Stockholders' Equity - Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Millions	Jan. 31, 2019	Jan. 31, 2018	Jan. 31, 2017	Jan. 31, 2016
Accumulated Other Comprehensive Income (Loss) [Line Items]
Total stockholders' equity	$ 3,130.9	$ 3,248.2	$ 3,028.4	$ 2,929.5
Foreign currency translation adjustments
Accumulated Other Comprehensive Income (Loss) [Line Items]
Total stockholders' equity	(108.2)	(48.0)
Unrealized loss on marketable securities
Accumulated Other Comprehensive Income (Loss) [Line Items]
Total stockholders' equity	0.0	(1.8)
Deferred hedging loss
Accumulated Other Comprehensive Income (Loss) [Line Items]
Total stockholders' equity	(24.5)	(22.9)
Net unrealized loss on benefit plans
Accumulated Other Comprehensive Income (Loss) [Line Items]
Total stockholders' equity	(72.1)	(65.3)
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income (Loss) [Line Items]
Total stockholders' equity	$ (204.8)	$ (138.0)	$ (256.2)	$ (278.1)