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Acquisitions - Additional Information (Details) $ in Millions |  |  | 12 Months Ended |  |  |
--- | --- | --- | --- | --- | --- | ---
Nov. 12, 2015 USD ($) | Jun. 27, 2014 USD ($) | Jan. 31, 2016 USD ($) | Jan. 31, 2015 USD ($) business_combination | May. 29, 2014 USD ($) | Feb. 06, 2014 USD ($) | Jan. 31, 2014 USD ($)
Business Acquisition [Line Items] |  |  |  |  |  |  |
Cost Method Investments |  |  | $ 104.3 | $ 52.6 |  |  |
Goodwill |  |  | 1,535.0 | 1,456.2 |  |  | $ 1,009.9
netfabb |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |
Payments to acquire business | $ 42.5 |  |  |  |  |  |
Goodwill, expected tax deductible amount | 29.8 |  |  |  |  |  |
Goodwill |  |  | 32.8 |  |  |  |
Shotgun Software Inc. |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |
Payments to acquire business |  | $ 51.2 |  |  |  |  |
Fair value of original convertible debt investment |  | $ 3.3 |  |  |  |  |
Goodwill |  |  |  | 43.2 |  |  |
Within Technologies Limited |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |
Goodwill |  |  |  | 80.6 | $ 78.9 |  |
Delcam plc |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |
Goodwill |  |  |  | 190.4 |  | $ 166.0 |
Series of Individually Immaterial Business Acquisitions |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |
Payments to acquire business |  |  | 106.8 | 234.5 |  |  |
Goodwill |  |  | $ 64.5 | $ 180.6 |  |  |
Number of Businesses Acquired | business_combination |  |  |  | 21 |  |  |
FIT AG |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |
Cost Method Investments | $ 27.4 |  |  |  |  |  |

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