Stockholders' Deficit (Details) - USD ($) shares in Millions, $ in Millions	3 Months Ended
	Apr. 30, 2020	Apr. 30, 2019
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ (139.1)	$ (210.9)
Common shares issued under stock plans	24.3	21.1
Stock-based compensation expense	88.2	75.2
Settlement of liability-classified restricted stock units	28.7	0.0
Post combination expense related to assumed equity	0.1	0.8
Net income (loss)	66.5	(24.2)
Other comprehensive income (loss)	(18.8)	(6.6)
Repurchase and retirement of common shares	(189.0)	(100.0)
Ending balance	$ (139.1)	$ (245.3)
Common stock and additional paid-in capital
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance (shares)	219.4	219.4
Beginning balance	$ 2,317.0	$ 2,071.5
Common shares issued under stock plans (shares)	1.0	0.8
Common shares issued under stock plans	$ 24.3	$ 21.1
Stock-based compensation expense	88.2	75.2
Settlement of liability-classified restricted stock units	28.7
Post combination expense related to assumed equity	$ 0.1	$ 0.8
Repurchase and retirement of common shares (shares)	(1.2)	(0.6)
Repurchase and retirement of common shares	$ (57.0)	$ (45.5)
Ending balance (shares)	219.2	219.6
Ending balance	$ 2,401.3	$ 2,123.1
Accumulated other comprehensive loss
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(160.3)	(135.0)
Other comprehensive income (loss)	(18.8)	(6.6)
Ending balance	(179.1)	(141.6)
Accumulated deficit
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(2,295.8)	(2,147.4)
Net income (loss)	66.5	(24.2)
Repurchase and retirement of common shares	(132.0)	(54.5)
Ending balance	$ (2,361.3)	(2,226.8)
Cumulative Effect, Period of Adoption, Adjustment
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance		(0.7)
Cumulative Effect, Period of Adoption, Adjustment | Accumulated deficit
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance		$ (0.7)