algebrite/sources/print.coffee

Computer Algebra System in Coffeescript

power_str = "^"
stringToBePrinted = ""

print_str = (s) ->
	stringToBePrinted += s

print_char = (c) ->
	stringToBePrinted += c

collectResultLine = (p) ->
	stringToBePrinted = ""
	print_expr(p)
	return stringToBePrinted

printline = (p) ->
	#debugger
	stringToBePrinted = ""
	print_expr(p)
	console.log stringToBePrinted


# prints stuff after the divide symbol "/"

# d is the number of denominators

#define BASE p1
#define EXPO p2

print_denom = (p, d) ->
	save()

	p1 = cadr(p); # p1 is BASE
	p2 = caddr(p); # p2 is EXPO

	# i.e. 1 / (2^(1/3))

	if (d == 1 && !isminusone(p2)) # p2 is EXPO
		print_char('(')

	if (isfraction(p1) || car(p1) == symbol(ADD) || car(p1) == symbol(MULTIPLY) || car(p1) == symbol(POWER) || lessp(p1, zero)) # p1 is BASE
			print_char('(')
			print_expr(p1); # p1 is BASE
			print_char(')')
	else
		print_expr(p1); # p1 is BASE

	if (isminusone(p2)) # p2 is EXPO
		restore()
		return

	if (test_flag == 0)
		print_str(power_str)
	else
		print_char('^')

	push(p2); # p2 is EXPO
	negate()
	p2 = pop(); # p2 is EXPO

	if (isfraction(p2) || car(p2) == symbol(ADD) || car(p2) == symbol(MULTIPLY) || car(p2) == symbol(POWER)) # p2 is EXPO
		print_char('(')
		print_expr(p2); # p2 is EXPO
		print_char(')')
	else
		print_expr(p2); # p2 is EXPO

	if (d == 1)
		print_char(')')

	restore()


#define A p3
#define B p4

print_a_over_b = (p) ->
	flag = 0
	n = 0
	d = 0

	save()

	# count numerators and denominators

	n = 0
	d = 0

	p1 = cdr(p)
	p2 = car(p1)

	if (isrational(p2))
		push(p2)
		mp_numerator()
		absval()
		p3 = pop(); # p3 is A
		push(p2)
		mp_denominator()
		p4 = pop(); # p4 is B
		if (!isplusone(p3)) # p3 is A
			n++
		if (!isplusone(p4)) # p4 is B
			d++
		p1 = cdr(p1)
	else
		p3 = one; # p3 is A
		p4 = one; # p4 is B

	while (iscons(p1))
		p2 = car(p1)
		if (is_denominator(p2))
			d++
		else
			n++
		p1 = cdr(p1)

	if (n == 0)
		print_char('1')
	else
		flag = 0
		p1 = cdr(p)
		if (isrational(car(p1)))
			p1 = cdr(p1)
		if (!isplusone(p3)) # p3 is A
			print_factor(p3); # p3 is A
			flag = 1
		while (iscons(p1))
			p2 = car(p1)
			if (is_denominator(p2))
				doNothing = 1
			else
				if (flag)
					print_multiply_sign()
				print_factor(p2)
				flag = 1
			p1 = cdr(p1)

	if (test_flag == 0)
		print_str(" / ")
	else
		print_str("/")

	if (d > 1)
		print_char('(')


	flag = 0
	p1 = cdr(p)

	if (isrational(car(p1)))
		p1 = cdr(p1)

	if (!isplusone(p4)) # p4 is B
		print_factor(p4); # p4 is B
		flag = 1

	while (iscons(p1))
		p2 = car(p1)
		if (is_denominator(p2))
			if (flag)
				print_multiply_sign()
			print_denom(p2, d)
			flag = 1
		p1 = cdr(p1)

	if (d > 1)
		print_char(')')

	restore()


print_expr = (p) ->
	if (isadd(p))
		p = cdr(p)
		if (sign_of_term(car(p)) == '-')
			print_str("-")
		print_term(car(p))
		p = cdr(p)
		while (iscons(p))
			if (sign_of_term(car(p)) == '+')
				if (test_flag == 0)
					print_str(" + ")
				else
					print_str("+")
			else
				if (test_flag == 0)
					print_str(" - ")
				else
					print_str("-")
			print_term(car(p))
			p = cdr(p)
	else
		if (sign_of_term(p) == '-')
			print_str("-")
		print_term(p)

sign_of_term = (p) ->
	if (car(p) == symbol(MULTIPLY) && isnum(cadr(p)) && lessp(cadr(p), zero))
		return '-'
	else if (isnum(p) && lessp(p, zero))
		return '-'
	else
		return '+'

print_term = (p) ->
	if (car(p) == symbol(MULTIPLY) && any_denominators(p))
		print_a_over_b(p)
		return

	if (car(p) == symbol(MULTIPLY))
		p = cdr(p)

		# coeff -1?

		if (isminusone(car(p)))
			#			print_char('-')
			p = cdr(p)

		print_factor(car(p))
		p = cdr(p)
		while (iscons(p))
			print_multiply_sign()
			print_factor(car(p))
			p = cdr(p)
	else
		print_factor(p)

print_subexpr = (p) ->
	print_char('(')
	print_expr(p)
	print_char(')')

print_factorial_function = (p) ->
	p = cadr(p)
	if (car(p) == symbol(ADD) || car(p) == symbol(MULTIPLY) || car(p) == symbol(POWER) || car(p) == symbol(FACTORIAL))
		print_subexpr(p)
	else
		print_expr(p)
	print_char('!')


