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-- complex.lua
-- complex arithmetic package for lua
-- Luiz Henrique de Figueiredo (lhf@csg.uwaterloo.ca)
-- 24 Oct 95
$debug
Complex={type="package"}
function complex(x,y)
return { re=x, im=y, type="complex" }
end
function Complex.conj(x,y)
return complex(x.re,-x.im)
end
function Complex.norm2(x)
local n=Complex.mul(x,Complex.conj(x))
return n.re
end
function Complex.abs(x)
return sqrt(Complex.norm2(x))
end
function Complex.add(x,y)
return complex(x.re+y.re,x.im+y.im)
end
function Complex.sub(x,y)
return complex(x.re-y.re,x.im-y.im)
end
function Complex.mul(x,y)
return complex(x.re*y.re-x.im*y.im,x.re*y.im+x.im*y.re)
end
function Complex.div(x,y)
local z=x*Complex.conj(y)
local t=Complex.norm2(y)
z.re=z.re/t
z.im=z.im/t
return z
end
function Complex.fallback(x,y,op)
if type(x)=="number" then x=complex(x,0) end
if type(y)=="number" then y=complex(y,0) end
if type(x)=="complex" and type(y)=="complex" then
return Complex[op](x,y)
else
return Complex.oldfallback(x,y)
end
end
function Complex.newtype(x)
local t=Complex.oldtype(x)
if t=="table" and x.type then return x.type else return t end
end
function Complex.print(x)
if type(x)~="complex" then
Complex.oldprint(x)
else
local s
if x.im>=0 then s="+" else s="" end
Complex.oldprint(x.re..s..x.im.."I")
end
end
function Complex.newabs(x)
if type(x)~="complex" then
return Complex.oldabs(x)
else
return Complex.abs(x)
end
end
Complex.oldfallback=setfallback("arith",Complex.fallback)
Complex.oldtype=type type=Complex.newtype
Complex.oldprint=print print=Complex.print
Complex.oldabs=abs abs=Complex.abs
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