Stock-based Compensation Expense Stock Based Compensation Expense (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Oct. 31, 2017	Oct. 31, 2016	Oct. 31, 2017	Oct. 31, 2016
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense related to stock awards and ESPP purchases	$ 65.1	$ 56.6	$ 199.5	$ 162.5
Tax benefit	(1.3)	0.0	(1.6)	0.0
Stock-based compensation expense related to stock awards and ESPP purchases, net of tax	63.8	56.6	197.9	162.5
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	2.8	2.2	8.5	6.2
Cost of license and 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	1.0	1.3	3.1	4.1
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	27.7	24.2	80.1	69.0
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	20.1	20.9	61.7	60.0
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	$ 13.5	$ 8.0	$ 46.1	$ 23.2