algebrite/tests/factorpoly.coffee

Computer Algebra System in Coffeescript

test_factorpoly = ->
	run_test [

		"bake=0",
		"",

		"factor((x+1)*(x+2)*(x+3),x)",
		"(1+x)*(2+x)*(3+x)",

		"factor((x+a)*(x^2+x+1),x)",
		"(1+x+x^2)*(a+x)",

		"factor(x*(x+1)*(x+2),x)",
		"x*(1+x)*(2+x)",

	#	"factor((x+1)*(x+2)*(y+3)*(y+4),x,y)",
	#	"(1+x)*(2+x)*(3+y)*(4+y)",

	#	"factor((x+1)*(x+2)*(y+3)*(y+4),(x,y))",
	#	"(1+x)*(2+x)*(3+y)*(4+y)",

	#	"factor((x+1)*(x+2)*(y+3)*(y+4))",
	#	"(1+x)*(2+x)*(3+y)*(4+y)",

		"factor((-2*x+3)*(x+4),x)",
		"-(-3+2*x)*(4+x)",

		"(-2*x+3)*(x+4)+(-3+2*x)*(4+x)",
		"0",

		# make sure sign of remaining poly is factored

		"factor((x+1)*(-x^2+x+1),x)",
		"-(-1-x+x^2)*(1+x)",

	# sign handling

	#++++++

		"factor((x+1/2)*(+x+1/3)*(+x+1/4),x)",
		"1/24*(1+2*x)*(1+3*x)*(1+4*x)",

		"(x+1/2)*(+x+1/3)*(+x+1/4)-1/24*(1+2*x)*(1+3*x)*(1+4*x)",
		"0",

	#+++++-

		"factor((x+1/2)*(+x+1/3)*(+x-1/4),x)",
		"1/24*(-1+4*x)*(1+2*x)*(1+3*x)",

		"(x+1/2)*(+x+1/3)*(+x-1/4)-1/24*(-1+4*x)*(1+2*x)*(1+3*x)",
		"0",

	#++++-+

		"factor((x+1/2)*(+x+1/3)*(-x+1/4),x)",
		"-1/24*(-1+4*x)*(1+2*x)*(1+3*x)",

		"(x+1/2)*(+x+1/3)*(-x+1/4)+1/24*(-1+4*x)*(1+2*x)*(1+3*x)",
		"0",

	#++++--

		"factor((x+1/2)*(+x+1/3)*(-x-1/4),x)",
		"-1/24*(1+2*x)*(1+3*x)*(1+4*x)",

		"(x+1/2)*(+x+1/3)*(-x-1/4)+1/24*(1+2*x)*(1+3*x)*(1+4*x)",
		"0",

	#+++-++

		"factor((x+1/2)*(+x-1/3)*(+x+1/4),x)",
		"1/24*(-1+3*x)*(1+2*x)*(1+4*x)",

		"(x+1/2)*(+x-1/3)*(+x+1/4)-1/24*(-1+3*x)*(1+2*x)*(1+4*x)",
		"0",

	#+++-+-

		"factor((x+1/2)*(+x-1/3)*(+x-1/4),x)",
		"1/24*(-1+3*x)*(-1+4*x)*(1+2*x)",

		"(x+1/2)*(+x-1/3)*(+x-1/4)-1/24*(-1+3*x)*(-1+4*x)*(1+2*x)",
		"0",

	#+++--+

		"factor((x+1/2)*(+x-1/3)*(-x+1/4),x)",
		"-1/24*(-1+3*x)*(-1+4*x)*(1+2*x)",

		"(x+1/2)*(+x-1/3)*(-x+1/4)+1/24*(-1+3*x)*(-1+4*x)*(1+2*x)",
		"0",

	#+++---

		"factor((x+1/2)*(+x-1/3)*(-x-1/4),x)",
		"-1/24*(-1+3*x)*(1+2*x)*(1+4*x)",

		"(x+1/2)*(+x-1/3)*(-x-1/4)+1/24*(-1+3*x)*(1+2*x)*(1+4*x)",
		"0",

	#++-+++

		"factor((x+1/2)*(-x+1/3)*(+x+1/4),x)",
