Accounting Policies [Abstract] Accounting Policies [Abstract] Accounting Standards Update 2014-09 [Member] Accounting Standards Update 2014-09 [Member] Accounting Standards Update 2016-02 [Member] Accounting Standards Update 2016-02 [Member] Accounting Standards Update 2016-16 [Member] Accounting Standards Update 2016-16 [Member] Accounts Payable, Current Accounts payable Accounts Receivable [Member] Accounts Receivable [Member] Accounts Receivable, Net, Current Accounts receivable, net Amount of netted accounts receivable charged against deferred revenue. Accounts Receivables Allowances Accounts receivable allowances were netted against deferred revenue Amount of ongoing expenses incurred but not yet paid, due within one year or the normal operating cycle, if longer. Accrued Expenses Ongoing accrued expenses Carrying value as of the balance sheet date of short-term obligations incurred and payable, pertaining to costs incurred on contractual obligations, or accumulate over time and for which invoices have not yet been received or will not be rendered. Accrued Expenses And Other Current Liabilities Accrued expenses and other current liabilities Total accrued expenses and other current liabilities Accrued expenses and other current liabilities. Accrued Expenses And Other Current Liabilities [Member] Accrued Expenses and Other Current Liabilities [Member] Accrued Expenses And Other Current Liabilities Table [Text Block] Accrued Expenses And Other Current Liabilities [Table Text Block] Schedule of Accrued Expenses and Other Current Liabilities Carrying value as of the balance sheet date of obligations incurred and payable within one year of the balance sheet date, incurred on contractual obligations, or accumulate over time and for which invoices have not yet been received or will not be rendered. Accrued Expenses And Other Current Liabilities [Text Block] Accrued Expenses and Other Current Liabilities Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment Less accumulated depreciation Accumulated Other Comprehensive Income (Loss), Debt Securities, Available-for-sale, Adjustment, after Tax Unrealized loss on short-term interest-bearing investments, net of tax Accumulated Other Comprehensive Income (Loss), Cumulative Changes in Net Gain (Loss) from Cash Flow Hedges, Effect Net of Tax Net unrealized gain (loss) on cash flow hedges, net of tax, end of period Net unrealized (loss) gain on cash flow hedges, net of tax, beginning of period Unrealized gain (loss) on derivatives, net of tax Accumulated Other Comprehensive (Income) Loss, Defined Benefit Plan, after Tax Unrealized loss on defined benefit plan, net of tax Accumulated Other Comprehensive Income (Loss), Net of Tax Accumulated other comprehensive (loss) income AOCI Attributable to Parent [Member] Accumulated Other Comprehensive (Loss) Income Additional Paid in Capital Additional paid-in capital Additional Paid-in Capital [Member] Additional Paid-in Capital Address Type [Domain] Address Type [Domain] Adjustments for New Accounting Pronouncements [Axis] Adjustments for New Accounting Pronouncements [Axis] Adjustments to Additional Paid in Capital, Share-based Compensation, Requisite Service Period Recognition Equity-based compensation expense related to employees Adjustments to Additional Paid in Capital, Income Tax Benefit from Share-based Compensation Tax benefit from equity-based awards Adjustments to Reconcile Net Income (Loss) to Cash Provided by (Used in) Operating Activities [Abstract] Reconciliation of net income to net cash provided by operating activities: Allocated Share-based Compensation Expense Equity-based compensation pre-tax expense Accounts receivable allowances. Allowance For Doubtful Accounts Current1 [Member] Accounts Receivable Allowances [Member] Allowance for Doubtful Accounts Receivable, Current Allowance for doubtful accounts Allowance for Doubtful Accounts Receivable, Write-offs Accounts receivable allowances written off against related accounts receivables Amendment Flag Amendment Flag Amortization Of Definite - Lived Purchased Intangible Assets Amortization Of Definite Lived Purchased Intangible Assets Amortization of definite-lived purchased intangible assets Amortization of Intangible Assets Amortization of purchased intangible assets and other Amortization of intangible assets net. Amortization Of Intangible Assets Net Total Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount Weighted average number of shares attributable to antidilutive outstanding stock options not included in the calculation of diluted earnings per share Asset-backed Securities [Member] Asset Backed Obligations [Member] Assets Total assets Total assets Assets [Abstract] ASSETS Assets, Current Total current assets Assets, Current [Abstract] Current assets: Debt Securities, Available-for-sale, Accumulated Gross Unrealized Gain, before Tax Gross Unrealized Gains Debt Securities, Available-for-sale, Accumulated Gross Unrealized Loss, before Tax Gross Unrealized Losses Debt Securities, Available-for-sale, Amortized Cost Amortized