Business and Summary of Significant Accounting Policies - Stock Based Compensation Expense (Details) $ in Millions	12 Months Ended
Jan. 31, 2018 USD ($) period	Jan. 31, 2017 USD ($)	Jan. 31, 2016 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	$ 261.4	$ 221.8	$ 197.2
Tax benefit	(2.6)	(2.6)	(1.6)
Stock-based compensation expense related to stock awards and ESPP purchases, net	258.8	219.2	195.6
Market capitalization level of peer group	2,000.0
Cost of maintenance and subscription 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	11.9	8.6	5.8
Cost of license and 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	4.0	5.5	6.0
Marketing and sales
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense related to stock awards and Employee Qualified Stock Purchase Plan (ESPP) purchases	107.3	94.1	85.2
Research and development
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Stock-based compensation expense related to stock awards and Employee Qualified Stock Purchase Plan (ESPP) purchases	82.9	81.3	70.4
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	$ 55.3	$ 32.3	$ 29.8
ESP Plan
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Number of exercise periods \| period	4
Term of exercise period	6 months
Term of offering period	24 months

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Market Capitalization Level of Peer Group

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Represents the expense recognized during the period arising from equity-based compensation arrangements (for example, shares of stock, unit, stock options or other equity instruments) with employees, directors and certain consultants qualifying for treatment as employees.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 14.F)
-URI http://asc.fasb.org/extlink&oid=27013229&loc=d3e301413-122809

Reference 2: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=96867065&loc=d3e5047-113901

Reference 3: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
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The amount of expense, net of income tax, recognized during the period arising from equity-based compensation arrangements (for example, shares of stock, unit, stock options or other equity instruments) with employees, directors and certain consultants qualifying for treatment as employees.

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The total recognized tax benefit related to compensation cost for equity-based payment arrangements recognized in income during the period.

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