Computer Equipment, Software, Furniture and Leasehold Improvements, Net (Details) - USD ($) $ in Millions	Jul. 31, 2017	Jan. 31, 2017
Property, Plant and Equipment [Line Items]
Computer software, hardware, leasehold improvements, furniture and equipment, gross	$ 574.7	$ 544.1
Less: Accumulated depreciation	(421.7)	(385.5)
Computer software, hardware, leasehold improvements, furniture and equipment, net	153.0	158.6
Computer hardware, at cost
Property, Plant and Equipment [Line Items]
Computer software, hardware, leasehold improvements, furniture and equipment, gross	217.0	206.1
Computer software, at cost
Property, Plant and Equipment [Line Items]
Computer software, hardware, leasehold improvements, furniture and equipment, gross	78.7	73.5
Leasehold improvements, land and buildings, at cost
Property, Plant and Equipment [Line Items]
Computer software, hardware, leasehold improvements, furniture and equipment, gross	218.5	206.3
Furniture and equipment, at cost
Property, Plant and Equipment [Line Items]
Computer software, hardware, leasehold improvements, furniture and equipment, gross	$ 60.5	$ 58.2