Retirement Benefit Plans - Funded Status (Details) - USD ($) $ in Millions	12 Months Ended
Jan. 31, 2019	Jan. 31, 2018	Jan. 31, 2017
Defined Benefit Plan, Change in Benefit Obligation [Roll Forward]
Beginning projected benefit obligation	$ 158.1	$ 146.4
Service cost	4.1	5.2	$ 5.6
Interest cost	2.3	2.7	3.0
Actuarial (gain) loss	(4.3)	(2.8)
Benefits paid	(2.6)	(3.3)
Foreign currency exchange rate changes	(10.0)	13.9
Curtailments and settlements	(61.0)	(8.2)
Contributions by plan participants	5.0	4.0
Plan amendment	0.0	0.2
Ending projected benefit obligation	91.6	158.1	146.4
Defined Benefit Plan, Change in Fair Value of Plan Assets [Roll Forward]
Beginning fair value of plan assets	121.1	107.4
Actual return on plan assets	1.4	3.8
Contributions paid by employer	5.9	6.5
Contributions paid by plan participants	5.0	4.0
Benefit payments	(2.6)	(3.3)
Curtailments and settlements	(42.3)	(8.0)
Foreign currency exchange rate changes	(7.7)	10.7
Ending fair value of plan assets	80.8	121.1	$ 107.4
Funded status	$ (10.8)	$ (37.0)

Defined Benefit Plan, Curtailments and Settlements, Benefit Obligation

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Defined Benefit Plan, Curtailments and Settlements, Plan Assets

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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.

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

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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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Amount of asset segregated and restricted to provide benefit under defined benefit plan. Asset includes, but is not limited to, stock, bond, other investment, earning from investment, and contribution by employer and employee.

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

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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.

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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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