Condensed Consolidated Statements of Comprehensive Income (Loss) - USD ($) shares in Millions, $ in Millions	3 Months Ended		6 Months Ended
	Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020
Revenues:
Total revenues	$ 1,259.0	$ 1,138.1	$ 2,492.4	$ 2,311.7
Cost of revenues:
Total cost of revenues	664.0	626.8	1,338.3	1,292.4
Gross profit	595.0	511.3	1,154.1	1,019.3
Operating expenses:
Selling and marketing	97.7	84.3	189.7	175.7
Research and development	100.8	96.8	208.7	201.7
General and administrative	83.6	88.9	173.7	181.8
Total operating expenses	282.1	270.0	572.1	559.2
Operating income	312.9	241.3	582.0	460.1
Interest expense, net	(51.0)	(60.5)	(102.4)	(137.9)
Other income, net	6.5	19.0	24.5	3.7
Equity in earnings of unconsolidated affiliates, net	(0.4)	(1.0)	(0.1)	(0.3)
(Loss) gain on extinguishment of debt	(1.5)	0.2	(1.8)	(2.6)
Income before income taxes	266.5	199.0	502.2	323.0
Provision for income taxes	76.7	29.5	137.5	54.3
Net income	$ 189.8	$ 169.5	$ 364.7	$ 268.7
Basic earnings per share	$ 0.74	$ 0.66	$ 1.42	$ 1.05
Diluted earnings per share	$ 0.71	$ 0.64	$ 1.36	$ 1.01
Basic weighted-average number of common shares outstanding	255.7	257.0	256.4	256.1
Diluted weighted-average number of common and common equivalent shares outstanding	267.6	265.8	267.8	265.7
Net income	$ 189.8	$ 169.5	$ 364.7	$ 268.7
Other comprehensive income (loss), net of tax:
Change in unrealized (loss) gain on interest rate swaps	(0.2)	(0.3)	0.3	(2.7)
Foreign currency exchange translation adjustment	1.9	34.1	10.3	(116.6)
Change in defined benefit pension obligation	0.1		0.1
Total other comprehensive income (loss), net of tax	1.8	33.8	10.7	(119.3)
Comprehensive income	191.6	203.3	375.4	149.4
Software-enabled Services [Member]
Revenues:
Total revenues	1,057.1	945.0	2,100.5	1,934.5
Cost of revenues:
Total cost of revenues	582.8	549.9	1,178.3	1,133.4
License, Maintenance and Related [Member]
Revenues:
Total revenues	201.9	193.1	391.9	377.2
Cost of revenues:
Total cost of revenues	$ 81.2	$ 76.9	$ 160.0	$ 159.0