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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, 2018 | Jan. 31, 2017 | Jan. 31, 2016
Finite-Lived Intangible Assets, Net [Abstract] |  |  |
Amortization of intangible assets | $ 20.2 | $ 31.8 | $ 33.2
Developed technologies, at cost | 578.5 | 583.6 |
Customer relationships, trade names, patents, and user lists, at cost | 372.5 | 375.9 |
Other intangible assets, at cost | 951.0 | 959.5 |
Less: Accumulated amortization | (895.8) | (862.0) |
Other intangible assets, net | $ 55.2 | 97.5 |
Weighted average useful life | 4 years 10 months 24 days |  |
Customer Relationships, Trade Names, Patents, and User List |  |  |
Finite-Lived Intangible Assets, Net [Abstract] |  |  |
Amortization of intangible assets | $ 36.6 | $ 72.2 | $ 82.6
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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- Definition 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. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 30 -Section 50 -Paragraph 1 -Subparagraph (a)(3) -URI http://asc.fasb.org/extlink&oid=66006027&loc=d3e16265-109275 + Details
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- Definition 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. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 30 -Section 45 -Paragraph 2 -URI http://asc.fasb.org/extlink&oid=6388964&loc=d3e16225-109274 Reference 2: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 230 -SubTopic 10 -Section 45 -Paragraph 28 -Subparagraph (b) -URI http://asc.fasb.org/extlink&oid=98514028&loc=d3e3602-108585 Reference 3: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 30 -Section 50 -Paragraph 2 -Subparagraph (a)(2) -URI http://asc.fasb.org/extlink&oid=66006027&loc=d3e16323-109275 + Details
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