Other Intangible Assets, Net (Details) - USD ($) $ in Millions	Jul. 31, 2020	Jan. 31, 2020
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	$ 1,187.5	$ 1,179.3
Less: Accumulated amortization	(1,009.4)	(972.2)
Other intangible assets, net	178.1	207.1
Developed technologies
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	653.3	647.1
Customer relationships, trade names, patents, and user lists
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	$ 534.2	$ 532.2