Equity Compensation - Stock Based Compensation Expense (Details) - USD ($) $ in Millions	3 Months Ended
	Apr. 30, 2021	Apr. 30, 2020
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense related to stock awards and ESPP purchases	$ 115.8	$ 98.2
Tax benefit	(16.0)	(0.1)
Stock-based compensation expense related to stock awards and ESPP purchases, net of tax	99.8	98.1
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	5.3	3.7
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	1.8	1.5
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	48.3	40.7
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	46.7	32.9
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	$ 13.7	$ 19.4