Stock-based Compensation Expense (Additional Information) (Details) $ in Millions	3 Months Ended
Apr. 30, 2018 USD ($) period shares	Apr. 30, 2017 USD ($)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Allocated share-based compensation expense	$ 54.4	$ 66.8
Acceleration of eligible stock awards		3.2
Market capitalization	2,000.0
Restricted Stock Units (RSUs) and Performance Shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Awards vested in period, fair value	$ 96.2	76.9
Awards granted in period (shares) \| shares	391,900
Restricted Stock Units (RSUs)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Awards granted in period (shares) \| shares	200,000
Allocated share-based compensation expense	$ 41.7	50.0
Performance Stock Unit
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Awards granted in period (shares) \| shares	200,000
Allocated share-based compensation expense	$ 6.5	10.9
Acceleration of eligible stock awards		$ 4.6
Award vesting period	3 years
Employee Qualified Stock Purchase Plan 1998 ESP Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Employee stock purchase plan maximum percentage of compensation to purchase shares by eligible participants	15.00%
Employee stock purchase plan minimum percentage of common stock fair value defined to purchase shares by eligible participants	85.00%
Employee stock purchase plan, number of exercise periods \| period	4
Employee stock purchase plan, term of exercise period	6 months
Employee stock purchase plan, term of offering period	24 months
Share-based Compensation Award, Tranche One \| Performance Stock Unit
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
PSU annual vesting percentage	33.33%
Share-based Compensation Award, Tranche Two \| Performance Stock Unit
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
PSU annual vesting percentage	33.33%
Share-based Compensation Award, Tranche Three \| Performance Stock Unit
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
PSU annual vesting percentage	33.33%

Employee Stock Purchase Plan, Maximum Percentage of Compensation to Purchase Shares By Eligible Participants

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Employee Stock Purchase Plan, Minimum Percentage of Common Stock Fair Value Defined to Purchase Shares By Eligible Participants

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Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Expected Volatility, Market Capitalization

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Represents the expense recognized during the period arising from equity-based compensation arrangements (for example, shares of stock, unit, stock options or other equity instruments) with employees, directors and certain consultants qualifying for treatment as employees.

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Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
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Additional share-based compensation cost recognized as a result of an occurrence of an event that accelerates its recognition.

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Period which an employee's right to exercise an award is no longer contingent on satisfaction of either a service condition, market condition or a performance condition, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

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The number of grants made during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).

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Fair value of share-based awards for which the grantee gained the right by satisfying service and performance requirements, to receive or retain shares or units, other instruments, or cash.

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Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

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Percentage of vesting of share-based compensation awards.

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