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Segment and Geographic Area Information - Schedule of Reporting Information (Details) - USD ($) $ in Millions | 3 Months Ended | 12 Months Ended
--- | --- | ---
Dec. 31, 2023 | Sep. 30, 2023 | Jun. 30, 2023 | Mar. 31, 2023 | Dec. 31, 2022 | Sep. 30, 2022 | Jun. 30, 2022 | Mar. 31, 2022 | Dec. 31, 2023 | Dec. 31, 2022 | Dec. 31, 2021
Segment Reporting Information [Line Items] |  |  |  |  |  |  |  |  |  |  |
Net revenues | $ 1,613.5 | $ 1,563.4 | $ 1,531.2 | $ 1,469.7 | $ 1,430.9 | $ 1,350.3 | $ 1,310.8 | $ 1,279.8 | $ 6,177.8 | $ 5,371.8 | $ 4,833.8
Cost of sales |  |  |  |  |  |  |  |  | 1,870.6 | 1,619.0 | 1,426.2
Selling, general and administrative expenses |  |  |  |  |  |  |  |  | 2,562.0 | 2,228.3 | 2,072.0
Research, development and engineering costs |  |  |  |  |  |  |  |  | 646.1 | 529.8 | 484.8
Operating profit |  |  |  |  |  |  |  |  | 1,745.2 | 1,524.5 | 1,335.6
Assets: |  |  |  |  |  |  |  |  |  |  |
Operating assets | 1,338.9 |  |  |  | 1,163.9 |  |  |  | 1,338.9 | 1,163.9 | 1,057.6
Intangible assets, net | 25,330.9 |  |  |  | 23,976.8 |  |  |  | 25,330.9 | 23,976.8 | 19,985.4
Other | 1,497.7 |  |  |  | 1,840.1 |  |  |  | 1,497.7 | 1,840.1 | 788.0
Total assets | 28,167.5 |  |  |  | 26,980.8 |  |  |  | 28,167.5 | 26,980.8 | 21,831.0
Capital expenditures |  |  |  |  |  |  |  |  | 68.0 | 40.1 | 28.5
Capitalized software expenditures |  |  |  |  |  |  |  |  | 40.0 | 30.2 | 29.7
Depreciation and other amortization |  |  |  |  |  |  |  |  | 755.2 | 650.1 | 615.9
Stock-based compensation |  |  |  |  |  |  |  |  | 123.5 | 117.8 | 123.0
Impairment of intangible assets |  |  |  |  |  |  |  |  | 0.0 | 0.0 | 94.4
Disposal group, held-for-sale, not discontinued operations | Industrial Businesses |  |  |  |  |  |  |  |  |  |  |
Assets: |  |  |  |  |  |  |  |  |  |  |
Operating assets classified as held for sale |  |  |  |  |  |  |  |  |  |  | 1,882.9
Application Software |  |  |  |  |  |  |  |  |  |  |
Segment Reporting Information [Line Items] |  |  |  |  |  |  |  |  |  |  |
Net revenues |  |  |  |  |  |  |  |  | 3,186.9 | 2,639.5 | 2,366.7
Network Software |  |  |  |  |  |  |  |  |  |  |
Segment Reporting Information [Line Items] |  |  |  |  |  |  |  |  |  |  |
Net revenues |  |  |  |  |  |  |  |  | 1,439.4 | 1,378.5 | 1,223.8
Technology Enabled Products |  |  |  |  |  |  |  |  |  |  |
Segment Reporting Information [Line Items] |  |  |  |  |  |  |  |  |  |  |
Net revenues |  |  |  |  |  |  |  |  | 1,551.5 | 1,353.8 | 1,243.3
Operating Segments | Application Software |  |  |  |  |  |  |  |  |  |  |
Segment Reporting Information [Line Items] |  |  |  |  |  |  |  |  |  |  |
Net revenues |  |  |  |  |  |  |  |  | 3,186.9 | 2,639.5 | 2,366.7
Operating profit |  |  |  |  |  |  |  |  | 820.8 | 714.0 | 633.1
