Other Intangible Assets, Net (Details) - USD ($) $ in Millions	Apr. 30, 2019	Jan. 31, 2019
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	$ 1,201.7	$ 1,203.3
Less: Accumulated amortization	(939.9)	(922.5)
Other intangible assets, net	261.8	280.8
Developed technologies
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	669.6	670.2
Customer relationships, trade names, patents, and user lists
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	$ 532.1	$ 533.1