algebrite/sources/gcd.coffee

Computer Algebra System in Coffeescript

# Greatest common denominator



Eval_gcd = ->
	p1 = cdr(p1)
	push(car(p1))
	Eval()
	p1 = cdr(p1)
	while (iscons(p1))
		push(car(p1))
		Eval()
		gcd()
		p1 = cdr(p1)

gcd = ->
	prev_expanding = expanding
	save()
	gcd_main()
	restore()
	expanding = prev_expanding

gcd_main = ->
	expanding = 1

	p2 = pop()
	p1 = pop()

	if (equal(p1, p2))
		push(p1)
		return

	if (isrational(p1) && isrational(p2))
		push(p1)
		push(p2)
		gcd_numbers()
		return

	if (car(p1) == symbol(ADD) && car(p2) == symbol(ADD))
		gcd_expr_expr()
		return

	if (car(p1) == symbol(ADD))
		gcd_expr(p1)
		p1 = pop()

	if (car(p2) == symbol(ADD))
		gcd_expr(p2)
		p2 = pop()

	if (car(p1) == symbol(MULTIPLY) && car(p2) == symbol(MULTIPLY))
		gcd_term_term()
		return

	if (car(p1) == symbol(MULTIPLY))
		gcd_term_factor()
		return

	if (car(p2) == symbol(MULTIPLY))
		gcd_factor_term()
		return

	# gcd of factors

	if (car(p1) == symbol(POWER))
		p3 = caddr(p1)
		p1 = cadr(p1)
	else
		p3 = one

	if (car(p2) == symbol(POWER))
		p4 = caddr(p2)
		p2 = cadr(p2)
	else
		p4 = one

	if (!equal(p1, p2))
		push(one)
		return

	# are both exponents numerical?

	if (isnum(p3) && isnum(p4))
		push(p1)
		if (lessp(p3, p4))
			push(p3)
		else
			push(p4)
		power()
		return

	# are the exponents multiples of eah other?

	push(p3)
	push(p4)
	divide()

	p5 = pop()

	if (isnum(p5))

		push(p1)

		# choose the smallest exponent

		if (car(p3) == symbol(MULTIPLY) && isnum(cadr(p3)))
			p5 = cadr(p3)
		else
			p5 = one

		if (car(p4) == symbol(MULTIPLY) && isnum(cadr(p4)))
			p6 = cadr(p4)
		else
			p6 = one

		if (lessp(p5, p6))
			push(p3)
		else
			push(p4)

		power()
		return

	push(p3)
	push(p4)
	subtract()

	p5 = pop()

	if (!isnum(p5))
		push(one)
		return

	# can't be equal because of test near beginning

	push(p1)

	if (isnegativenumber(p5))
		push(p3)
	else
		push(p4)

	power()

# in this case gcd is used as a composite function, i.e. gcd(gcd(gcd...

gcd_expr_expr = ->
	if (length(p1) != length(p2))
		push(one)
		return

	p3 = cdr(p1)
	push(car(p3))
	p3 = cdr(p3)
	while (iscons(p3))
		push(car(p3))
		gcd()
		p3 = cdr(p3)
	p3 = pop()

	p4 = cdr(p2)
	push(car(p4))
	p4 = cdr(p4)
	while (iscons(p4))
		push(car(p4))
		gcd()
		p4 = cdr(p4)
	p4 = pop()

	push(p1)
	push(p3)
	divide()
	p5 = pop()

	push(p2)
	push(p4)
	divide()
	p6 = pop()

	if (equal(p5, p6))
		push(p5)
		push(p3)
		push(p4)
		gcd()
		multiply()
	else
		push(one)

gcd_expr = (p) ->
	p = cdr(p)
	push(car(p))
	p = cdr(p)
	while (iscons(p))
		push(car(p))
		gcd()
		p = cdr(p)

gcd_term_term = ->
	push(one)
	p3 = cdr(p1)
	while (iscons(p3))
		p4 = cdr(p2)
		while (iscons(p4))
			push(car(p3))
			push(car(p4))
			gcd()
			multiply()
			p4 = cdr(p4)
		p3 = cdr(p3)

gcd_term_factor = ->
	push(one)
	p3 = cdr(p1)
	while (iscons(p3))
		push(car(p3))
		push(p2)
		gcd()
		multiply()
		p3 = cdr(p3)

gcd_factor_term = ->
	push(one)
	p4 = cdr(p2)
	while (iscons(p4))
		push(p1)
		push(car(p4))
		gcd()
		multiply()
		p4 = cdr(p4)