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Summary of Significant Accounting Policies (Narrative) (Details)
3 Months Ended 6 Months Ended
Oct. 27, 2017
shares
Mar. 31, 2018
USD ($)
Mar. 31, 2017
USD ($)
Mar. 31, 2018
USD ($)
Mar. 31, 2018
USD ($)
Mar. 31, 2018
USD ($)
shares
Mar. 31, 2018
USD ($)
segment
Mar. 31, 2018
USD ($)
$ / shares
Mar. 31, 2018
USD ($)
Mar. 31, 2017
USD ($)
Oct. 25, 2017
USD ($)
Sep. 30, 2017
USD ($)
Apr. 20, 2016
USD ($)
Revenue Recognition                          
VSOE percentage which constitutes substantial majority of transactions priced within a narrow range                 80.00%        
Range of VSOE to median sales price                 15.00%        
Number of Reportable Segments             1   1        
Stock-Based Compensation                          
Share-based compensation expense   $ 41,300,000 $ 43,900,000   $ 82,300,000         $ 90,500,000      
Unrecognized stock-based compensation cost   177,800,000   $ 177,800,000 177,800,000 $ 177,800,000 $ 177,800,000 $ 177,800,000 $ 177,800,000        
Unrecognized stock-based compensation cost, period for recognition       2 years                  
Common Stock Repurchase                          
Stock Repurchase Program, Number Of Shares Repurchased And Retired | shares           2,307,936              
Treasury Stock Acquired, Average Cost Per Share | $ / shares               $ 130.01          
Stock Repurchase Program, Remaining Authorized Repurchase Amount   873,600,000   $ 873,600,000 873,600,000 $ 873,600,000 $ 873,600,000 $ 873,600,000 $ 873,600,000        
New Accounting Pronouncements and Changes in Accounting Principles [Abstract]                          
Excess tax benefit (deficiency) from share-based compensation recorded to the consolidated income statements due to adoption of ASU 2016-09   $ 1,300,000     $ 1,200,000                
Restricted Stock Units (RSUs) [Member]                          
Stock-Based Compensation                          
Approved RSUs to employees and executive officers pursuant to the Company's annual equity awards program | shares 1,086,939                        
Minimum [Member]                          
Revenue Recognition                          
Domestic accounts receivable terms of payment       30 days                  
International accounts receivable terms of payment       30 days                  
Finite-Lived Intangible Asset, Useful Life       3 years                  
Maximum [Member]                          
Revenue Recognition                          
Domestic accounts receivable terms of payment       45 days                  
International accounts receivable terms of payment       120 days                  
Finite-Lived Intangible Asset, Useful Life       10 years                  
October Twenty Six Two Thousand Ten Program [Member]                          
Common Stock Repurchase                          
Stock Repurchase Program, Authorized Amount                     $ 1,000,000,000   $ 3,400,000,000
Annual Equity Program [Member] | Restricted Stock Units (RSUs) [Member]                          
Stock-Based Compensation                          
Percentage of the aggregate number of RSUs granted that vest in equal quarterly increments                 50.00%        
Portion of RSU grant subject to Company achieving specified quarterly revenue and EBITDA goals                 50.00%        
Percentage of quarterly performance stock grant based on achieving quarterly revenue goal                 70.00%        
Percentage of quarterly revenue goal to be achieved for performance stock grant                 80.00%        
Percentage of quarterly performance stock grant based on achieving EBITDA goal                 30.00%        
Percentage Of Quarterly Ebitda Goal To Be Achieved For Performance Stock Grant                 80.00%        
Threshold percentage of targeted goals above which quarterly performance stock grant is paid linearly                 80.00%        
Percentage of over-achievement threshold to which the goals are entitled                 100.00%        
Percentage Of Over-Achievement To Which Quarterly Performance Based Vesting Cannot Exceed                 200.00%        
Percentage Of Annual Performance Stock Grant Based On Achieving Annual Revenue Goal                 50.00%        
Percentage Of Annual Revenue Goal To Be Achieved For Performance Stock Grant                 80.00%        
Percentage Of Annual Performance Stock Grant Based On Achieving Annual Increase in Stand-alone Software Goal                 25.00%        
Percentage Of Annual Increase in Stand-alone Software Goal To Be Achieved For Performance Stock Grant                 15.00%        
Percentage Of Annual Performance Stock Grant Based On Achieving Relative Total Shareholder Return Benchmarked to the S&P 500 Index Goal                 25.00%        
Percentage Of Over-Achievement To Which Annual Performance Based Vesting Cannot Exceed                 200.00%        
Annual Equity Program [Member] | November 1, 2017 [Member] | Restricted Stock Units (RSUs) [Member]                          
Stock-Based Compensation                          
Approved RSUs to employees and executive officers pursuant to the Company's annual equity awards program | shares           140,135              
Annual equity awards program vesting period       4 years                  
Annual Equity Program [Member] | November 1, 2016 [Member] | Restricted Stock Units (RSUs) [Member]                          
Stock-Based Compensation                          
Approved RSUs to employees and executive officers pursuant to the Company's annual equity awards program | shares           115,347              
Annual equity awards program vesting period       4 years                  
Annual Equity Program [Member] | November 2, 2015 [Member] | Restricted Stock Units (RSUs) [Member]                          
Stock-Based Compensation                          
Approved RSUs to employees and executive officers pursuant to the Company's annual equity awards program | shares           145,508              
Annual equity awards program vesting period       4 years                  
Annual Equity Program [Member] | November 1, 2014 [Member] | Restricted Stock Units (RSUs) [Member]                          
Stock-Based Compensation                          
Approved RSUs to employees and executive officers pursuant to the Company's annual equity awards program | shares           171,575              
Annual equity awards program vesting period       4 years                  
Software and Software Development Costs [Member] | Minimum [Member]                          
Revenue Recognition                          
Finite-Lived Intangible Asset, Useful Life       3 years                  
Software and Software Development Costs [Member] | Maximum [Member]                          
Revenue Recognition                          
Finite-Lived Intangible Asset, Useful Life       5 years                  
Accounting Standards Update 2015-17 [Member]                          
New Accounting Pronouncements and Changes in Accounting Principles [Abstract]                          
Deferred tax assets, net, current                       $ (53,000,000)  
Deferred income tax assets, net                       $ 53,000,000