Disaggregation of Revenue - Schedule of disaggregation of revenue (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2023	Jun. 30, 2022	Jun. 30, 2023	Jun. 30, 2022
Disaggregation of Revenue
Total revenues	$ 504,279	$ 468,685	$ 976,133	$ 924,792
Corporate
Disaggregation of Revenue
Total revenues	519	(1,732)	(4,564)	(7,321)
Intercompany
Disaggregation of Revenue
Total revenues	(6,852)	(5,342)	(11,935)	(10,931)
Corporate and Elimination
Disaggregation of Revenue
Total revenues	519	(1,732)	(4,564)	(7,321)
Enterprise Software \| Intercompany
Disaggregation of Revenue
Total revenues	6,852	5,342	11,935	10,931
Enterprise Software \| Operating segments
Disaggregation of Revenue
Total revenues	342,475	315,570	670,820	626,556
Platform Technologies \| Intercompany
Disaggregation of Revenue
Total revenues	0	0	0	0
Platform Technologies \| Operating segments
Disaggregation of Revenue
Total revenues	161,285	154,847	309,877	305,557
Recurring revenues
Disaggregation of Revenue
Total revenues	414,328	372,631	809,924	735,103
Recurring revenues \| Corporate
Disaggregation of Revenue
Total revenues	0	0	0	0
Recurring revenues \| Enterprise Software
Disaggregation of Revenue
Total revenues	264,507	239,454	523,003	470,465
Recurring revenues \| Platform Technologies
Disaggregation of Revenue
Total revenues	149,821	133,177	286,921	264,638
Non-recurring revenues
Disaggregation of Revenue
Total revenues	89,951	96,054	166,209	189,689
Non-recurring revenues \| Corporate
Disaggregation of Revenue
Total revenues	7,371	3,610	7,371	3,610
Non-recurring revenues \| Enterprise Software
Disaggregation of Revenue
Total revenues	71,116	70,774	135,882	145,160
Non-recurring revenues \| Platform Technologies
Disaggregation of Revenue
Total revenues	11,464	21,670	22,956	40,919
Products and services transferred at a point in time
Disaggregation of Revenue
Total revenues	22,545	21,791	37,025	42,974
Products and services transferred over time
Disaggregation of Revenue
Total revenues	481,734	446,894	939,108	881,818
SaaS
Disaggregation of Revenue
Total revenues	131,456	109,505	258,051	211,287
SaaS \| Corporate
Disaggregation of Revenue
Total revenues	0	0	0	0
SaaS \| Enterprise Software
Disaggregation of Revenue
Total revenues	115,877	97,703	226,919	188,474
SaaS \| Platform Technologies
Disaggregation of Revenue
Total revenues	15,579	11,802	31,132	22,813
SaaS \| Products and services transferred at a point in time
Disaggregation of Revenue
Total revenues	0	0	0	0
SaaS \| Products and services transferred over time
Disaggregation of Revenue
Total revenues	131,456	109,505	258,051	211,287
Transaction-based fees
Disaggregation of Revenue
Total revenues	166,333	146,311	320,203	289,972
Transaction-based fees \| Corporate
Disaggregation of Revenue
Total revenues	0	0	0	0
Transaction-based fees \| Enterprise Software
Disaggregation of Revenue
Total revenues	38,677	30,991	76,049	60,536
Transaction-based fees \| Platform Technologies
Disaggregation of Revenue
Total revenues	127,656	115,320	244,154	229,436
Transaction-based fees \| Products and services transferred at a point in time
Disaggregation of Revenue
Total revenues	0	0	0	0
Transaction-based fees \| Products and services transferred over time
Disaggregation of Revenue
Total revenues	166,333	146,311	320,203	289,972
Maintenance
Disaggregation of Revenue
Total revenues	116,539	116,815	231,670	233,844
Maintenance \| Corporate
Disaggregation of Revenue
Total revenues	0	0	0	0
Maintenance \| Enterprise Software
Disaggregation of Revenue
Total revenues	109,953	110,760	220,035	221,455
Maintenance \| Platform Technologies
Disaggregation of Revenue
Total revenues	6,586	6,055	11,635	12,389
Maintenance \| Products and services transferred at a point in time
Disaggregation of Revenue
Total revenues	0	0	0	0
Maintenance \| Products and services transferred over time
Disaggregation of Revenue
Total revenues	116,539	116,815	231,670	233,844
Professional services
Disaggregation of Revenue
Total revenues	66,420	71,937	127,349	141,952
Professional services \| Corporate
Disaggregation of Revenue
Total revenues	0	0	0	0
Professional services \| Enterprise Software
Disaggregation of Revenue
Total revenues	55,256	50,653	106,755	101,820
Professional services \| Platform Technologies
Disaggregation of Revenue
Total revenues	11,164	21,284	20,594	40,132
Professional services \| Products and services transferred at a point in time
Disaggregation of Revenue
Total revenues	0	0	0	0
Professional services \| Products and services transferred over time
Disaggregation of Revenue
Total revenues	66,420	71,937	127,349	141,952
Software licenses and royalties
Disaggregation of Revenue
Total revenues	9,779	15,009	19,909	31,515
Software licenses and royalties \| Corporate
Disaggregation of Revenue
Total revenues	0	0	0	0
Software licenses and royalties \| Enterprise Software
Disaggregation of Revenue
Total revenues	9,479	14,623	17,547	30,728
Software licenses and royalties \| Platform Technologies
Disaggregation of Revenue
Total revenues	300	386	2,362	787
Software licenses and royalties \| Products and services transferred at a point in time
Disaggregation of Revenue
Total revenues	8,793	12,683	18,074	26,752
Software licenses and royalties \| Products and services transferred over time
Disaggregation of Revenue
Total revenues	986	2,326	1,835	4,763
Hardware and other
Disaggregation of Revenue
Total revenues	13,752	9,108	18,951	16,222
Hardware and other \| Corporate
Disaggregation of Revenue
Total revenues	7,371	3,610	7,371	3,610
Hardware and other \| Enterprise Software
Disaggregation of Revenue
Total revenues	6,381	5,498	11,580	12,612
Hardware and other \| Platform Technologies
Disaggregation of Revenue
Total revenues	0	0	0	0
Hardware and other \| Products and services transferred at a point in time
Disaggregation of Revenue
Total revenues	13,752	9,108	18,951	16,222
Hardware and other \| Products and services transferred over time
Disaggregation of Revenue
Total revenues	$ 0	$ 0	$ 0	$ 0