Business and Summary of Significant Accounting Policies - Changes In the Carrying Amount of Goodwill (Details) - USD ($) $ in Millions		12 Months Ended
		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.