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Business and Summary of Significant Accounting Policies - Other Intangible Assets and Related Accumulated Amortization (Details) - USD ($) $ in Millions | 12 Months Ended
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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 |  |

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