Assets: |  |  |  |  |  |  |  |  |  |  |
Operating assets | 730.8 |  |  |  | 624.7 |  |  |  | 730.8 | 624.7 | 576.0
Intangible assets, net | 19,242.4 |  |  |  | 17,758.4 |  |  |  | 19,242.4 | 17,758.4 | 13,498.4
Other | 377.7 |  |  |  | 340.2 |  |  |  | 377.7 | 340.2 | 205.8
Capital expenditures |  |  |  |  |  |  |  |  | 20.1 | 20.7 | 18.0
Capitalized software expenditures |  |  |  |  |  |  |  |  | 39.5 | 28.5 | 26.3
Depreciation and other amortization |  |  |  |  |  |  |  |  | 563.0 | 455.8 | 418.7
Operating Segments | Network Software |  |  |  |  |  |  |  |  |  |  |
Segment Reporting Information [Line Items] |  |  |  |  |  |  |  |  |  |  |
Net revenues |  |  |  |  |  |  |  |  | 1,439.4 | 1,378.5 | 1,223.8
Operating profit |  |  |  |  |  |  |  |  | 632.4 | 570.6 | 476.8
Assets: |  |  |  |  |  |  |  |  |  |  |
Operating assets | 235.6 |  |  |  | 224.7 |  |  |  | 235.6 | 224.7 | 215.5
Intangible assets, net | 5,005.9 |  |  |  | 5,118.5 |  |  |  | 5,005.9 | 5,118.5 | 5,364.8
Other | 122.3 |  |  |  | 124.2 |  |  |  | 122.3 | 124.2 | 50.4
Capital expenditures |  |  |  |  |  |  |  |  | 6.4 | 8.8 | 5.0
Capitalized software expenditures |  |  |  |  |  |  |  |  | 0.5 | 1.7 | 3.4
Depreciation and other amortization |  |  |  |  |  |  |  |  | 162.5 | 164.2 | 164.8
Operating Segments | Technology Enabled Products |  |  |  |  |  |  |  |  |  |  |
Segment Reporting Information [Line Items] |  |  |  |  |  |  |  |  |  |  |
Net revenues |  |  |  |  |  |  |  |  | 1,551.5 | 1,353.8 | 1,243.3
Operating profit |  |  |  |  |  |  |  |  | 518.7 | 449.1 | 415.6
Assets: |  |  |  |  |  |  |  |  |  |  |
Operating assets | 337.5 |  |  |  | 307.4 |  |  |  | 337.5 | 307.4 | 250.7
Intangible assets, net | 1,082.6 |  |  |  | 1,099.9 |  |  |  | 1,082.6 | 1,099.9 | 1,122.2
Other | 65.5 |  |  |  | 95.4 |  |  |  | 65.5 | 95.4 | 33.8
Capital expenditures |  |  |  |  |  |  |  |  | 13.8 | 9.2 | 4.5
Capitalized software expenditures |  |  |  |  |  |  |  |  | 0.0 | 0.0 | 0.0
Depreciation and other amortization |  |  |  |  |  |  |  |  | 29.1 | 29.8 | 32.1
Corporate |  |  |  |  |  |  |  |  |  |  |
Segment Reporting Information [Line Items] |  |  |  |  |  |  |  |  |  |  |
Net revenues |  |  |  |  |  |  |  |  | 0.0 | 0.0 | 0.0
Operating profit |  |  |  |  |  |  |  |  | (226.7) | (209.2) | (189.9)
Assets: |  |  |  |  |  |  |  |  |  |  |
Operating assets | 35.0 |  |  |  | 7.1 |  |  |  | 35.0 | 7.1 | 15.4
Intangible assets, net | 0.0 |  |  |  | 0.0 |  |  |  | 0.0 | 0.0 | 0.0
Other | $ 932.2 |  |  |  | $ 1,280.3 |  |  |  | 932.2 | 1,280.3 | 498.0
Capital expenditures |  |  |  |  |  |  |  |  | 27.7 | 1.4 | 1.0
Capitalized software expenditures |  |  |  |  |  |  |  |  | 0.0 | 0.0 | 0.0
Depreciation and other amortization |  |  |  |  |  |  |  |  | $ 0.6 | $ 0.3 | $ 0.3

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