Stockholders' Equity (Details) - USD ($) shares in Millions, $ in Millions	3 Months Ended						9 Months Ended
	Oct. 31, 2021	Jul. 31, 2021	Apr. 30, 2021	Oct. 31, 2020	Jul. 31, 2020	Apr. 30, 2020	Oct. 31, 2021	Oct. 31, 2020
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ 1,327.8	$ 1,128.4	$ 965.5	$ 67.3	$ (139.1)	$ (139.1)	$ 965.5	$ (139.1)
Common shares issued under stock plans	(51.4)	(6.5)	9.0	(29.3)	(4.6)	24.3
Stock-based compensation expense	140.2	148.2	114.1	97.0	95.9	88.2
Post combination expense related to assumed equity	(0.1)	0.1	0.1	0.1	0.1	0.1
Settlement of liability-classified restricted stock units	2.7					28.7	2.7	28.7
Shares issued related to business combination			2.6
Net income	136.7	115.6	155.6	132.2	98.2	66.5	407.9	296.9
Other comprehensive income (loss)	11.0	(11.7)	24.2	(1.9)	24.6	(18.8)
Repurchase and retirement of common shares	(287.0)	(46.3)	(142.7)	(196.1)	(7.8)	(189.0)
Ending balance	$ 1,279.9	$ 1,327.8	$ 1,128.4	$ 69.3	$ 67.3	$ (139.1)	$ 1,279.9	$ 69.3
Common stock and additional paid-in capital
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance (in shares)	219.9	220.0	219.6	219.3	219.2	219.4	219.6	219.4
Beginning balance	$ 2,780.7	$ 2,639.4	$ 2,578.9	$ 2,492.7	$ 2,401.3	$ 2,317.0	$ 2,578.9	$ 2,317.0
Common shares issued under stock plans (in shares)	1.3	0.1	0.9	1.2	0.2	1.0
Common shares issued under stock plans	$ (51.4)	$ (6.5)	$ 9.0	$ (29.3)	$ (4.6)	$ 24.3
Stock-based compensation expense	140.2	148.2	114.1	97.0	95.9	88.2
Post combination expense related to assumed equity	$ (0.1)	$ 0.1	0.1	$ 0.1	$ 0.1	0.1
Settlement of liability-classified restricted stock units						$ 28.7	$ 2.7	$ 28.7
Shares issued related to business combination			$ 2.6
Repurchase and retirement of common shares (in shares)	(1.0)	(0.2)	(0.5)	(0.8)	(0.1)	(1.2)
Repurchase and retirement of common shares	$ (50.7)	$ (0.5)	$ (65.3)	$ (53.4)	$ 0.0	$ (57.0)
Ending balance (in shares)	220.2	219.9	220.0	219.7	219.3	219.2	220.2	219.7
Ending balance	$ 2,821.4	$ 2,780.7	$ 2,639.4	$ 2,507.1	$ 2,492.7	$ 2,401.3	$ 2,821.4	$ 2,507.1
Accumulated other comprehensive loss
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(113.4)	(101.7)	(125.9)	(154.5)	(179.1)	(160.3)	(125.9)	(160.3)
Other comprehensive income (loss)	11.0	(11.7)	24.2	(1.9)	24.6	(18.8)
Ending balance	(102.4)	(113.4)	(101.7)	(156.4)	(154.5)	(179.1)	(102.4)	(156.4)
Accumulated deficit
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(1,339.5)	(1,409.3)	(1,487.5)	(2,270.9)	(2,361.3)	(2,295.8)	(1,487.5)	(2,295.8)
Net income	136.7	115.6	155.6	132.2	98.2	66.5
Repurchase and retirement of common shares	(236.3)	(45.8)	(77.4)	(142.7)	(7.8)	(132.0)
Ending balance	$ (1,439.1)	$ (1,339.5)	$ (1,409.3)	$ (2,281.4)	$ (2,270.9)	$ (2,361.3)	$ (1,439.1)	$ (2,281.4)