Equity Compensation - Stock Based Compensation Expense (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Jul. 31, 2021	Jul. 31, 2020	Jul. 31, 2021	Jul. 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	$ 153.2	$ 95.9	$ 269.0	$ 194.1
Tax benefit	(4.1)	(0.2)	(20.1)	(0.3)
Stock-based compensation expense related to stock awards and ESPP purchases, net of tax	149.1	95.7	248.9	193.8
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	7.5	4.2	12.8	7.9
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	2.4	1.5	4.2	3.0
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	64.5	43.4	112.8	84.1
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	60.1	35.3	106.8	68.2
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	$ 18.7	$ 11.5	$ 32.4	$ 30.9