Business and Summary of Significant Accounting Policies - Other Intangible Assets and Related Accumulated Amortization (Details) - USD ($) $ in Millions		12 Months Ended
		Jan. 31, 2016	Jan. 31, 2015	Jan. 31, 2014
Finite-Lived Intangible Assets, Net [Abstract]
Amortization of intangible assets		$ 33.2	$ 39.8	$ 36.5
Developed technologies, at cost		571.4	538.4
Customer relationships, trade names, patents, and user lists, at cost	[1]	371.6	348.9
Other intangible assets, at cost	[2]	943.0	887.3
Less: Accumulated amortization		(796.2)	(715.4)
Other intangible assets, net		$ 146.8	171.9
Weighted average useful life		4 years 2 months 12 days
Customer Relationships, Trade Names, Patents, and User List
Finite-Lived Intangible Assets, Net [Abstract]
Amortization of intangible assets		$ 82.6	$ 92.9	$ 80.7
Customer Relationships, Trade Names, Patents, and User List | Minimum
Finite-Lived Intangible Assets [Line Items]
Finite-Lived Intangible Asset, Useful Life		1 year
Customer Relationships, Trade Names, Patents, and User List | Maximum
Finite-Lived Intangible Assets [Line Items]
Finite-Lived Intangible Asset, Useful Life		10 years

[1] Included in “Other assets” in the accompanying Condensed Consolidated Balance Sheets.

[2] Includes the effects of foreign currency translation.