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Business and Summary of Significant Accounting Policies - Changes In the Carrying Amount of Goodwill (Details) - USD ($) $ in Millions | 12 Months Ended
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Jan. 31, 2018 | Jan. 31, 2017 | Jan. 31, 2016
Accounting Policies [Abstract] |  |  |
Impairment of goodwill | $ 0.0 | $ 0.0 | $ 0.0
Goodwill, beginning of period, gross |  | 1,710.3 | 1,684.2
Less: accumulated impairment losses, beginning of the year |  | (149.2) | $ (149.2)
Additions arising from acquisitions during the year | 0.0 | 62.8 |
Effect of foreign currency translation, measurement period adjustments, and other (1) | 59.1 | (36.7) |
Goodwill, end of period, net | $ 1,620.2 | $ 1,561.1 |

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- Definition Amount after accumulated impairment loss of an asset representing future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 20 -Section 50 -Paragraph 1 -Subparagraph (a) -URI http://asc.fasb.org/extlink&oid=35741047&loc=d3e13816-109267 Reference 2: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 20 -Section 45 -Paragraph 1 -URI http://asc.fasb.org/extlink&oid=6388280&loc=d3e13770-109266 Reference 3: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 20 -Section 45 -Paragraph 5 -URI http://asc.fasb.org/extlink&oid=77989000&loc=SL49117168-202975 + Details
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- Definition Amount of increase in asset representing future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized resulting from a business combination. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 20 -Section 50 -Paragraph 1 -Subparagraph (b) -URI http://asc.fasb.org/extlink&oid=35741047&loc=d3e13816-109267 + Details
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