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