Debt - Credit Agreement - Additional Information (Details) - USD ($) $ in Millions			12 Months Ended
	Oct. 02, 2023	Jan. 03, 2023	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022	Jan. 31, 2023
Debt Instrument [Line Items]
Financing cost current				$ 4.2
Deferred debt issuance cost				9.2
Interest expense			$ 119.7	129.4	$ 54.3
Periodic interest payment			137.0	$ 89.8	$ 48.5
Amount borrowed from credit facility foreign subsidiary			$ 83.0
Interest rate during period			5.40%	4.90%	3.40%
Servicemax acquisition
Debt Instrument [Line Items]
Interest related to the deferred acquisition payment				$ 30.0
Deferred acquisition payments	$ 650.0	$ 650.0		650.0
Line of Credit
Debt Instrument [Line Items]
Unused commitments under credit facility			$ 988.0
Amounts available for borrowing			972.1
Investment limit in foreign subsidiaries			$ 100.0
Financing costs				$ 13.4
Line of Credit | Minimum
Debt Instrument [Line Items]
Variable interest rate, length of time between updates			30 days
Credit facility commitment fees percentage			0.175%
Line of Credit | Maximum
Debt Instrument [Line Items]
Variable interest rate, length of time between updates			180 days
Credit facility commitment fees percentage			0.325%
Secured Debt
Debt Instrument [Line Items]
Credit facility amount						$ 500.0
Annual rate for borrowings outstanding			6.90%
Revolving Credit Facility
Debt Instrument [Line Items]
Credit facility amount						$ 1,250.0