Stockholders' Equity (Details) - USD ($) shares in Millions	3 Months Ended
	Apr. 30, 2021	Apr. 30, 2020
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ 965,500,000	$ (139,100,000)
Common shares issued under stock plans	9,000,000.0	24,300,000
Stock-based compensation expense	114,100,000	88,200,000
Settlement of liability-classified restricted stock units	0	28,700,000
Post combination expense related to assumed equity	100,000	100,000
Shares issued related to business combination	2,600,000
Net income	155,600,000	66,500,000
Other comprehensive income	24,200,000	(18,800,000)
Repurchase and retirement of common shares	(142,700,000)	(189,000,000.0)
Ending balance	$ 1,128,400,000	$ (139,100,000)
Common stock and additional paid-in capital
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance (in shares)	219.6	219.4
Beginning balance	$ 2,578,900,000	$ 2,317,000,000.0
Common shares issued under stock plans (in shares)	0.9	1.0
Common shares issued under stock plans	$ 9,000,000.0	$ 24,300,000
Stock-based compensation expense	114,100,000	88,200,000
Settlement of liability-classified restricted stock units	0	28,700,000
Post combination expense related to assumed equity	100,000	$ 100,000
Shares issued related to business combination	$ 2,600,000
Repurchase and retirement of common shares (in shares)	(0.5)	(1.2)
Repurchase and retirement of common shares	$ (65,300,000)	$ (57,000,000.0)
Ending balance (in shares)	220.0	219.2
Ending balance	$ 2,639,400,000	$ 2,401,300,000
Accumulated other comprehensive loss
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(125,900,000)	(160,300,000)
Other comprehensive income	24,200,000	(18,800,000)
Ending balance	(101,700,000)	(179,100,000)
Accumulated deficit
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(1,487,500,000)	(2,295,800,000)
Net income	155,600,000	66,500,000
Repurchase and retirement of common shares	(77,400,000)	(132,000,000.0)
Ending balance	$ (1,409,300,000)	$ (2,361,300,000)