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Business and Summary of Significant Accounting Policies - Computer Equipment, Software, Furniture and Leasehold Improvements, Net (Details) - USD ($)
$ in Millions
12 Months Ended
Jan. 31, 2022
Jan. 31, 2021
Jan. 31, 2020
Property, Plant and Equipment [Abstract]      
Useful life 3 years    
Depreciation $ 52.0 $ 51.4 $ 51.0
Computer hardware, at cost 137.2 153.3  
Computer software, at cost 55.0 57.9  
Leasehold improvements, land and buildings, at cost 350.5 335.9  
Furniture and equipment, at cost 93.4 88.4  
Computer software, hardware, leasehold improvements, furniture, and equipment, at cost 636.1 635.5  
Less: Accumulated depreciation (473.6) (442.7)  
Computer software, hardware, leasehold improvements, furniture, and equipment, net 162.5 192.8  
Capitalized software development costs 128.4 72.2  
Amortization 11.8 3.7 $ 1.2
Cloud-based Software Hosting Arrangements      
Property, Plant and Equipment [Abstract]      
Accumulated amortization $ 16.7 $ 4.9  
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