Stock-based Compensation Expense (Stock Based Compensation Expense) (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Oct. 31, 2019	Oct. 31, 2018	Oct. 31, 2019	Oct. 31, 2018
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense related to stock awards and ESPP purchases	$ 94.0	$ 64.2	$ 257.4	$ 175.5
Tax benefit	(0.5)	(1.6)	(0.8)	(2.2)
Stock-based compensation expense related to stock awards and ESPP purchases, net of tax	93.5	62.6	256.6	173.3
Cost of subscription and maintenance 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	3.6	10.1	9.4
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	1.6	1.3	4.3	3.0
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	38.7	27.8	107.2	77.7
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	30.8	20.6	88.3	57.1
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	$ 19.8	$ 10.9	$ 47.5	$ 28.3