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Stock-based Compensation Expense Additional Information (Details)
$ / shares in Units, $ in Millions
3 Months Ended 6 Months Ended
Jul. 31, 2017
USD ($)
Jul. 31, 2016
USD ($)
Jul. 31, 2017
USD ($)
period
$ / shares
shares
Jul. 31, 2016
USD ($)
$ / shares
shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Allocated share-based compensation expense $ 67.6 $ 54.3 $ 134.4 $ 105.9
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     $ 116.9 93.4
Awards granted in period (shares) | shares     815,800  
Restricted Stock Units (RSUs)        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Awards granted in period (shares) | shares     500,000  
Allocated share-based compensation expense 52.0 41.5 $ 102.0 80.3
Acceleration of eligible stock awards 5.9   $ 9.1  
Performance Stock Unit        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Awards granted in period (shares) | shares     300,000  
Allocated share-based compensation expense 9.7 $ 5.9 $ 20.6 $ 12.2
Acceleration of eligible stock awards $ 2.8   $ 7.5  
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  
Shares issued under employee stock purchase plans (shares) | shares     1,100,000 1,200,000
Awards issued, share average price (in usd per share) | $ / shares     $ 38.34 $ 36.67
Weighted average grant date fair value per share of stock options granted (in dollars per share) | $ / shares     $ 25.13 $ 17.88
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%