Business and Summary of Significant Accounting Policies - Other Intangible Assets and Related Accumulated Amortization (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 31, 2019	Jan. 31, 2018	Jan. 31, 2017
Finite-Lived Intangible Assets, Net [Abstract]
Amortization of intangible assets	$ 18.0	$ 20.2	$ 31.8
Developed technologies, at cost	670.2	578.5
Customer relationships, trade names, patents, and user lists, at cost	533.1	372.5
Other intangible assets, at cost	1,203.3	951.0
Less: accumulated amortization	(922.5)	(895.8)
Other intangible assets, net	$ 280.8	55.2
Weighted average useful life	5 years 4 months 24 days
Customer Relationships, Trade Names, Patents, and User List
Finite-Lived Intangible Assets, Net [Abstract]
Amortization of intangible assets	$ 33.5	$ 36.6	$ 72.2
Customer Relationships, Trade Names, Patents, and User List | Minimum
Finite-Lived Intangible Assets [Line Items]
Finite-lived intangible asset, useful life	2 years
Customer Relationships, Trade Names, Patents, and User List | Maximum
Finite-Lived Intangible Assets [Line Items]
Finite-lived intangible asset, useful life	10 years