Other Intangible Assets, Net (Details) - USD ($) $ in Millions	Oct. 31, 2019	Jan. 31, 2019
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	$ 1,178.8	$ 1,203.3
Less: Accumulated amortization	(953.6)	(922.5)
Other intangible assets, net	225.2	280.8
Developed technologies
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	647.0	670.2
Customer relationships, trade names, patents, and user lists
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	$ 531.8	$ 533.1