Stockholders' Deficit (Details) - USD ($) shares in Millions, $ in Millions	3 Months Ended						6 Months Ended
	Jul. 31, 2019	Apr. 30, 2019	Jan. 31, 2019	Oct. 31, 2018	Jul. 31, 2018	Apr. 30, 2018	Jul. 31, 2019	Jul. 31, 2018	Feb. 01, 2019	May 01, 2018	Feb. 01, 2018
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ (245.3)	$ (210.9)	$ (338.3)	$ (241.6)	$ (128.6)	$ (256.0)	$ (210.9)	$ (256.0)
Common shares issued under stock plans	(2.6)	21.1	(21.9)	(28.0)	(12.9)	10.3
Stock-based compensation expense	82.9	75.2	74.0	64.2	56.9	54.4
Purchase price accounting adjustment			10.3
Post-combination expense related to equity awards assumed	0.1	0.8
Cumulative effect of accounting changes									$ (0.7)	$ 1.4	$ 176.1
Net income (loss)	40.2	(24.2)	64.7	(23.7)	(39.4)	(82.4)	16.0	(121.8)
Other comprehensive income (loss)	$ (29.1)	(6.6)	22.5	(6.6)	(17.1)	(10.0)
Shares issued for acquisition					44.8
Repurchase and retirement of common shares (shares)	(37.7)
Repurchase and retirement of common shares	$ (40.5)	(100.0)	(22.2)	(102.6)	(146.7)	(21.0)
Ending balance	$ (194.3)	$ (245.3)	$ (210.9)	$ (338.3)	$ (241.6)	$ (128.6)	$ (194.3)	$ (241.6)
Common stock and additional paid-in capital
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance (shares)	219.6	219.4	219.1	218.5	219.1	218.3	219.4	218.3
Beginning balance	$ 2,123.1	$ 2,071.5	$ 2,009.1	$ 2,012.5	$ 2,001.0	$ 1,952.7	$ 2,071.5	$ 1,952.7
Common shares issued under stock plans (shares)	0.2	0.8	0.4	1.4	0.2	1.0
Common shares issued under stock plans	$ (2.6)	$ 21.1	$ (21.9)	$ (28.0)	$ (12.9)	$ 10.3
Stock-based compensation expense	82.9	75.2	74.0	$ 64.2	$ 56.9	$ 54.4
Purchase price accounting adjustment			$ 10.3
Post-combination expense related to equity awards assumed	$ 0.1	$ 0.8
Shares issued for acquisition (shares)					0.3
Shares issued for acquisition					$ 44.8
Repurchase and retirement of common shares (shares)	(0.3)	(0.6)	(0.1)	(0.8)	(1.1)	(0.2)
Repurchase and retirement of common shares	$ (2.8)	$ (45.5)	$ 0.0	$ (39.6)	$ (77.3)	$ (16.4)
Ending balance (shares)	219.5	219.6	219.4	219.1	218.5	219.1	219.5	218.5
Ending balance	$ 2,200.7	$ 2,123.1	$ 2,071.5	$ 2,009.1	$ 2,012.5	$ 2,001.0	$ 2,200.7	$ 2,012.5
Accumulated other comprehensive loss
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(141.6)	(135.0)	(157.5)	(150.9)	(133.8)	(123.8)	(135.0)	(123.8)
Other comprehensive income (loss)	(29.1)	(6.6)	22.5	(6.6)	(17.1)	(10.0)
Ending balance	(170.7)	(141.6)	(135.0)	(157.5)	(150.9)	(133.8)	(170.7)	(150.9)
Accumulated deficit
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(2,226.8)	(2,147.4)	(2,189.9)	(2,103.2)	(1,995.8)	(2,084.9)	(2,147.4)	(2,084.9)
Cumulative effect of accounting changes									$ (0.7)	$ 1.4	$ 176.1
Net income (loss)	40.2	(24.2)	64.7	(23.7)	(39.4)	(82.4)
Repurchase and retirement of common shares		(54.5)	(22.2)	(63.0)	(69.4)	(4.6)
Ending balance	$ (2,224.3)	$ (2,226.8)	$ (2,147.4)	$ (2,189.9)	$ (2,103.2)	$ (1,995.8)	$ (2,224.3)	$ (2,103.2)