Stock-based Compensation Expense (Stock Based Compensation Expense) (Details) - USD ($) $ in Millions	3 Months Ended
Apr. 30, 2018	Apr. 30, 2017
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense related to stock awards and ESPP purchases	$ 54.4	$ 66.8
Tax benefit	(0.4)	0.0
Stock-based compensation expense related to stock awards and ESPP purchases, net of tax	54.0	66.8
Cost of maintenance and subscription revenue
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense related to stock awards and ESPP purchases	2.7	2.8
Cost of other revenue
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense related to stock awards and ESPP purchases	0.8	1.1
Marketing and sales
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense related to stock awards and ESPP purchases	24.0	26.4
Research and development
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense related to stock awards and ESPP purchases	17.8	21.2
General and administrative
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense related to stock awards and ESPP purchases	$ 9.1	$ 15.3

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.

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 14.F)
-URI http://asc.fasb.org/extlink&oid=27013229&loc=d3e301413-122809

Reference 2: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=96867065&loc=d3e5047-113901

Reference 3: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (h)(1)(i)
-URI http://asc.fasb.org/extlink&oid=96867065&loc=d3e5070-113901

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The amount of expense, net of income tax, 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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The total recognized tax benefit related to compensation cost for equity-based payment arrangements recognized in income during the period.

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Reference 1: http://www.xbrl.org/2003/role/presentationRef
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-Name Accounting Standards Codification
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