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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, 2016 | Jan. 31, 2015 | Jan. 31, 2014
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill before accumulated impairments |  | $ 1,605.4 |  | $ 1,159.1 |  |  |
Accumulated impairment losses |  | (149.2) |  | (149.2) |  |  |
Goodwill, beginning of period |  | 1,456.2 |  | 1,009.9 |  |  |
Effect of foreign currency translation, purchase accounting adjustments, and other |  | (18.5) |  | (54.9) |  |  |
Goodwill before accumulated impairments |  | 1,684.2 |  | 1,605.4 |  | $ 1,159.1 |
Accumulated impairment losses |  | (149.2) |  | (149.2) |  | (149.2) |
Goodwill, end of period |  | 1,535.0 |  | 1,456.2 |  | 1,009.9 |
Impairment loss |  | 0.0 |  | 0.0 |  | 0.0 |
netfabb |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  | 32.8 |  |  |  |  |
Goodwill, end of period |  | 32.8 |  |  |  |  |
Delcam plc |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill, beginning of period |  | 190.4 |  |  |  |  |
Goodwill acquired during period |  |  |  | 196.1 |  |  |
Goodwill, end of period |  |  |  | 190.4 |  |  |
Within Technologies Limited |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill, beginning of period |  | 80.6 |  |  |  |  |
Goodwill acquired during period |  |  |  | 80.6 |  |  |
Goodwill, end of period |  |  |  | 80.6 |  |  |
Shotgun Software Inc. |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill, beginning of period |  | 43.2 |  |  |  |  |
Goodwill acquired during period |  |  |  | 43.2 |  |  |
Goodwill, end of period |  |  |  | 43.2 |  |  |
Goodwill acquired from other acquisitions |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  | 64.5 |  | 181.3 |  |  |
Platform Solutions and Emerging Business |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill before accumulated impairments |  | 327.5 |  | 142.3 |  |  |
Accumulated impairment losses |  | 0.0 |  | 0.0 |  |  |
Goodwill, beginning of period |  | 327.5 |  | 142.3 |  |  |
Effect of foreign currency translation, purchase accounting adjustments, and other |  | (6.8) |  | (13.2) |  |  |
Goodwill before accumulated impairments |  | 386.9 |  | 327.5 |  | 142.3 |
Accumulated impairment losses |  | 0.0 |  | 0.0 |  | 0.0 |
Goodwill, end of period |  | 386.9 |  | 327.5 |  | 142.3 |
Platform Solutions and Emerging Business | netfabb |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  | 32.8 |  |  |  |  |
Platform Solutions and Emerging Business | Delcam plc |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  |  |  | 0.0 |  |  |
Platform Solutions and Emerging Business | Within Technologies Limited |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  |  |  | 80.6 |  |  |
Platform Solutions and Emerging Business | Shotgun Software Inc. |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  |  |  | 0.0 |  |  |
Platform Solutions and Emerging Business | Goodwill acquired from other acquisitions |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  | 33.4 |  | 117.8 |  |  |
Architecture, Engineering, and Construction |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill before accumulated impairments |  | 427.0 |  | 415.2 |  |  |
Accumulated impairment losses |  | 0.0 |  | 0.0 |  |  |
Goodwill, beginning of period |  | 427.0 |  | 415.2 |  |  |
Effect of foreign currency translation, purchase accounting adjustments, and other |  | (3.9) |  | (16.3) |  |  |
Goodwill before accumulated impairments |  | 427.2 |  | 427.0 |  | 415.2 |
Accumulated impairment losses |  | 0.0 |  | 0.0 |  | 0.0 |
Goodwill, end of period |  | 427.2 |  | 427.0 |  | 415.2 |
Architecture, Engineering, and Construction | netfabb |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  | 0.0 |  |  |  |  |
Architecture, Engineering, and Construction | Delcam plc |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  |  |  | 0.0 |  |  |
Architecture, Engineering, and Construction | Within Technologies Limited |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  |  |  | 0.0 |  |  |
Architecture, Engineering, and Construction | Shotgun Software Inc. |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  |  |  | 0.0 |  |  |
