Computer Equipment, Software, Furniture and Leasehold Improvements, Net (Details) - USD ($) $ in Millions	Oct. 31, 2017	Jan. 31, 2017
Property, Plant and Equipment [Line Items]
Computer software, hardware, leasehold improvements, furniture and equipment, gross	$ 565.1	$ 544.1
Less: Accumulated depreciation	(417.0)	(385.5)
Computer software, hardware, leasehold improvements, furniture and equipment, net	148.1	158.6
Computer hardware, at cost
Property, Plant and Equipment [Line Items]
Computer software, hardware, leasehold improvements, furniture and equipment, gross	210.8	206.1
Computer software, at cost
Property, Plant and Equipment [Line Items]
Computer software, hardware, leasehold improvements, furniture and equipment, gross	70.5	73.5
Leasehold improvements, land and buildings, at cost
Property, Plant and Equipment [Line Items]
Computer software, hardware, leasehold improvements, furniture and equipment, gross	221.9	206.3
Furniture and equipment, at cost
Property, Plant and Equipment [Line Items]
Computer software, hardware, leasehold improvements, furniture and equipment, gross	$ 61.9	$ 58.2