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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

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