Architecture, Engineering, and Construction | Goodwill acquired from other acquisitions |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  | 4.1 |  | 28.1 |  |  |
Manufacturing |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill before accumulated impairments |  | 422.7 |  | 411.6 |  |  |
Accumulated impairment losses |  | 0.0 |  | 0.0 |  |  |
Goodwill, beginning of period |  | 422.7 |  | 411.6 |  |  |
Effect of foreign currency translation, purchase accounting adjustments, and other |  | (1.9) |  | (9.0) |  |  |
Goodwill before accumulated impairments |  | 437.4 |  | 422.7 |  | 411.6 |
Accumulated impairment losses |  | 0.0 |  | 0.0 |  | 0.0 |
Goodwill, end of period |  | 437.4 |  | 422.7 |  | 411.6 |
Manufacturing | netfabb |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  | 0.0 |  |  |  |  |
Manufacturing | Delcam plc |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  |  |  | 0.0 |  |  |
Manufacturing | Within Technologies Limited |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  |  |  | 0.0 |  |  |
Manufacturing | Shotgun Software Inc. |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  |  |  | 0.0 |  |  |
Manufacturing | Goodwill acquired from other acquisitions |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  | 16.6 |  | 20.1 |  |  |
Media and Entertainment |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill before accumulated impairments |  | 245.2 |  | 190.0 |  |  |
Accumulated impairment losses |  | (149.2) |  | (149.2) |  |  |
Goodwill, beginning of period |  | 96.0 |  | 40.8 |  |  |
Effect of foreign currency translation, purchase accounting adjustments, and other |  | 0.6 |  | (3.3) |  |  |
Goodwill before accumulated impairments |  | 256.2 |  | 245.2 |  | 190.0 |
Accumulated impairment losses |  | (149.2) |  | (149.2) |  | (149.2) |
Goodwill, end of period |  | 107.0 |  | 96.0 |  | 40.8 |
Media and Entertainment | netfabb |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  | 0.0 |  |  |  |  |
Media and Entertainment | Delcam plc |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  |  |  | 0.0 |  |  |
Media and Entertainment | Within Technologies Limited |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  |  |  | 0.0 |  |  |
Media and Entertainment | Shotgun Software Inc. |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  |  |  | 43.2 |  |  |
Media and Entertainment | Goodwill acquired from other acquisitions |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  | $ 10.4 |  | 15.3 |  |  |
Delcam plc |  |  |  |  |  |  |
Goodwill [Line Items] |  |  |  |  |  |  |
Reporting Unit, Percentage of Fair Value in Excess of Carrying Amount |  | 16.00% |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill before accumulated impairments |  | $ 183.0 | [1] | 0.0 | [2] |  |
Accumulated impairment losses |  | 0.0 | [1] | 0.0 | [2] |  |
Goodwill, beginning of period |  | 183.0 | [1] | 0.0 | [2] |  |
Effect of foreign currency translation, purchase accounting adjustments, and other |  | (6.5) | [1] | (13.1) | [2] |  |
Goodwill before accumulated impairments |  | 176.5 | [1] | 183.0 | [1] | 0.0 | [2]
Accumulated impairment losses |  | 0.0 | [1] | 0.0 | [1] | 0.0 | [2]
Goodwill, end of period |  | 176.5 | [1] | 183.0 | [1] | $ 0.0 | [2]
Delcam plc | netfabb |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period | [1] | 0.0 |  |  |  |  |
Delcam plc | Delcam plc |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period | [2] |  |  | $ 196.1 |  |  |
Delcam plc | Within Technologies Limited |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period | [2] |  |  |  |  |  |
Delcam plc | Shotgun Software Inc. |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period | [2] |  |  |  |  |  |
Delcam plc | Goodwill acquired from other acquisitions |  |  |  |  |  |  |
Goodwill [Roll Forward] |  |  |  |  |  |  |
Goodwill acquired during period |  | $ 0.0 | [1] |  | [2] |  |
[1] | Delcam is a separate reporting unit within the Manufacturing ("MFG") reporting segment.
[2] | Delcam is a separate reporting unit within the Manufacturing ("MFG") reporting segment.

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