Stock-based Compensation Expense (Stock Based Compensation Expense) (Details) - USD ($) $ in Millions	3 Months Ended	9 Months Ended
Oct. 31, 2018	Oct. 31, 2017	Oct. 31, 2018	Oct. 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	$ 64.2	$ 65.1	$ 175.5	$ 199.5
Tax benefit	(1.6)	(1.3)	(2.2)	(1.6)
Stock-based compensation expense related to stock awards and ESPP purchases, net of tax	62.6	63.8	173.3	197.9
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	3.6	2.8	9.4	8.5
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	1.3	1.0	3.0	3.1
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	27.8	27.7	77.7	80.1
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	20.6	20.1	57.1	61.7
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	$ 10.9	$ 13.5	$ 28.3	$ 46.1

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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