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

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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://fasb.org/us-gaap/role/ref/legacyRef -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://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 230 -SubTopic 10 -Section 45 -Paragraph 28 -Subparagraph (b) -URI http://asc.fasb.org/extlink&oid=123570139&loc=d3e3602-108585 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -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 Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef -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 + Details
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