print_tensor = (p) ->
	print_tensor_inner(p, 0, 0)

print_tensor_inner = (p, j, k) ->
	i = 0
	print_str("(")
	for i in [0...p.tensor.dim[j]]
		if (j + 1 == p.tensor.ndim)
			print_expr(p.tensor.elem[k])
			k++
		else
			k = print_tensor_inner(p, j + 1, k)
		if (i + 1 < p.tensor.dim[j])
			if (test_flag == 0)
				print_str(",")
			else
				print_str(",")
	print_str(")")
	return k

print_factor = (p) ->
	if (isnum(p))
		print_number(p)
		return

	if (isstr(p))
		#print_str("\"")
		print_str(p.str)
		#print_str("\"")
		return

	if (istensor(p))
		print_tensor(p)
		return

	if (isadd(p) || car(p) == symbol(MULTIPLY))
		print_str("(")
		print_expr(p)
		print_str(")")
		return

	if (car(p) == symbol(POWER))

		if (cadr(p) == symbol(E))
			print_str("exp(")
			print_expr(caddr(p))
			print_str(")")
			return

		if (isminusone(caddr(p)))
			if (test_flag == 0)
				print_str("1 / ")
			else
				print_str("1/")
			if (iscons(cadr(p)))
				print_str("(")
				print_expr(cadr(p))
				print_str(")")
			else
				print_expr(cadr(p))
			return

		if (isadd(cadr(p)) || caadr(p) == symbol(MULTIPLY) || caadr(p) == symbol(POWER) || isnegativenumber(cadr(p)))
			print_str("(")
			print_expr(cadr(p))
			print_str(")")
		else if (isnum(cadr(p)) && (lessp(cadr(p), zero) || isfraction(cadr(p))))
			print_str("(")
			print_factor(cadr(p))
			print_str(")")
		else
			print_factor(cadr(p))

		if (test_flag == 0)
			#print_str(" ^ ")
			print_str(power_str)
		else
			print_str("^")

		if (iscons(caddr(p)) || isfraction(caddr(p)) || (isnum(caddr(p)) && lessp(caddr(p), zero)))
			print_str("(")
			print_expr(caddr(p))
			print_str(")")
		else
			print_factor(caddr(p))
		return

	#	if (car(p) == _list) {
	#		print_str("{")
	#		p = cdr(p)
	#		if (iscons(p)) {
	#			print_expr(car(p))
	#			p = cdr(p)
	#		}
	#		while (iscons(p)) {
	#			print_str(",")
	#			print_expr(car(p))
	#			p = cdr(p)
	#		}
	#		print_str("}")
	#		return
	#	}

	if (car(p) == symbol(INDEX) && issymbol(cadr(p)))
		print_index_function(p)
		return

	if (car(p) == symbol(FACTORIAL))
		print_factorial_function(p)
		return

	if (iscons(p))
		#if (car(p) == symbol(FORMAL) && cadr(p)->k == SYM) {
		#	print_str(((struct symbol *) cadr(p))->name)
		#	return
		#}
		print_factor(car(p))
		p = cdr(p)
		print_str("(")
		if (iscons(p))
			print_expr(car(p))
			p = cdr(p)
			while (iscons(p))
				if (test_flag == 0)
					print_str(",")
				else
					print_str(",")
				print_expr(car(p))
				p = cdr(p)
		print_str(")")
		return

	if (p == symbol(DERIVATIVE))
		print_char('d')
	else if (p == symbol(E))
		print_str("exp(1)")
	else if (p == symbol(PI))
		print_str("pi")
	else
		print_str(get_printname(p))


print1 = (p, accumulator) ->
	topLevelCall = false
	if !accumulator?
		topLevelCall = true
		accumulator = ""
	switch (p.k)
		when CONS
			accumulator += ("(")
			accumulator = print1(car(p), accumulator)
			if p == cdr(p)
				console.log "oh no recursive!"
				debugger
			p = cdr(p)
			while (iscons(p))
				accumulator += (" ")
				accumulator = print1(car(p), accumulator)
				p = cdr(p)
				if p == cdr(p)
					console.log "oh no recursive!"
					debugger
			if (p != symbol(NIL))
				accumulator += (" . ")
				accumulator = print1(p, accumulator)
			accumulator += (")")
		when STR
			#print_str("\"")
			accumulator += (p.str)
			#print_str("\"")
		when NUM, DOUBLE
			accumulator = print_number(p, accumulator)
		when SYM
			accumulator += get_printname(p)
		else
			accumulator += ("<tensor>")
	if topLevelCall
		console.log accumulator
	else
		return accumulator

print_multiply_sign = ->
	if (test_flag == 0)
		print_str(" ")
	else
		print_str("*")

is_denominator = (p) ->
	if (car(p) == symbol(POWER) && cadr(p) != symbol(E) && isnegativeterm(caddr(p)))
		return 1
	else
		return 0

# don't consider the leading fraction
# we want 2/3*a*b*c instead of 2*a*b*c/3

any_denominators = (p) ->
	p = cdr(p)
	#	if (isfraction(car(p)))
	#		return 1
	while (iscons(p))
		q = car(p)
		if (is_denominator(q))
			return 1
		p = cdr(p)
	return 0