Stock-based Compensation Expense (Stock Based Compensation Expense) (Details) - USD ($) $ in Millions	3 Months Ended
	Apr. 30, 2020	Apr. 30, 2019
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense related to stock awards and ESPP purchases	$ 98.2	$ 75.2
Tax benefit	(0.1)	(0.2)
Stock-based compensation expense related to stock awards and ESPP purchases, net of tax	98.1	75.0
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	3.7	3.6
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	1.3
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	40.7	32.5
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	32.9	26.7
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	$ 19.4	$ 11.1