Retirement Benefit Plans - Funded Status (Details) - USD ($) $ in Millions	12 Months Ended
Jan. 31, 2018	Jan. 31, 2017	Jan. 31, 2016
Defined Benefit Plan, Change in Benefit Obligation [Roll Forward]
Beginning projected benefit obligation	$ 146.4	$ 145.2
Service cost	5.2	5.6	$ 5.7
Interest cost	2.7	3.0	3.3
Actuarial (gain) loss	(2.8)	7.1
Benefits paid	(3.3)	(2.6)
Foreign currency exchange rate changes	13.9	(9.5)
Curtailments and settlements	(8.2)	(6.8)
Contributions by plan participants	4.0	4.4
Plan amendment	0.2	0.0
Ending projected benefit obligation	158.1	146.4	145.2
Defined Benefit Plan, Change in Fair Value of Plan Assets [Roll Forward]
Beginning fair value of plan assets	107.4	101.4
Actual return on plan assets	3.8	4.2
Contributions paid by employer	6.5	15.3
Contributions paid by plan participants	4.0	4.4
Benefit payments	(3.3)	(2.6)
Curtailments and settlements	(8.0)	(6.8)
Foreign currency exchange rate changes	10.7	(8.5)
Ending fair value of plan assets	121.1	107.4	$ 101.4
Funded status	$ (37.0)	$ (39.0)

Defined Benefit Plan, Curtailments and Settlements, Benefit Obligation

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- Definition

Defined Benefit Plan, Curtailments and Settlements, Plan Assets

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No definition available.

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Amount of increase (decrease) in plan assets of defined benefit plan from actual return (loss) determined by change in fair value of plan assets adjusted for contributions, benefit payments, and other expenses.

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Amount of gain (loss) from change in actuarial assumptions which (increases) decreases benefit obligation of defined benefit plan. Assumptions include, but are not limited to, interest, mortality, employee turnover, salary, and temporary deviation from substantive plan.

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Amount of actuarial present value of benefits attributed to service rendered by employee for defined benefit plan.

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Amount of payment to participant of defined benefit plan which decreases benefit obligation. For pension plan, payment includes, but is not limited to, pension benefits and death benefits. For other postretirement plan, payment includes, but is not limited to, prescription drug benefits, health care benefits, life insurance benefits, and legal, educational and advisory services.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 715
-SubTopic 60
-Section 50
-Paragraph 4
-URI http://asc.fasb.org/extlink&oid=6414203&loc=d3e39716-114964

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-Publisher FASB
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-URI http://asc.fasb.org/extlink&oid=82843861&loc=d3e1928-114920

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- Definition

Amount of contributions received by defined benefit plan from participant which increase benefit obligation.

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- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

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No definition available.

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A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

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Amount of contribution received by defined benefit plan from employer which increases plan assets.

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Reference 1: http://www.xbrl.org/2003/role/presentationRef
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-Name Accounting Standards Codification
-Topic 715
-SubTopic 20
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Fair value of assets that have been segregated and restricted to provide pension or postretirement benefits. Assets include, but are not limited to, stocks, bonds, other investments, earnings from investments, and contributions by the employer and employees.

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Amount of foreign currency translation gain (loss) which (increases) decreases benefit obligation of defined benefit plan.

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- Definition

Amount of funded (unfunded) status of defined benefit plan, measured as difference between fair value of plan assets and benefit obligation. Includes, but is not limited to, overfunded (underfunded) status.

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Amount of cost recognized for passage of time related to defined benefit plan.

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Amount of increase (decrease) in benefit obligation of defined benefit plan from change in terms of existing plan or initiation of new plan.

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Amount of payment to participant under defined benefit plan which decreases plan assets. For pension plan, payment includes, but is not limited to, pension benefits and death benefits. For other postretirement plan, payment includes, but is not limited to, prescription drug benefits, health care benefits, life insurance benefits, and legal, educational and advisory services.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 715
-SubTopic 60
-Section 50
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-URI http://asc.fasb.org/extlink&oid=6414203&loc=d3e39716-114964

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Amount of contributions received by defined benefit plan from participant which increases plan assets.

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Amount of foreign currency translation gain (loss) which increases (decreases) plan assets of defined benefit plan.

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Amount of cost for actuarial present value of benefits attributed to service rendered by employee for defined benefit plan.

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