Goodwill Changes in the Carrying Amount of Goodwill (Details) - USD ($) $ in Millions	6 Months Ended
	Jul. 31, 2016	Jan. 31, 2016
Goodwill [Roll Forward]
Goodwill before accumulated impairment losses beginning balance	$ 1,684.2
Accumulated impairment losses	(149.2)	$ (149.2)
Goodwill	1,597.4	1,535.0
Effect of foreign currency translation, purchase accounting adjustments, and other	(0.4)
Goodwill before accumulated impairment losses ending balance	1,746.6
Platform Solutions and Emerging Business
Goodwill [Roll Forward]
Goodwill before accumulated impairment losses beginning balance	386.9
Accumulated impairment losses	0.0	0.0
Goodwill	405.0	386.9
Effect of foreign currency translation, purchase accounting adjustments, and other	0.7
Goodwill before accumulated impairment losses ending balance	405.0
Architecture, Engineering and Construction
Goodwill [Roll Forward]
Goodwill before accumulated impairment losses beginning balance	427.2
Accumulated impairment losses	0.0	0.0
Goodwill	429.2	427.2
Effect of foreign currency translation, purchase accounting adjustments, and other	2.0
Goodwill before accumulated impairment losses ending balance	429.2
Manufacturing
Goodwill [Roll Forward]
Goodwill before accumulated impairment losses beginning balance	613.9
Accumulated impairment losses	0.0	0.0
Goodwill	624.0	613.9
Effect of foreign currency translation, purchase accounting adjustments, and other	(3.5)
Goodwill before accumulated impairment losses ending balance	624.0
Media and Entertainment
Goodwill [Roll Forward]
Goodwill before accumulated impairment losses beginning balance	256.2
Accumulated impairment losses	(149.2)	(149.2)
Goodwill	139.2	$ 107.0
Effect of foreign currency translation, purchase accounting adjustments, and other	0.4
Goodwill before accumulated impairment losses ending balance	288.4
Other
Goodwill [Roll Forward]
Goodwill	62.8
Addition arising from other acquisitions	62.8
Other | Platform Solutions and Emerging Business
Goodwill [Roll Forward]
Addition arising from other acquisitions	17.4
Other | Architecture, Engineering and Construction
Goodwill [Roll Forward]
Addition arising from other acquisitions	0.0
Other | Manufacturing
Goodwill [Roll Forward]
Addition arising from other acquisitions	13.6
Other | Media and Entertainment
Goodwill [Roll Forward]
Addition arising from other acquisitions	$ 31.8