algebrite/sources/factorpoly.coffee

Computer Algebra System in Coffeescript

# Factor a polynomial




#define POLY p1
#define X p2
#define Z p3
#define A p4
#define B p5
#define Q p6
#define RESULT p7
#define FACTOR p8

polycoeff = 0
factpoly_expo = 0

factorpoly = ->
	save()

	p2 = pop()
	p1 = pop()

	if (!Find(p1, p2))
		push(p1)
		restore()
		return

	if (!ispoly(p1, p2))
		push(p1)
		restore()
		return

	if (!issymbol(p2))
		push(p1)
		restore()
		return

	push(p1)
	push(p2)
	yyfactorpoly()

	restore()

#-----------------------------------------------------------------------------
#
#	Input:		tos-2		true polynomial
#
#			tos-1		free variable
#
#	Output:		factored polynomial on stack
#
#-----------------------------------------------------------------------------

yyfactorpoly = ->
	h = 0
	i = 0

	save()

	p2 = pop()
	p1 = pop()

	h = tos

	if (isfloating(p1))
		stop("floating point numbers in polynomial")

	polycoeff = tos

	push(p1)
	push(p2)
	factpoly_expo = coeff() - 1

	rationalize_coefficients(h)

	# for univariate polynomials we could do factpoly_expo > 1

	while (factpoly_expo > 0)

		if (iszero(stack[polycoeff+0]))
			push_integer(1)
			p4 = pop()
			push_integer(0)
			p5 = pop()
		else if (get_factor() == 0)
			if (verbosing)
				printf("no factor found\n")
			break

		push(p4)
		push(p2)
		multiply()
		push(p5)
		add()
		p8 = pop()

		if (verbosing)
			printf("success\nFACTOR=")
			print(p8)
			printf("\n")

		# factor out negative sign (not req'd because p4 > 1)
		#if 0
		###
		if (isnegativeterm(p4))
			push(p8)
			negate()
			p8 = pop()
			push(p7)
			negate_noexpand()
			p7 = pop()
		###
		#endif
		push(p7)
		push(p8)
		multiply_noexpand()
		p7 = pop()

		yydivpoly()

		while (factpoly_expo and iszero(stack[polycoeff+factpoly_expo]))
			factpoly_expo--

	# unfactored polynomial

	push(zero)
	for i in [0..factpoly_expo]
		push(stack[polycoeff+i])
		push(p2)
		push_integer(i)
		power()
		multiply()
		add()
	p1 = pop()

	if (verbosing)
		printf("POLY=")
		print(p1)
		printf("\n")

	# factor out negative sign

	if (factpoly_expo > 0 && isnegativeterm(stack[polycoeff+factpoly_expo]))
		push(p1)
		negate()
		p1 = pop()
		push(p7)
		negate_noexpand()
		p7 = pop()

	push(p7)
	push(p1)
	multiply_noexpand()
	p7 = pop()

	if (verbosing)
		printf("RESULT=")
		print(p7)
		printf("\n")

	stack[h] = p7

	tos = h + 1

	restore()

rationalize_coefficients = (h) ->
	i = 0

	# LCM of all polynomial coefficients

	p7 = one
	for i in [h...tos]
		push(stack[i])
		denominator()
		push(p7)
		lcm()
		p7 = pop()

	# multiply each coefficient by RESULT

	for i in [h...tos]
		push(p7)
		push(stack[i])
		multiply()
		stack[i] = pop()

	# reciprocate RESULT

	push(p7)
	reciprocate()
	p7 = pop()
	if DEBUG then console.log("rationalize_coefficients result")
	#print1(p7)

get_factor = ->

	i = 0
	j = 0
	h = 0
	a0 = 0
	an = 0
	na0 = 0
	nan = 0

	if (verbosing)
		push(zero)
		for i in [0..factpoly_expo]
			push(stack[polycoeff+i])
			push(p2)
			push_integer(i)
			power()
			multiply()
			add()
		p1 = pop()
		printf("POLY=")
		print(p1)
		printf("\n")

	h = tos

	an = tos
	push(stack[polycoeff+factpoly_expo])

	divisors_onstack()

	nan = tos - an

	a0 = tos
	push(stack[polycoeff+0])
	divisors_onstack()
	na0 = tos - a0

	if (verbosing)
		printf("divisors of base term")
		for i in [0...na0]
			printf(", ")
			print(stack[a0 + i])
		printf("\n")
		printf("divisors of leading term")
		for i in [0...nan]
			printf(", ")
			print(stack[an + i])
		printf("\n")

	# try roots

	for rootsTries_i in [0...nan]
		for rootsTries_j in [0...na0]

			#if DEBUG then console.log "nan: " + nan + " na0: " + na0 + " i: " + rootsTries_i + " j: " + rootsTries_j

			p4 = stack[an + rootsTries_i]
			p5 = stack[a0 + rootsTries_j]

			push(p5)
			push(p4)
			divide()
			negate()
			p3 = pop()

			Evalpoly()

			if (verbosing)
				printf("try A=")
				print(p4)
				printf(", B=")
				print(p5)
				printf(", root ")
				print(p2)
				printf("=-B/A=")
				print(p3)
				printf(", POLY(")
				print(p3)
				printf(")=")
				print(p6)
				printf("\n")

			if (iszero(p6))
				tos = h
				if DEBUG then console.log "get_factor returning 1"
				return 1

			push(p5)
			negate()
			p5 = pop()

			push(p3)
			negate()
			p3 = pop()

			Evalpoly()

			if (verbosing)
				printf("try A=")
				print(p4)
				printf(", B=")
				print(p5)
				printf(", root ")
				print(p2)
				printf("=-B/A=")
				print(p3)
				printf(", POLY(")
				print(p3)
				printf(")=")
				print(p6)
				printf("\n")

			if (iszero(p6))
				tos = h
				if DEBUG then console.log "get_factor returning 1"
				return 1

	tos = h

	if DEBUG then console.log "get_factor returning 0"
	return 0

#-----------------------------------------------------------------------------
#
#	Divide a polynomial by Ax+B
#
#	Input:		polycoeff	Dividend coefficients
#
#			factpoly_expo		Degree of dividend
#
#			A		As above
#
#			B		As above
#
#	Output:		polycoeff	Contains quotient coefficients
#
#-----------------------------------------------------------------------------

yydivpoly = ->
	i = 0
	p6 = zero
	for i in [factpoly_expo...0]
		push(stack[polycoeff+i])
		stack[polycoeff+i] = p6
		push(p4)
		divide()
		p6 = pop()
		push(stack[polycoeff+i - 1])
		push(p6)
		push(p5)
		multiply()
		subtract()
		stack[polycoeff+i - 1] = pop()
	stack[polycoeff+0] = p6
	if DEBUG then console.log("yydivpoly Q:")
	#print1(p6)

Evalpoly = ->
	i = 0
	push(zero)
	for i in [factpoly_expo..0]
		push(p3)
		multiply()
		push(stack[polycoeff+i])
		if DEBUG
			console.log("Evalpoly top of stack:")
			print1(stack[tos-i])
		add()
	p6 = pop()