algebrite/tests/expand.coffee

Computer Algebra System in Coffeescript

test_expand = ->
	run_test [

		# general cases

		"expand(1/(x+1)/(x+2))",
		"1/(x+1)-1/(x+2)",

		"expand((2x^3-x+2)/(x^2-2x+1))",
		"4+2*x+5/(x-1)+3/(x^2-2*x+1)",

		"expand(1/x^2/(x-1))",
		"-1/(x^2)-1/x+1/(x-1)",

		"p=5s+2",
		"",

		"q=(s+1)(s+2)^2",
		"",

		"expand(p/q)",
		"-3/(s+1)+3/(s+2)+8/(s^2+4*s+4)",

		# ensure denominators are expanded (result seems preferable that way)

		"q=(x-1)(x-2)^3",
		"",

		"expand(1/q)",
		"1/(x^3-6*x^2+12*x-8)+1/(x-2)-1/(x-1)-1/(x^2-4*x+4)",

		# fractional poles

		"expand(1/(x+1/2)/(x+1/3))",
		"-12/(2*x+1)+18/(3*x+1)",

		# expand tensor

		"f=1/(x+1)/(x+2)",
		"",

		"g=1/(x+1)-1/(x+2)",
		"",

		"expand(((f,f),(f,f)))-((g,g),(g,g))",
		"((0,0),(0,0))",

		# denominator normalized?

		"expand(1/(1+1/x))",
		"1-1/(x+1)",

		# poles at zero

		"expand(1/x/(x+1))",
		"1/x-1/(x+1)",

		"expand(1/x^2/(x+1))",
		"x^(-2)-1/x+1/(x+1)",

		# other corner cases

		"expand(1/x)",
		"1/x",

		"expand(1/x^2)",
		"x^(-2)",

		"expand(1/(x^2-4x+4))",
		"1/(x^2-4*x+4)",
	]