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Acquisitions - Additional Information (Details) - USD ($) $ in Millions |  | 12 Months Ended |
--- | --- | --- | ---
Nov. 12, 2015 | Jan. 31, 2017 | Jan. 31, 2016
Business Acquisition [Line Items] |  |  |
Cost Method Investments |  | $ 117.2 | $ 104.3
Goodwill |  | 1,561.1 | 1,535.0
netfabb |  |  |
Business Acquisition [Line Items] |  |  |
Payments to acquire business | $ 42.5 |  |
Goodwill |  |  | 36.1
Cash consideration transferred for acqusitions and business combinations |  |  | 42.5
Delcam plc |  |  |
Business Acquisition [Line Items] |  |  |
Goodwill |  | 29.8 |
Series of Individually Immaterial Business Acquisitions |  |  |
Business Acquisition [Line Items] |  |  |
Payments to acquire business |  | 87.0 |
Goodwill |  | 62.8 | 63.7
Cash consideration transferred for acqusitions and business combinations |  | $ 87.0 | $ 106.8
FIT AG |  |  |
Business Acquisition [Line Items] |  |  |
Cost Method Investments | $ 27.4 |  |

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- Definition Amount recognized for assets, including goodwill, in excess of (less than) the aggregate liabilities assumed. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 805 -SubTopic 20 -Section 50 -Paragraph 1 -Subparagraph (c) -URI http://asc.fasb.org/extlink&oid=73530397&loc=d3e4845-128472 + Details
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