Other Intangible Assets, Net (Details) - USD ($) $ in Millions	Jul. 31, 2019	Jan. 31, 2019
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	$ 1,197.5	$ 1,203.3
Less: Accumulated amortization	(954.3)	(922.5)
Other intangible assets, net	243.2	280.8
Developed technologies
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	668.3	670.2
Customer relationships, trade names, patents, and user lists
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	$ 529.2	$ 533.1