Business and Summary of Significant Accounting Policies - Computer Equipment, Software, Furniture and Leasehold Improvements, Net (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 31, 2021	Jan. 31, 2020	Jan. 31, 2019
Property, Plant and Equipment [Abstract]
Useful life	3 years
Depreciation	$ 51.4	$ 51.0	$ 59.2
Computer hardware, at cost	153.3	159.7
Computer software, at cost	57.9	64.0
Leasehold improvements, land and buildings, at cost	335.9	284.0
Furniture and equipment, at cost	88.4	69.0
Computer software, hardware, leasehold improvements, furniture, and equipment, at cost	635.5	576.7
Less: Accumulated depreciation	(442.7)	(415.0)
Computer software, hardware, leasehold improvements, furniture, and equipment, net	192.8	161.7
Capitalized software development costs	72.2	22.3
Amortization	3.7	1.2	$ 0.0
Cloud-based Software Hosting Arrangements
Property, Plant and Equipment [Abstract]
Accumulated amortization	$ 4.9	$ 1.2
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