Acquisitions and Disposition of Businesses - Additional Information (Details) $ in Thousands						3 Months Ended		6 Months Ended		12 Months Ended
	Oct. 02, 2023 USD ($)	Jan. 03, 2023 USD ($) Employees	Jun. 01, 2022 USD ($) Employees	Apr. 29, 2022 USD ($) Employees	Jan. 15, 2021 USD ($) Employees	Jun. 30, 2022 USD ($)	Dec. 31, 2021 USD ($)	Sep. 30, 2023 USD ($)	Mar. 31, 2023 USD ($)	Sep. 30, 2023 USD ($)	Sep. 30, 2022 USD ($)	Sep. 30, 2021 USD ($)	Jan. 31, 2023 USD ($)
Business Acquisition [Line Items]
Business combination, acquisition and transaction related costs										$ 18,700	$ 13,200	$ 15,000
Borrowings under credit facility										1,540,000	264,000	600,000
Revenue										$ 2,097,053	1,933,347	1,807,159
Acquired finite-lived intangible asset, weighted average useful life										15 years
Goodwill								$ 3,358,511		$ 3,358,511	2,353,654	2,191,887
Customer Relationships
Business Acquisition [Line Items]
Acquired finite-lived intangible asset, weighted average useful life										17 years
Purchased Software
Business Acquisition [Line Items]
Acquired finite-lived intangible asset, weighted average useful life										11 years
Trademarks
Business Acquisition [Line Items]
Acquired finite-lived intangible asset, weighted average useful life										11 years
Revolving Credit Facility
Business Acquisition [Line Items]
Credit facility amount													$ 1,250,000
Term Loan Facility
Business Acquisition [Line Items]
Borrowings under credit facility		$ 500,000
Arena Solutions
Business Acquisition [Line Items]
Preliminary purchase price					$ 715,000
Cash acquired from acquisition					$ 11,100
Number Of Employees | Employees					170
Revenue							$ 29,800
Fair value adjustments related to purchase accounting for acquisition							$ 9,100
Goodwill					$ 562,838
Arena Solutions | Customer Relationships
Business Acquisition [Line Items]
Acquired finite-lived intangible asset, weighted average useful life					13 years
Arena Solutions | Purchased Software
Business Acquisition [Line Items]
Acquired finite-lived intangible asset, weighted average useful life					9 years
Arena Solutions | Trademarks
Business Acquisition [Line Items]
Acquired finite-lived intangible asset, weighted average useful life					12 years
Arena Solutions | Line of Credit
Business Acquisition [Line Items]
Borrowings under credit facility					$ 600,000
PLM Services Business Disposition
Business Acquisition [Line Items]
Number Of Employees | Employees			160
Liabilities			$ 2,400
Total consideration			60,400							$ 0	$ 6,844	$ 0
Cash Consideration			32,500
Gain On Sale			29,800
Net Assets			30,600
Goodwill			33,000
Contingent Consideration			20,000
PLM Services Business Disposition | Service To Be Performed [Member]
Business Acquisition [Line Items]
Non Cash Consideration			$ 28,000
Servicemax Inc. acquisition
Business Acquisition [Line Items]
Preliminary purchase price		1,448,200
Deferred acquisition payments	$ 650,000	650,000								650,000
Payments to acquire business		828,200
Payments to acquire business, net of cash acquired	620,000	$ 620,000
Number Of Employees | Employees		500
Revenue										$ 137,600
Goodwill		$ 974,850
Increase in Goodwill								$ 300
Imputed interest payable	$ 30,000
Servicemax Inc. acquisition | Net Tax Liablity [Member]
Business Acquisition [Line Items]
Increase in net tax liability									$ 3,200
Servicemax Inc. acquisition | Customer Relationships
Business Acquisition [Line Items]
Acquired finite-lived intangible asset, weighted average useful life		20 years
Increase in customer relationships									$ 3,500
Servicemax Inc. acquisition | Purchased Software
Business Acquisition [Line Items]
Acquired finite-lived intangible asset, weighted average useful life		10 years
Servicemax Inc. acquisition | Trademarks
Business Acquisition [Line Items]
Acquired finite-lived intangible asset, weighted average useful life		10 years
Servicemax Inc. acquisition | Revolving Credit Facility
Business Acquisition [Line Items]
Borrowings under credit facility		$ 630,000
Intland Software
Business Acquisition [Line Items]
Preliminary purchase price				$ 278,100
Borrowings under credit facility				$ 264,000
Number Of Employees | Employees				150
Goodwill				$ 240,971
Increase in Goodwill						$ 900
Increase in goodwill by Working capital adjustments						$ 240,000
Intland Software | Customer Relationships
Business Acquisition [Line Items]
Acquired finite-lived intangible asset, weighted average useful life				11 years
Intland Software | Purchased Software
Business Acquisition [Line Items]
Acquired finite-lived intangible asset, weighted average useful life				10 years
Intland Software | Trademarks
Business Acquisition [Line Items]
Acquired finite-lived intangible asset, weighted average useful life				10 years