Goodwill and Other Intangible Assets, Net - Components of Other Intangible Assets (Details) - USD ($) $ in Millions	Feb. 02, 2024	Oct. 31, 2023	Feb. 03, 2023
Other Intangible Assets
Weighted-Average Useful Life in Years	13 years 7 months 6 days	13 years 3 months 18 days	13 years 4 months 24 days
Gross Carrying Amount	$ 458.6	$ 471.0	$ 465.0
Accumulated Amortization	(198.7)	(202.4)	(177.4)
Net	259.9	268.6	287.6
Indefinite-lived - trade names	271.6	271.5	289.5
Total other intangible assets, gross	730.2	742.5	754.5
Total other intangible assets, net	$ 531.5	$ 540.1	$ 577.1
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	$ 18.3
Accumulated Amortization	(16.2)	(16.0)	(15.5)
Net	$ 2.0	$ 2.2	$ 2.8
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	16 years
Gross Carrying Amount	$ 327.6	$ 327.5	$ 321.3
Accumulated Amortization	(112.7)	(106.7)	(89.9)
Net	$ 214.9	$ 220.8	$ 231.4
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	$ 102.1	$ 102.0	$ 102.1
Accumulated Amortization	(65.6)	(63.1)	(55.8)
Net	$ 36.5	$ 38.9	$ 46.3
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	(4.2)	(4.0)	(3.6)
Net	$ 6.5	$ 6.7	$ 7.1
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