		"-1/24*(-1+3*x)*(1+2*x)*(1+4*x)",

		"(x+1/2)*(-x+1/3)*(+x+1/4)+1/24*(-1+3*x)*(1+2*x)*(1+4*x)",
		"0",

	#++-++-

		"factor((x+1/2)*(-x+1/3)*(+x-1/4),x)",
		"-1/24*(-1+3*x)*(-1+4*x)*(1+2*x)",

		"(x+1/2)*(-x+1/3)*(+x-1/4)+1/24*(-1+3*x)*(-1+4*x)*(1+2*x)",
		"0",

	#++-+-+

		"factor((x+1/2)*(-x+1/3)*(-x+1/4),x)",
		"1/24*(-1+3*x)*(-1+4*x)*(1+2*x)",

		"(x+1/2)*(-x+1/3)*(-x+1/4)-1/24*(-1+3*x)*(-1+4*x)*(1+2*x)",
		"0",

	#++-+--

		"factor((x+1/2)*(-x+1/3)*(-x-1/4),x)",
		"1/24*(-1+3*x)*(1+2*x)*(1+4*x)",

		"(x+1/2)*(-x+1/3)*(-x-1/4)-1/24*(-1+3*x)*(1+2*x)*(1+4*x)",
		"0",

	#++--++

		"factor((x+1/2)*(-x-1/3)*(+x+1/4),x)",
		"-1/24*(1+2*x)*(1+3*x)*(1+4*x)",

		"(x+1/2)*(-x-1/3)*(+x+1/4)+1/24*(1+2*x)*(1+3*x)*(1+4*x)",
		"0",

	#++--+-

		"factor((x+1/2)*(-x-1/3)*(+x-1/4),x)",
		"-1/24*(-1+4*x)*(1+2*x)*(1+3*x)",

		"(x+1/2)*(-x-1/3)*(+x-1/4)+1/24*(-1+4*x)*(1+2*x)*(1+3*x)",
		"0",

	#++---+

		"factor((x+1/2)*(-x-1/3)*(-x+1/4),x)",
		"1/24*(-1+4*x)*(1+2*x)*(1+3*x)",

		"(x+1/2)*(-x-1/3)*(-x+1/4)-1/24*(-1+4*x)*(1+2*x)*(1+3*x)",
		"0",

	#++----

		"factor((x+1/2)*(-x-1/3)*(-x-1/4),x)",
		"1/24*(1+2*x)*(1+3*x)*(1+4*x)",

		"(x+1/2)*(-x-1/3)*(-x-1/4)-1/24*(1+2*x)*(1+3*x)*(1+4*x)",
		"0",

	#++++++

		"factor((+x+a)*(+x+b)*(+x+c),x)",
		"(a+x)*(b+x)*(c+x)",

		"(a+x)*(b+x)*(c+x)-(a+x)*(b+x)*(c+x)",
		"0",

	#+++++-

		"factor((+x+a)*(+x+b)*(+x-c),x)",
		"(a+x)*(b+x)*(-c+x)",

		"(+x+a)*(+x+b)*(+x-c)-(a+x)*(b+x)*(-c+x)",
		"0",

	#++++-+

		"factor((+x+a)*(+x+b)*(-x+c),x)",
		"-(a+x)*(b+x)*(-c+x)",

		"(+x+a)*(+x+b)*(-x+c)+(a+x)*(b+x)*(-c+x)",
		"0",

	#++++--

		"factor((+x+a)*(+x+b)*(-x-c),x)",
		"-(a+x)*(b+x)*(c+x)",

		"(+x+a)*(+x+b)*(-x-c)+(a+x)*(b+x)*(c+x)",
		"0",

	#++++

		"factor((+a*x+b)*(+c*x+d),x)",
		"(b+a*x)*(d+c*x)",

		"(+a*x+b)*(+c*x+d)-(b+a*x)*(d+c*x)",
		"0",

	#+++-

		"factor((+a*x+b)*(+c*x-d),x)",
		"(b+a*x)*(-d+c*x)",

		"(+a*x+b)*(+c*x-d)-(b+a*x)*(-d+c*x)",
		"0",

	#++-+

		"factor((+a*x+b)*(-c*x+d),x)",
		"-(b+a*x)*(-d+c*x)",

		"(+a*x+b)*(-c*x+d)+(b+a*x)*(-d+c*x)",
