Intangible Assets, Net (Details) - USD ($) $ in Millions	Oct. 31, 2021	Jan. 31, 2021
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 1,612.6	$ 1,247.2
Accumulated Amortization	(1,114.4)	(1,047.9)
Total intangible assets	498.2	199.3
Customer relationships
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	666.7	437.3
Accumulated Amortization	(367.8)	(345.1)
Total intangible assets	298.9	92.2
Developed technologies
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	829.7	698.4
Accumulated Amortization	(647.6)	(609.8)
Total intangible assets	182.1	88.6
Trade names and patents
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	115.9	111.5
Accumulated Amortization	(98.7)	(93.0)
Total intangible assets	17.2	$ 18.5
Other
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	0.3
Accumulated Amortization	(0.3)
Total intangible assets	$ 0.0