Revenue from Contracts with Customers (Disaggregation of Revenue) (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 30, 2019	Mar. 31, 2018	Mar. 30, 2019	Mar. 31, 2018
Disaggregation of Revenue [Line Items]
Revenue	$ 290,451	$ 307,883	$ 625,140	$ 614,527
Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Disaggregation of Revenue [Line Items]
Revenue	315,499	307,883	654,256	614,527
Subscription license
Disaggregation of Revenue [Line Items]
Revenue	51,540		115,057
Subscription support & cloud services
Disaggregation of Revenue [Line Items]
Revenue	83,228		160,652
Subscription Services
Disaggregation of Revenue [Line Items]
Revenue	134,768		275,709
Subscription Services | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Disaggregation of Revenue [Line Items]
Revenue	162,070	112,931	310,483	212,939
Perpetual support
Disaggregation of Revenue [Line Items]
Revenue	104,417		214,914
Perpetual support | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Disaggregation of Revenue [Line Items]
Revenue	103,564	126,683	212,789	257,880
Recurring Services
Disaggregation of Revenue [Line Items]
Revenue	239,185		490,623
Recurring Services | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Disaggregation of Revenue [Line Items]
Revenue	265,634	239,614	523,272	470,819
Perpetual license
Disaggregation of Revenue [Line Items]
Revenue	10,336		52,141
Perpetual license | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Disaggregation of Revenue [Line Items]
Revenue	11,267	22,839	53,017	56,824
Software
Disaggregation of Revenue [Line Items]
Revenue	249,521	262,453	542,764	527,643
Software | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Disaggregation of Revenue [Line Items]
Revenue	276,901	262,453	576,289	527,643
Professional services
Disaggregation of Revenue [Line Items]
Revenue	40,930	45,430	82,376	86,884
Professional services | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Disaggregation of Revenue [Line Items]
Revenue	$ 38,598	$ 45,430	$ 77,967	$ 86,884