Business and Summary of Significant Accounting Policies - Computer Equipment, Software, Furniture and Leasehold Improvements, Net (Details) - USD ($)	12 Months Ended
	Jan. 31, 2020	Jan. 31, 2019	Jan. 31, 2018
Property, Plant and Equipment [Abstract]
Depreciation	$ 51,000,000.0	$ 59,200,000	$ 67,600,000
Computer hardware, at cost	159,700,000	190,200,000
Computer software, at cost	64,000,000.0	66,700,000
Leasehold improvements, land and buildings, at cost	284,000,000.0	247,800,000
Furniture and equipment, at cost	69,000,000.0	67,200,000
Computer software, hardware, leasehold improvements, furniture, and equipment, at cost	576,700,000	571,900,000
Less: Accumulated depreciation	(415,000,000.0)	(422,200,000)
Computer software, hardware, leasehold improvements, furniture, and equipment, net	161,700,000	149,700,000
Capitalized software development costs	22,300,000	4,900,000
Amortization	$ 1,200,000	$ 0
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