Computer Equipment, Software, Leasehold Improvements, and Furniture, Net (Details) - USD ($) $ in Millions	Jul. 31, 2021	Jan. 31, 2021
Property, Plant and Equipment [Line Items]
Computer software, hardware, leasehold improvements, furniture and equipment, gross	$ 631.1	$ 635.5
Less: Accumulated depreciation	(432.8)	(442.7)
Computer hardware, software, leasehold improvements, and furniture and equipment, net	198.3	192.8
Computer hardware, at cost
Property, Plant and Equipment [Line Items]
Computer software, hardware, leasehold improvements, furniture and equipment, gross	129.9	153.3
Computer software, at cost
Property, Plant and Equipment [Line Items]
Computer software, hardware, leasehold improvements, furniture and equipment, gross	55.1	57.9
Leasehold improvements, land and buildings, at cost
Property, Plant and Equipment [Line Items]
Computer software, hardware, leasehold improvements, furniture and equipment, gross	350.2	335.9
Furniture and equipment, at cost
Property, Plant and Equipment [Line Items]
Computer software, hardware, leasehold improvements, furniture and equipment, gross	$ 95.9	$ 88.4