Intangible Assets, Net (Details) - USD ($) $ in Millions	Jul. 31, 2021	Jan. 31, 2021
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 1,602.0	$ 1,247.2
Accumulated Amortization	(1,090.7)	(1,047.9)
Total intangible assets	511.3	199.3
Customer relationships
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	668.9	437.3
Accumulated Amortization	(360.3)	(345.1)
Total intangible assets	308.6	92.2
Developed technologies
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	817.1	698.4
Accumulated Amortization	(633.4)	(609.8)
Total intangible assets	183.7	88.6
Trade names and patents
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	116.0	111.5
Accumulated Amortization	(97.0)	(93.0)
Total intangible assets	$ 19.0	$ 18.5