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Other Intangible Assets, Net (Details) - USD ($)
$ in Millions
Apr. 30, 2018
Jan. 31, 2018
Finite-Lived Intangible Assets [Line Items]    
Other intangible assets, at cost $ 947.3 $ 951.0
Less: Accumulated amortization (900.4) (895.8)
Other intangible assets, net 46.9 55.2
Developed technologies    
Finite-Lived Intangible Assets [Line Items]    
Other intangible assets, at cost 577.2 578.5
Customer relationships, trade names, patents, and user lists    
Finite-Lived Intangible Assets [Line Items]    
Other intangible assets, at cost $ 370.1 $ 372.5