Recursive function definition results in stack overflow

Question

I am writing a library script to handle some basic calculations with complex numbers which includes a function, powerN(), that raises (or is supposed to raise) a complex number to the Nth power. The function compiles but gives a stack overflow error when called. The language guide has an example (p. 286 in PDF version- recursive subroutines section) of a recursive definition of a function which gives the factorial of a number, and my powerN function seems to be analogous. Can anyone shed some light on whatever the problem is? Relevant code examples are below. Thanks for any insights.
-----Apple recursive subroutine for factorials------
on factorial(x)
if x > 0 then
return x * (factorial(x - 1))
else
return 1
end if
end factorial
-----End Apple recursive subroutine for factorials------
-----My script with problematic powerN() function------
--Complex numbers a+b(i), x+y(i) represented by {a,b}, {x,y}
on multiply({a, b}, {x, y})
return {(a * x + b * y), (b * x + a * y)}
end multiply
--above multiply function works
on powerN({a, b}, N)
return multiply({a, b}, powerN({a, b}, N - 1))
end powerN
--above powerN function gives stack overflow error
-----End my script with problematic powerN() function------

Answer 1

the problem is that your recursion has no end case, thus causing a stack overflow
you should add a test as follows :
on powerN({a, b}, N)
if N>0 then
return multiply({a, b}, powerN({a, b}, N - 1))
else
return 1
end if
end powerN
by the way, shouldn't your complex multiplication look like :
on multiply({a, b}, {x, y})
return {(a * x - b * y), (b * x + a * y)}
end multiply