Equity Compensation - Stock Based Compensation Expense (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Oct. 31, 2021	Oct. 31, 2020	Oct. 31, 2021	Oct. 31, 2020
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense related to stock awards and ESPP purchases	$ 143.7	$ 97.4	$ 412.7	$ 291.5
Tax benefit	(26.3)	(2.0)	(46.4)	(2.3)
Stock-based compensation expense related to stock awards and ESPP purchases, net of tax	117.4	95.4	366.3	289.2
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	5.5	4.5	18.3	12.3
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	2.3	1.6	6.5	4.7
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	60.0	45.4	172.8	129.5
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	56.6	35.4	163.4	103.6
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	$ 19.3	$ 10.5	$ 51.7	$ 41.4