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Business and Summary of Significant Accounting Policies - Stock Based Compensation Expense (Details) $ in Millions | 12 Months Ended
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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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- Definition 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 -Section 50 -Paragraph 2 -Subparagraph (h)(1)(i) -URI http://asc.fasb.org/extlink&oid=96867065&loc=d3e5070-113901 + Details
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