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Acquisitions and Disposition of Businesses - Additional Information (Details) $ in Thousands |  |  |  |  |  | 3 Months Ended | 6 Months Ended | 12 Months Ended |
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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 |  |  |  |  |  |  |  |  |

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