Other Intangible Assets, Net (Details) - USD ($) $ in Millions	Jul. 31, 2018	Jan. 31, 2018
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	$ 961.7	$ 951.0
Less: Accumulated amortization	(903.8)	(895.8)
Other intangible assets, net	57.9	55.2
Developed technologies
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	580.0	578.5
Customer relationships, trade names, patents, and user lists
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	$ 381.7	$ 372.5