Other Intangible Assets and Related Accumulated Amortization (Details) - USD ($) $ in Millions	Jul. 31, 2017	Jan. 31, 2017
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	$ 944.1	$ 959.5
Less: Accumulated amortization	(873.7)	(862.0)
Other intangible assets, net	70.4	97.5
Developed technologies, at cost
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	577.0	583.6
Customer relationships, trade names, patents, and user lists, at cost
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	$ 367.1	$ 375.9