Stockholders' Deficit (Details) - USD ($) shares in Millions, $ in Millions	3 Months Ended							9 Months Ended
	Oct. 31, 2018	Jul. 31, 2018	Apr. 30, 2018	Jan. 31, 2018	Oct. 31, 2017	Jul. 31, 2017	Apr. 30, 2017	Oct. 31, 2018	Oct. 31, 2017
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ (241.6)	$ (128.6)	$ (256.0)	$ 107.3	$ 315.5	$ 508.1	$ 733.6	$ (256.0)	$ 733.6
Common shares issued under stock plans	(28.0)	(12.9)	10.3	(21.3)	(33.5)	(11.0)	17.1
Stock-based compensation expense	64.2	56.9	54.4	61.9	65.1	67.6	66.8
Cumulative effect of accounting changes		1.4	176.1
Net loss	(23.7)	(39.4)	(82.4)	(173.5)	(119.8)	(144.0)	(129.6)	(145.5)	(393.4)
Other comprehensive (loss)	$ (6.6)	$ (17.1)	(10.0)	31.7	(2.6)	13.4	12.2
Shares issued for Assemble Systems acquisition (shares)		0.3
Shares issued for Assemble Systems acquisition		$ 44.8
Repurchase and retirement of common shares (shares)	(63.0)	(69.4)
Repurchase and retirement of common shares	$ (102.6)	$ (146.7)	(21.0)	(262.1)	(117.4)	(118.6)	(192.0)
Ending balance	$ (338.3)	$ (241.6)	$ (128.6)	$ (256.0)	$ 107.3	$ 315.5	$ 508.1	$ (338.3)	$ 107.3
Common stock and additional paid-in capital
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance (shares)	218.5	219.1	218.3	220.3	219.1	219.9	220.3	218.3	220.3
Beginning balance	$ 2,012.5	$ 2,001.0	$ 1,952.7	$ 1,930.8	$ 1,934.8	$ 1,899.0	$ 1,876.3	$ 1,952.7	$ 1,876.3
Common shares issued under stock plans (shares)	1.4	0.2	1.0	0.5	2.2	0.4	1.8
Common shares issued under stock plans	$ (28.0)	$ (12.9)	$ 10.3	$ (21.3)	$ (33.5)	$ (11.0)	$ 17.1
Stock-based compensation expense	$ 64.2	$ 56.9	$ 54.4	$ 61.9	$ 65.1	$ 67.6	$ 66.8
Repurchase and retirement of common shares (shares)	(0.8)	(1.1)	(0.2)	(2.5)	(1.0)	(1.2)	(2.2)
Repurchase and retirement of common shares	$ (39.6)	$ (77.3)	$ (16.4)	$ (18.7)	$ (35.6)	$ (20.8)	$ (61.2)
Ending balance (shares)	219.1	218.5	219.1	218.3	220.3	219.1	219.9	219.1	220.3
Ending balance	$ 2,009.1	$ 2,012.5	$ 2,001.0	$ 1,952.7	$ 1,930.8	$ 1,934.8	$ 1,899.0	$ 2,009.1	$ 1,930.8
Accumulated other comprehensive loss
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(150.9)	(133.8)	(123.8)	(155.5)	(152.9)	(166.3)	(178.5)	(123.8)	(178.5)
Other comprehensive (loss)	(6.6)	(17.1)	(10.0)	31.7	(2.6)	13.4	12.2
Ending balance	(157.5)	(150.9)	(133.8)	(123.8)	(155.5)	(152.9)	(166.3)	(157.5)	(155.5)
Accumulated deficit
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(2,103.2)	(1,995.8)	(2,084.9)	(1,668.0)	(1,466.4)	(1,224.6)	(964.2)	(2,084.9)	(964.2)
Net loss	(23.7)	(39.4)	(82.4)	(173.5)	(119.8)	(144.0)	(129.6)
Repurchase and retirement of common shares			(4.6)	(243.4)	(81.8)	(97.8)	(130.8)
Ending balance	$ (2,189.9)	$ (2,103.2)	$ (1,995.8)	$ (2,084.9)	$ (1,668.0)	$ (1,466.4)	$ (1,224.6)	$ (2,189.9)	$ (1,668.0)