Business and Summary of Significant Accounting Policies - Intangible Assets and Related Accumulated Amortization (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 31, 2022	Jan. 31, 2021	Jan. 31, 2020
Finite-Lived Intangible Assets, Net [Abstract]
Amortization of intangible assets	$ 40.7	$ 37.5	$ 38.9
Gross Carrying Amount	1,629.7	1,247.2
Accumulated Amortization	(1,135.9)	(1,047.9)
Total	$ 493.8	199.3
Weighted average useful life	8 years 8 months 1 day
Customer Relationships, Trade Names, Patents, and User List
Finite-Lived Intangible Assets, Net [Abstract]
Amortization of intangible assets	$ 93.5	69.9	$ 73.7
Customer relationships
Finite-Lived Intangible Assets, Net [Abstract]
Gross Carrying Amount	666.7	437.3
Accumulated Amortization	(374.5)	(345.1)
Total	292.2	92.2
Developed technologies
Finite-Lived Intangible Assets, Net [Abstract]
Gross Carrying Amount	846.6	698.4
Accumulated Amortization	(660.9)	(609.8)
Total	185.7	88.6
Trade names and patents
Finite-Lived Intangible Assets, Net [Abstract]
Gross Carrying Amount	116.1	111.5
Accumulated Amortization	(100.2)	(93.0)
Total	15.9	$ 18.5
Other
Finite-Lived Intangible Assets, Net [Abstract]
Gross Carrying Amount	0.3
Accumulated Amortization	(0.3)
Total	$ 0.0
Minimum | Customer Relationships, Trade Names, Patents, and User List
Finite-Lived Intangible Assets [Line Items]
Finite-lived intangible asset, useful life	1 year
Maximum | Customer Relationships, Trade Names, Patents, and User List
Finite-Lived Intangible Assets [Line Items]
Finite-lived intangible asset, useful life	15 years