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Summary of Accounting Policies - Narrative (Details)
shares in Thousands
 12 Months Ended
Oct. 01, 2020
intangibleAsset
reportingUnit
Dec. 31, 2020
USD ($)
reportingUnit
shares
Dec. 31, 2019
USD ($)
shares
Dec. 31, 2018
USD ($)
shares
Jan. 01, 2020
USD ($)
Jan. 01, 2019
USD ($)
Jan. 01, 2018
USD ($)
Dec. 31, 2017
USD ($)
Summary Of Accounting Policies [Line Items]                
Increase (decrease) in retained earnings   $ 10,479,800,000 $ 9,491,900,000 $ 7,738,500,000       $ 6,863,600,000
Operating lease ROU assets   265,000,000.0 266,900,000          
Operating lease liabilities   284,300,000 276,800,000          
Cash equivalents   $ 0.0 $ 370,100,000          
Antidilutive securities excluded from computation of earnings per share (in shares) | shares   208 627 724        
Foreign currency transaction gains (losses)   $ (4,300,000) $ (3,700,000) $ 200,000        
Number of reporting units | reportingUnit   36            
Goodwill   $ 14,395,200,000 10,815,400,000 9,346,800,000        
Number of reporting units not requiring goodwill impairment | reportingUnit 35              
Research and development expense   446,100,000 403,500,000 376,900,000        
Contracts revenue percentage of completion   345,000,000.0 247,800,000 245,900,000        
Allowance for doubtful accounts receivable and sales returns and allowances net current   29,100,000 20,300,000          
Deferred commissions   42,500,000 31,400,000          
Deferred commissions expense   30,100,000 30,100,000          
Remaining performance obligations   4,298,000,000.0            
Capitalized computer software, net   $ 43,100,000 30,000,000.0          
Cumulative Effect, Period of Adoption, Adjustment                
Summary Of Accounting Policies [Line Items]                
Increase (decrease) in retained earnings     (1,700,000)         14,300,000
Operating lease ROU assets           $ 274,000,000.0    
Operating lease liabilities           $ 282,700,000    
Software-as-a-service                
Summary Of Accounting Policies [Line Items]                
Number of days for payment   30 days            
Subscription term   1 year            
Software licenses                
Summary Of Accounting Policies [Line Items]                
Subscription term   1 year            
Minimum                
Summary Of Accounting Policies [Line Items]                
Goodwill   $ 0            
Minimum | Software licenses                
Summary Of Accounting Policies [Line Items]                
Number of days for payment   30 days            
Minimum | PCS                
Summary Of Accounting Policies [Line Items]                
Number of days for payment   30 days            
Minimum | Engineered products                
Summary Of Accounting Policies [Line Items]                
Number of days for payment   30 days            
Maximum                
Summary Of Accounting Policies [Line Items]                
Goodwill   $ 3,228,700,000            
Maximum | Software licenses                
Summary Of Accounting Policies [Line Items]                
Number of days for payment   60 days            
Maximum | PCS                
Summary Of Accounting Policies [Line Items]                
Number of days for payment   60 days            
Maximum | Engineered products                
Summary Of Accounting Policies [Line Items]                
Number of days for payment   60 days            
Trade names                
Summary Of Accounting Policies [Line Items]                
Number of intangible assets evaluated for impairment | intangibleAsset 2              
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]: 2021-01-01                
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction [Line Items]                
Remaining performance obligations, percentage   59.00%            
Remaining performance obligations, expected timing of revenue recognition   12 months            
Retained earnings                
Summary Of Accounting Policies [Line Items]                
Increase (decrease) in retained earnings   $ 8,546,200,000 7,818,000,000.0 $ 6,247,700,000       5,464,600,000
Retained earnings | Cumulative Effect, Period of Adoption, Adjustment                
Summary Of Accounting Policies [Line Items]                
Increase (decrease) in retained earnings     $ (1,700,000)   $ (1,700,000)   $ 14,300,000 $ 14,300,000