Business and Summary of Significant Accounting Policies - Computer Equipment, Software, Furniture and Leasehold Improvements, Net (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 31, 2018	Jan. 31, 2017	Jan. 31, 2016
Property, Plant and Equipment [Abstract]
Depreciation	$ 67.6	$ 73.1	$ 60.6
Computer hardware, at cost	217.1	206.1
Computer software, at cost	72.6	73.5
Leasehold improvements, land and buildings, at cost	228.9	206.3
Furniture and equipment, at cost	63.4	58.2
Computer software, hardware, leasehold improvements, furniture, and equipment, at cost	582.0	544.1
Less: Accumulated depreciation	(437.0)	(385.5)
Computer software, hardware, leasehold improvements, furniture, and equipment, net	$ 145.0	$ 158.6
Software and Software Development Costs
Property, Plant and Equipment [Abstract]
Useful Life	3 years
Minimum
Property, Plant and Equipment [Abstract]
Useful Life	3 years
Maximum
Property, Plant and Equipment [Abstract]
Useful Life	5 years