Business and Summary of Significant Accounting Policies - Other Intangible Assets and Related Accumulated Amortization (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 31, 2018	Jan. 31, 2017	Jan. 31, 2016
Finite-Lived Intangible Assets, Net [Abstract]
Amortization of intangible assets	$ 20.2	$ 31.8	$ 33.2
Developed technologies, at cost	578.5	583.6
Customer relationships, trade names, patents, and user lists, at cost	372.5	375.9
Other intangible assets, at cost	951.0	959.5
Less: Accumulated amortization	(895.8)	(862.0)
Other intangible assets, net	$ 55.2	97.5
Weighted average useful life	4 years 10 months 24 days
Customer Relationships, Trade Names, Patents, and User List
Finite-Lived Intangible Assets, Net [Abstract]
Amortization of intangible assets	$ 36.6	$ 72.2	$ 82.6
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