Stock-based Compensation Expense (Stock Based Compensation Expense) (Details) - USD ($) $ in Millions	3 Months Ended	6 Months Ended
Jul. 31, 2018	Jul. 31, 2017	Jul. 31, 2018	Jul. 31, 2017
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense related to stock awards and ESPP purchases	$ 56.9	$ 67.6	$ 111.3	$ 134.4
Tax benefit	(0.2)	(0.3)	(0.6)	(0.3)
Stock-based compensation expense related to stock awards and ESPP purchases, net of tax	56.7	67.3	110.7	134.1
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	3.1	2.9	5.8	5.7
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	0.9	1.0	1.7	2.1
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	25.9	26.0	49.9	52.4
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	18.7	20.4	36.5	41.6
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	$ 8.3	$ 17.3	$ 17.4	$ 32.6

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

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