Amount of stockholders' equity (deficit), net of receivables from officers, directors, owners, and affiliates of the entity, attributable to both the parent and noncontrolling interests. Amount excludes temporary equity. Alternate caption for the concept is permanent equity.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 810
-SubTopic 10
-Section 45
-Paragraph 16
-URI http://asc.fasb.org/extlink&oid=108774443&loc=SL4568740-111683

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 810
-SubTopic 10
-Section 55
-Paragraph 4I
-URI http://asc.fasb.org/extlink&oid=84234705&loc=SL4590271-111686

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 810
-SubTopic 10
-Section 45
-Paragraph 15
-URI http://asc.fasb.org/extlink&oid=108774443&loc=SL4568447-111683

Name:	us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

Stockholders' Equity - Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Millions	Apr. 30, 2019	Jan. 31, 2019	Apr. 30, 2018	Jan. 31, 2018
Accumulated Other Comprehensive Income (Loss) [Line Items]
Stockholders' equity	$ 3,172.0	$ 3,130.9	$ 3,268.6	$ 3,248.2
Foreign currency translation adjustments
Accumulated Other Comprehensive Income (Loss) [Line Items]
Stockholders' equity	(132.2)	(108.2)	(73.0)
Deferred hedging loss
Accumulated Other Comprehensive Income (Loss) [Line Items]
Stockholders' equity	(20.5)	(24.5)	(30.2)
Accumulated Defined Benefit Plans Adjustment, Net Gain (Loss) Attributable to Parent [Member]
Accumulated Other Comprehensive Income (Loss) [Line Items]
Stockholders' equity	(91.3)	(72.1)	(62.9)
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income (Loss) [Line Items]
Stockholders' equity	$ (244.0)	$ (204.8)	$ (166.1)	$ (138.0)