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Stock-based Compensation Expense (Additional Information) (Details)
$ in Millions
3 Months Ended 9 Months Ended
Oct. 31, 2018
USD ($)
Oct. 31, 2017
USD ($)
Oct. 31, 2018
USD ($)
period
shares
Oct. 31, 2017
USD ($)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Allocated share-based compensation expense $ 64.2 $ 65.1 $ 175.5 $ 199.5
Market capitalization     2,000.0  
Restricted Stock Units (RSUs) and Performance Shares        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Awards vested in period, fair value     $ 355.1 332.8
Awards granted in period (shares) | shares     1,784,600  
Restricted Stock Units (RSUs)        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Awards granted in period (shares) | shares     1,600,000  
Allocated share-based compensation expense 49.8 51.5 $ 135.6 153.5
Performance Stock Unit        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Awards granted in period (shares) | shares     200,000  
Allocated share-based compensation expense $ 7.5 $ 7.1 $ 19.9 27.7
Award vesting period     3 years  
Employee Qualified Stock Purchase Plan 1998 ESP Plan        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Employee stock purchase plan maximum percentage of compensation to purchase shares by eligible participants     15.00%  
Employee stock purchase plan minimum percentage of common stock fair value defined to purchase shares by eligible participants     85.00%  
Employee stock purchase plan, number of exercise periods | period     4  
Employee stock purchase plan, term of exercise period     6 months  
Employee stock purchase plan, term of offering period     24 months  
Share-based Compensation Award, Tranche One | Performance Stock Unit        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
PSU annual vesting percentage     33.33%  
Share-based Compensation Award, Tranche Two | Performance Stock Unit        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
PSU annual vesting percentage     33.33%  
Share-based Compensation Award, Tranche Three | Performance Stock Unit        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
PSU annual vesting percentage     33.33%  
Chief Executive Officer | Restricted Stock Units (RSUs)        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Allocated share-based compensation expense       9.1
Chief Executive Officer | Performance Stock Unit        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Allocated share-based compensation expense       $ 7.5