Other Intangible Assets, Net (Details) - USD ($) $ in Millions	Apr. 30, 2021	Jan. 31, 2021
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	$ 1,569.6	$ 1,247.2
Less: Accumulated amortization	(1,066.5)	(1,047.9)
Other intangible assets, net	503.1	199.3
Developed Technologies
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	794.1	698.4
Customer Relationships, Trade Names, Patents, and User Lists
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	$ 775.5	$ 548.8