Other Intangible Assets, Net (Details) - USD ($) $ in Millions	Oct. 31, 2018	Jan. 31, 2018
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	$ 958.4	$ 951.0
Less: Accumulated amortization	(909.0)	(895.8)
Other intangible assets, net	49.4	55.2
Developed technologies
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	578.9	578.5
Customer relationships, trade names, patents, and user lists
Finite-Lived Intangible Assets [Line Items]
Other intangible assets, at cost	$ 379.5	$ 372.5