Stock-based Compensation Expense (Stock Based Compensation Expense) (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Jul. 31, 2019	Jul. 31, 2018	Jul. 31, 2019	Jul. 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	$ 88.2	$ 56.9	$ 163.4	$ 111.3
Tax benefit	(0.1)	(0.2)	(0.3)	(0.6)
Stock-based compensation expense related to stock awards and ESPP purchases, net of tax	88.1	56.7	163.1	110.7
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	3.4	3.1	7.0	5.8
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	1.4	0.9	2.7	1.7
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	36.0	25.9	68.5	49.9
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	18.7	57.5	36.5
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	$ 16.6	$ 8.3	$ 27.7	$ 17.4