Business and Summary of Significant Accounting Policies - Stock Based Compensation Expense (Details) $ in Millions	12 Months Ended
	Jan. 31, 2019 USD ($) period	Jan. 31, 2018 USD ($)	Jan. 31, 2017 USD ($)
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense related to stock awards and Employee Qualified Stock Purchase Plan (ESPP) purchases	$ 249.5	$ 261.4	$ 221.8
Tax benefit	(2.6)	(2.6)	(2.6)
Stock-based compensation expense related to stock awards and ESPP purchases, net	246.9	258.8	219.2
Market capitalization level of peer group	$ 2,000.0
Number of exercise periods | period	4
Term of exercise period	6 months
Term of offering period	24 months
Dividend yield	0.00%
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 Employee Qualified Stock Purchase Plan (ESPP) purchases	$ 13.2	11.9	8.6
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 Employee Qualified Stock Purchase Plan (ESPP) purchases	4.3	4.0	5.5
Marketing and sales
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense related to stock awards and Employee Qualified Stock Purchase Plan (ESPP) purchases	109.4	107.3	94.1
Research and development
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense related to stock awards and Employee Qualified Stock Purchase Plan (ESPP) purchases	82.6	82.9	81.3
General and administrative
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense related to stock awards and Employee Qualified Stock Purchase Plan (ESPP) purchases	$ 40.0	$ 55.3	$ 32.3