		"0",

	#++--

		"factor((+a*x+b)*(-c*x-d),x)",
		"-(b+a*x)*(d+c*x)",

		"(+a*x+b)*(-c*x-d)+(b+a*x)*(d+c*x)",
		"0",

	#+-++

		"factor((+a*x-b)*(+c*x+d),x)",
		"(d+c*x)*(-b+a*x)",

		"(+a*x-b)*(+c*x+d)-(d+c*x)*(-b+a*x)",
		"0",

	#+-+-

		"factor((+a*x-b)*(+c*x-d),x)",
		"(-b+a*x)*(-d+c*x)",

		"(+a*x-b)*(+c*x-d)-(-b+a*x)*(-d+c*x)",
		"0",

	#+--+

		"factor((+a*x-b)*(-c*x+d),x)",
		"-(-b+a*x)*(-d+c*x)",

		"(+a*x-b)*(-c*x+d)+(-b+a*x)*(-d+c*x)",
		"0",

	#+---

		"factor((+a*x-b)*(-c*x-d),x)",
		"-(d+c*x)*(-b+a*x)",

		"(+a*x-b)*(-c*x-d)+(d+c*x)*(-b+a*x)",
		"0",

	#-+++

		"factor((-a*x+b)*(+c*x+d),x)",
		"-(d+c*x)*(-b+a*x)",

		"(-a*x+b)*(+c*x+d)+(d+c*x)*(-b+a*x)",
		"0",

	#-++-

		"factor((-a*x+b)*(+c*x-d),x)",
		"-(-b+a*x)*(-d+c*x)",

		"(-a*x+b)*(+c*x-d)+(-b+a*x)*(-d+c*x)",
		"0",

	#-+-+

		"factor((-a*x+b)*(-c*x+d),x)",
		"(-b+a*x)*(-d+c*x)",

		"(-a*x+b)*(-c*x+d)-(-b+a*x)*(-d+c*x)",
		"0",

	#-+--

		"factor((-a*x+b)*(-c*x-d),x)",
		"(d+c*x)*(-b+a*x)",

		"(-a*x+b)*(-c*x-d)-(d+c*x)*(-b+a*x)",
		"0",

	#--++

		"factor((-a*x-b)*(+c*x+d),x)",
		"-(b+a*x)*(d+c*x)",

		"(-a*x-b)*(+c*x+d)+(b+a*x)*(d+c*x)",
		"0",

	#--+-

		"factor((-a*x-b)*(+c*x-d),x)",
		"-(b+a*x)*(-d+c*x)",

		"(-a*x-b)*(+c*x-d)+(b+a*x)*(-d+c*x)",
		"0",

	#---+

		"factor((-a*x-b)*(-c*x+d),x)",
		"(b+a*x)*(-d+c*x)",

		"(-a*x-b)*(-c*x+d)-(b+a*x)*(-d+c*x)",
		"0",

	#----

		"factor((-a*x-b)*(-c*x-d),x)",
		"(b+a*x)*(d+c*x)",

		"(-a*x-b)*(-c*x-d)-(b+a*x)*(d+c*x)",
		"0",

		# this used to cause divide by zero

		# fixed by calling ispoly before calling coeff

	#	"factor(1/x+1)",
	#	"(1+x)/x",

		# see if poly gets rationalized

	#	"(x+1)(x+2)(x+3)/x^3",
	#	"1+6/(x^3)+11/(x^2)+6/x",

	#	"factor(last)",
	#	"(1+x)*(2+x)*(3+x)/(x^3)",

		# this used to fail

		"factor(x,x)",
		"x",

		"factor(x^2,x)",
		"x^2",

		"factor(x^3,x)",
		"x^3",

		"bake=1",
		"",

		"y=(x+1)*(x+2)",
		"",

		"factor(y,z)",
		"x^2+3*x+2",

		"factor(y,y)",
		"x^2+3*x+2",

		"y=x^2+exp(x)",
		"",

		"factor(y)",
		"x^2+exp(x)",
	]