Business and Summary of Significant Accounting Policies - Changes In the Carrying Amount of Goodwill (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 31, 2018	Jan. 31, 2017	Jan. 31, 2016
Accounting Policies [Abstract]
Impairment of goodwill	$ 0.0	$ 0.0	$ 0.0
Goodwill, beginning of period, gross		1,710.3	1,684.2
Less: accumulated impairment losses, beginning of the year		(149.2)	$ (149.2)
Additions arising from acquisitions during the year	0.0	62.8
Effect of foreign currency translation, measurement period adjustments, and other (1)	59.1	(36.7)
Goodwill, end of period, net	$ 1,620.2	$ 1,561.1