)
print(#a)
print(#b)
print(a*b)
print(3*a)
print(a+b)
--print(a-b) geht nicht