algebrite/tests/power.coffee

Computer Algebra System in Coffeescript

test_power = ->
	run_test [

		"2^(1/2)",
		"2^(1/2)",

		"2^(3/2)",
		"2*2^(1/2)",

		"(-2)^(1/2)",
		"i*2^(1/2)",

		"3^(4/3)",
		"3*3^(1/3)",

		"3^(-4/3)",
		"1/(3*3^(1/3))",

		"3^(5/3)",
		"3*3^(2/3)",

		"3^(2/3)-9^(1/3)",
		"0",

		"3^(10/3)",
		"27*3^(1/3)",

		"3^(-10/3)",
		"1/(27*3^(1/3))",

		"(1/3)^(10/3)",
		"1/(27*3^(1/3))",

		"(1/3)^(-10/3)",
		"27*3^(1/3)",

		"27^(2/3)",
		"9",

		"27^(-2/3)",
		"1/9",

		"102^(1/2)",
		"2^(1/2)*3^(1/2)*17^(1/2)",

		"32^(1/3)",
		"2*2^(2/3)",

		"9999^(1/2)",
		"3*11^(1/2)*101^(1/2)",

		"10000^(1/3)",
		"10*2^(1/3)*5^(1/3)",

		"sqrt(1000000)",
		"1000",

		"sqrt(-1000000)",
		"1000*i",

		"sqrt(2^60)",
		"1073741824",

		# this is why we factor irrationals

		"6^(1/3) 3^(2/3)",
		"3*2^(1/3)",

		# inverse of complex numbers

		"1/(2+3*i)",
		"2/13-3/13*i",

		"1/(2+3*i)^2",
		"-5/169-12/169*i",

		"(-1+3i)/(2-i)",
		"-1+i",

		# other

		"(0.0)^(0.0)",
		"1",

		"(-4.0)^(1.5)",
		"-8*i",

		"(-4.0)^(0.5)",
		"2*i",

		"(-4.0)^(-0.5)",
		"-0.5*i",

		"(-4.0)^(-1.5)",
		"0.125*i",

		# more complex number cases

		"(1+i)^2",
		"2*i",

		"(1+i)^(-2)",
		"-1/2*i",

		"(1+i)^(1/2)",
		"(-1)^(1/8)*2^(1/4)",

		"(1+i)^(-1/2)",
		"-(-1)^(7/8)/(2^(1/4))",

		"(1+i)^(0.5)",
		"1.09868+0.45509*i",

		"(1+i)^(-0.5)",
		"0.776887-0.321797*i",

		# test cases for simplification of polar forms, counterclockwise

		"exp(i*pi/2)",
		"i",

		"exp(i*pi)",
		"-1",

		"exp(i*3*pi/2)",
		"-i",

		"exp(i*2*pi)",
		"1",

		"exp(i*5*pi/2)",
		"i",

		"exp(i*3*pi)",
		"-1",

		"exp(i*7*pi/2)",
		"-i",

		"exp(i*4*pi)",
		"1",

		"exp(A+i*pi/2)",
		"i*exp(A)",

		"exp(A+i*pi)",
		"-exp(A)",

		"exp(A+i*3*pi/2)",
		"-i*exp(A)",

		"exp(A+i*2*pi)",
		"exp(A)",

		"exp(A+i*5*pi/2)",
		"i*exp(A)",

		"exp(A+i*3*pi)",
		"-exp(A)",

		"exp(A+i*7*pi/2)",
		"-i*exp(A)",

		"exp(A+i*4*pi)",
		"exp(A)",

		# test cases for simplification of polar forms, clockwise

		"exp(-i*pi/2)",
		"-i",

		"exp(-i*pi)",
		"-1",

		"exp(-i*3*pi/2)",
		"i",

		"exp(-i*2*pi)",
		"1",

		"exp(-i*5*pi/2)",
		"-i",

		"exp(-i*3*pi)",
		"-1",

		"exp(-i*7*pi/2)",
		"i",

		"exp(-i*4*pi)",
		"1",

		"exp(A-i*pi/2)",
		"-i*exp(A)",

		"exp(A-i*pi)",
		"-exp(A)",

		"exp(A-i*3*pi/2)",
		"i*exp(A)",

		"exp(A-i*2*pi)",
		"exp(A)",

		"exp(A-i*5*pi/2)",
		"-i*exp(A)",

		"exp(A-i*3*pi)",
		"-exp(A)",

		"exp(A-i*7*pi/2)",
		"i*exp(A)",

		"exp(A-i*4*pi)",
		"exp(A)",
	]