Segment and Geographic Area Information - Schedule of Reporting Information (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Dec. 31, 2022	Sep. 30, 2022	Jun. 30, 2022	Mar. 31, 2022	Dec. 31, 2021	Sep. 30, 2021	Jun. 30, 2021	Mar. 31, 2021	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Segment Reporting Information [Line Items]
Net revenues	$ 1,430.9	$ 1,350.3	$ 1,310.8	$ 1,279.8	$ 1,256.6	$ 1,232.1	$ 1,189.8	$ 1,155.3	$ 5,371.8	$ 4,833.8	$ 4,022.4
Operating profit									1,524.5	1,335.6	1,082.9
Assets:
Operating assets	1,163.9				1,057.6				1,163.9	1,057.6	958.6
Intangible assets, net	23,976.8				19,985.4				23,976.8	19,985.4	20,409.1
Other	1,840.1				788.0				1,840.1	788.0	712.6
Total assets	26,980.8				21,831.0				26,980.8	21,831.0	22,080.3
Capital expenditures									40.1	28.5	24.7
Capitalized software expenditures									30.2	29.7	17.7
Depreciation and other amortization									650.1	615.9	491.6
Impairment of intangible assets									0.0	94.4	0.0
Disposal group, held-for-sale, not discontinued operations | Industrial Businesses
Assets:
Operating assets classified as held for sale					1,882.9					1,882.9	1,944.5
Application Software
Segment Reporting Information [Line Items]
Net revenues									2,639.5	2,366.7	1,785.8
Network Software
Segment Reporting Information [Line Items]
Net revenues									1,378.5	1,223.8	1,069.4
Technology Enabled Products
Segment Reporting Information [Line Items]
Net revenues									1,353.8	1,243.3	1,167.2
Operating Segments | Application Software
Segment Reporting Information [Line Items]
Net revenues									2,639.5	2,366.7	1,785.8
Operating profit									714.0	633.1	467.9
Assets:
Operating assets	624.7				576.0				624.7	576.0	524.7
Intangible assets, net	17,758.4				13,498.4				17,758.4	13,498.4	13,837.1
Other	340.2				205.8				340.2	205.8	173.1
Capital expenditures									20.7	18.0	12.9
Capitalized software expenditures									28.5	26.3	16.3
Depreciation and other amortization									455.8	418.7	293.2
Operating Segments | Network Software
Segment Reporting Information [Line Items]
Net revenues									1,378.5	1,223.8	1,069.4
Operating profit									570.6	476.8	382.7
Assets:
Operating assets	224.7				215.5				224.7	215.5	196.0
Intangible assets, net	5,118.5				5,364.8				5,118.5	5,364.8	5,428.6
Other	124.2				50.4				124.2	50.4	48.4
Capital expenditures									8.8	5.0	5.8
Capitalized software expenditures									1.7	3.4	1.4
Depreciation and other amortization									164.2	164.8	164.9
Operating Segments | Technology Enabled Products
Segment Reporting Information [Line Items]
Net revenues									1,353.8	1,243.3	1,167.2
Operating profit									449.1	415.6	412.1
Assets:
Operating assets	307.4				250.7				307.4	250.7	234.1
Intangible assets, net	1,099.9				1,122.2				1,099.9	1,122.2	1,143.4
Other	95.4				33.8				95.4	33.8	46.9
Capital expenditures									9.2	4.5	5.9
Capitalized software expenditures									0.0	0.0	0.0
Depreciation and other amortization									29.8	32.1	33.2
Corporate
Segment Reporting Information [Line Items]
Net revenues									0.0	0.0	0.0
Operating profit									(209.2)	(189.9)	(179.8)
Assets:
Operating assets	7.1				15.4				7.1	15.4	3.8
Intangible assets, net	0.0				0.0				0.0	0.0	0.0
Other	$ 1,280.3				$ 498.0				1,280.3	498.0	444.2
Capital expenditures									1.4	1.0	0.1
Capitalized software expenditures									0.0	0.0	0.0
Depreciation and other amortization									$ 0.3	$ 0.3	$ 0.3