Business and Summary of Significant Accounting Policies - Other Intangible Assets and Related Accumulated Amortization (Details) - USD ($) $ in Millions	12 Months Ended
Jan. 31, 2020	Jan. 31, 2019	Jan. 31, 2018
Finite-Lived Intangible Assets, Net [Abstract]
Amortization of intangible assets	$ 38.9	$ 18.0	$ 20.2
Developed technologies, at cost	647.1	670.2
Customer relationships, trade names, patents, and user lists, at cost	532.2	533.1
Other intangible assets, at cost	1,179.3	1,203.3
Less: accumulated amortization	(972.2)	(922.5)
Other intangible assets, net	$ 207.1	280.8
Weighted average useful life	5 years 6 months
Customer Relationships, Trade Names, Patents, and User List
Finite-Lived Intangible Assets, Net [Abstract]
Amortization of intangible assets	$ 73.7	$ 33.5	$ 36.6
Customer Relationships, Trade Names, Patents, and User List \| Minimum
Finite-Lived Intangible Assets [Line Items]
Finite-lived intangible asset, useful life	2 years
Customer Relationships, Trade Names, Patents, and User List \| Maximum
Finite-Lived Intangible Assets [Line Items]
Finite-lived intangible asset, useful life	10 years

Finite Lived Purchased Technologies Gross

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Weighted average amortization period of finite-lived intangible assets acquired either individually or as part of a group of assets, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

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The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method.

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Useful life of finite-lived intangible assets, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

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Accumulated amount of amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

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Amount before amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

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Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

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Amount after amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

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Amount before accumulated amortization of finite-lived intangible assets classified as other.

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