Stock-based Compensation Expense (Stock Based Compensation Expense) (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Jul. 31, 2020	Jul. 31, 2019	Jul. 31, 2020	Jul. 31, 2019
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense related to stock awards and ESPP purchases	$ 95.9	$ 88.2	$ 194.1	$ 163.4
Tax benefit	(0.2)	(0.1)	(0.3)	(0.3)
Stock-based compensation expense related to stock awards and ESPP purchases, net of tax	95.7	88.1	193.8	163.1
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	4.2	3.4	7.9	7.0
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	1.5	1.4	3.0	2.7
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	43.4	36.0	84.1	68.5
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	35.3	30.8	68.2	57.5
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	$ 11.5	$ 16.6	$ 30.9	$ 27.7