Stock-based Compensation Expense (Stock Based Compensation Expense) (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Oct. 31, 2020	Oct. 31, 2019	Oct. 31, 2020	Oct. 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	$ 97.4	$ 94.0	$ 291.5	$ 257.4
Tax benefit	(2.0)	(0.5)	(2.3)	(0.8)
Stock-based compensation expense related to stock awards and ESPP purchases, net of tax	95.4	93.5	289.2	256.6
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	4.5	3.1	12.3	10.1
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	1.6	1.6	4.7	4.3
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	45.4	38.7	129.5	107.2
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	35.4	30.8	103.6	88.3
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	$ 10.5	$ 19.8	$ 41.4	$ 47.5