Goodwill and Other Intangible Assets, Net - Schedule of the Components of Other Intangible Assets (Details) - USD ($) $ in Millions	Aug. 02, 2024	Oct. 31, 2023	Aug. 04, 2023
Other Intangible Assets
Weighted-Average Useful Life in Years	13 years 6 months	13 years 3 months 18 days	13 years 2 months 12 days
Gross Carrying Amount	$ 459.5	$ 471.0	$ 472.7
Accumulated Amortization	(218.7)	(202.4)	(195.1)
Net	240.8	268.6	277.6
Indefinite-lived - trade names	271.6	271.5	271.6
Total other intangible assets, gross	731.1	742.5	744.3
Total other intangible assets, net	$ 512.4	$ 540.1	$ 549.2
Patents
Other Intangible Assets
Weighted-Average Useful Life in Years	9 years 10 months 24 days	9 years 10 months 24 days	9 years 10 months 24 days
Gross Carrying Amount	$ 18.2	$ 18.2	$ 18.2
Accumulated Amortization	(16.6)	(16.0)	(15.8)
Net	$ 1.6	$ 2.2	$ 2.4
Non-compete agreements
Other Intangible Assets
Weighted-Average Useful Life in Years		5 years 6 months	5 years 6 months
Gross Carrying Amount		$ 6.9	$ 6.9
Accumulated Amortization		(6.9)	(6.9)
Net		$ 0.0	$ 0.0
Customer-related
Other Intangible Assets
Weighted-Average Useful Life in Years	15 years 9 months 18 days	15 years 9 months 18 days	15 years 8 months 12 days
Gross Carrying Amount	$ 327.7	$ 327.5	$ 329.1
Accumulated Amortization	(124.8)	(106.7)	(102.0)
Net	$ 202.9	$ 220.8	$ 227.1
Developed technology
Other Intangible Assets
Weighted-Average Useful Life in Years	7 years 1 month 6 days	7 years 1 month 6 days	7 years 1 month 6 days
Gross Carrying Amount	$ 102.9	$ 102.0	$ 102.1
Accumulated Amortization	(70.4)	(63.1)	(60.8)
Net	$ 32.5	$ 38.9	$ 41.3
Backlog and other
Other Intangible Assets
Weighted-Average Useful Life in Years		7 months 6 days	7 months 6 days
Gross Carrying Amount		$ 5.7	$ 5.7
Accumulated Amortization		(5.7)	(5.7)
Net		$ 0.0	$ 0.0
Trade names
Other Intangible Assets
Weighted-Average Useful Life in Years	13 years 8 months 12 days	13 years 8 months 12 days	13 years 8 months 12 days
Gross Carrying Amount	$ 10.7	$ 10.7	$ 10.7
Accumulated Amortization	(6.9)	(4.0)	(3.9)
Net	$ 3.8	$ 6.7	$ 6.8