# factor a polynomial or integer



Eval_factor = ->
	push(cadr(p1))
	Eval()

	push(caddr(p1))
	Eval()

	p2 = pop()
	if (p2 == symbol(NIL))
		guess()
	else
		push(p2)

	factor()

	# more factoring?

	p1 = cdddr(p1)
	while (iscons(p1))
		push(car(p1))
		Eval()
		factor_again()
		p1 = cdr(p1)

factor_again = ->

	save()

	p2 = pop()
	p1 = pop()

	h = tos

	if (car(p1) == symbol(MULTIPLY))
		p1 = cdr(p1)
		while (iscons(p1))
			push(car(p1))
			push(p2)
			factor_term()
			p1 = cdr(p1)
	else
		push(p1)
		push(p2)
		factor_term()

	n = tos - h

	if (n > 1)
		multiply_all_noexpand(n)

	restore()

factor_term = ->
	save()
	factorpoly()
	p1 = pop()
	if (car(p1) == symbol(MULTIPLY))
		p1 = cdr(p1)
		while (iscons(p1))
			push(car(p1))
			p1 = cdr(p1)
	else
		push(p1)
	restore()

factor = ->
	save()
	p2 = pop()
	p1 = pop()
	if (isinteger(p1))
		push(p1)
		factor_number(); # see pollard.cpp
	else
		push(p1)
		push(p2)
		factorpoly()
	restore()

# for factoring small integers (2^32 or less)

factor_small_number = ->

	i = 0
	save()

	n = pop_integer()

	if (isNaN(n))
		stop("number too big to factor")

	if (n < 0)
		n = -n

	for i in [0...MAXPRIMETAB]

		d = primetab[i]

		if (d > n / d)
			break

		expo = 0

		while (n % d == 0)
			n /= d
			expo++

		if (expo)
			push_integer(d)
			push_integer(expo)

	if (n > 1)
		push_integer(n)
		push_integer(1)

	restore()