Computer Equipment, Software, Furniture and Leasehold Improvements, Net (Details) - USD ($) $ in Millions	Apr. 30, 2018	Jan. 31, 2018
Property, Plant and Equipment [Line Items]
Computer software, hardware, leasehold improvements, furniture and equipment, gross	$ 590.8	$ 582.0
Less: Accumulated depreciation	(432.6)	(437.0)
Computer software, hardware, leasehold improvements, furniture and equipment, net	158.2	145.0
Computer hardware
Property, Plant and Equipment [Line Items]
Computer software, hardware, leasehold improvements, furniture and equipment, gross	211.8	217.1
Computer software
Property, Plant and Equipment [Line Items]
Computer software, hardware, leasehold improvements, furniture and equipment, gross	72.9	72.6
Leasehold improvements, land and buildings
Property, Plant and Equipment [Line Items]
Computer software, hardware, leasehold improvements, furniture and equipment, gross	244.9	228.9
Furniture and equipment
Property, Plant and Equipment [Line Items]
Computer software, hardware, leasehold improvements, furniture and equipment, gross	$ 61.2	$ 63.4