Cost Debt Securities, Available-for-sale [Abstract] Available-for-sale securities: Debt Securities, Available-for-sale, Fair Value, Fiscal Year Maturity [Abstract] Available-for-sale Securities, Debt Maturities, Fair Value, Fiscal Year Maturity [Abstract] Debt Securities, Available-for-sale, Maturity, Allocated and Single Maturity Date, within One Year, Fair Value Due within one year Debt Securities, Available-for-sale Fair value, Measured on recurring basis, Investments Available-for-sale securities Fair Value Debt Securities, Available-for-sale, Current Short-term interest-bearing investments Balance Sheet Location [Axis] Balance Sheet Location [Axis] Balance Sheet Location [Domain] Balance Sheet Location [Domain] Basis of Accounting, Policy [Policy Text Block] Basis of Presentation Billed Contracts Receivable Accounts receivable-billed (net of allowances for doubtful accounts of $21,211 as of September 30 and October 1, 2018 and $36,121 as of September 30, 2019) Building [Member] Office Space [Member] Business Acquisition, Acquiree [Domain] Business Acquisition, Acquiree [Domain] Business Acquisition [Axis] Business Acquisition [Axis] Business Acquisition [Line Items] Business Acquisition [Line Items] Business Combination Disclosure [Text Block] Acquisitions Business Combinations [Abstract] Business Combinations [Abstract] Business Combinations Policy [Policy Text Block] Business Combinations Capitalized Computer Software, Net Software assets developed for internal use costs, net of accumulated depreciation Cash and Cash Equivalents, at Carrying Value Cash and cash equivalents at end of year Cash and cash equivalents at beginning of year Cash and cash equivalents Cash and Cash Equivalents [Member] Cash and Cash Equivalents [Member] Cash and Cash Equivalents, Policy [Policy Text Block] Cash and Cash Equivalents Cash, Cash Equivalents, Restricted Cash and Restricted Cash Equivalents, Period Increase (Decrease), Including Exchange Rate Effect Net increase (decrease) in cash and cash equivalents Cash Flow Hedge Gain (Loss) to be Reclassified within Twelve Months Foreign currency cash flow hedge, reclassified into earnings during fiscal year 2020 Cash paid for. Cash Paid For [Abstract] Cash paid for: City Area Code City Area Code Class of Treasury Stock [Table] Class of Treasury Stock [Table] Commitments and Contingencies Disclosure [Abstract] Commitments and Contingencies Disclosure [Abstract] Commitments And Contingencies Disclosure [Line Items] Commitments And Contingencies Disclosure [Line Items] Commitments and Contingencies Disclosure [Line Items] Commitments And Contingencies Disclosure [Table] Commitments And Contingencies Disclosure [Table] Commitments And Contingencies Disclosure [Table] Commitments and Contingencies Disclosure [Text Block] Contingencies and Commitments Common Stock, Dividends, Per Share, Declared Cash dividends declared per ordinary share Dividends Per Ordinary Share Common Stock Outstanding [Member] Common Stock Outstanding [Member] Ordinary Shares Common Stock, Par or Stated Value Per Share Ordinary Shares, par value Common Stock, Shares Authorized Ordinary Shares, authorized Common Stock, Shares, Issued Ordinary Shares, issued Common Stock, Shares, Outstanding Balance, Shares Balance, Shares Ordinary Shares, outstanding Common Stock, Value, Issued Ordinary Shares - Authorized 700,000 shares; £0.01 par value; 277,148 and 275,896 issued and 134,773 and 140,177 outstanding, in 2019 and 2018, respectively Retirement Benefits [Abstract] Retirement Benefits [Abstract] Compensation Related Costs, Policy [Policy Text Block] Equity-Based Compensation Components of Deferred Tax Assets [Abstract] Deferred tax assets: Components of Deferred Tax Liabilities [Abstract] Deferred tax liabilities: Comprehensive Income (Loss), Net of Tax, Attributable to Parent Comprehensive income Comprehensive income Comprehensive Income (Loss), Net of Tax, Attributable to Parent [Abstract] Comprehensive income: Comprehensive Income, Policy [Policy Text Block] Comprehensive Income Computers equipment and software. Computers Equipment And Software [Member] Computers, Related Equipment and Software [Member] Concentration Risk Benchmark [Domain] Concentration Risk Benchmark [Domain] Concentration Risk Benchmark [Axis] Concentration Risk Benchmark [Axis] Concentration Risk Type [Axis] Concentration Risk Type [Axis] Concentration Risk, Credit Risk, Policy [Policy Text Block] Concentrations of Credit Risk Concentration Risk [Line Items] Concentration Risk [Line Items] Concentration Risk, Percentage Aggregate account receivable of more than 10% of total accounts receivable Percentage of revenue from significant customer Concentration Risk [Table] Concentration Risk [Table] Concentration Risk Type [Domain] Concentration Risk Type [Domain] Consolidation, Policy [Policy Text Block] Consolidation Contact Address [Member] Contact Address [Member] Contact Personnel Email Address Contact Personnel Email Address Contact Personnel Name Contact Personnel Name Contact Phone [Member] Contact Phone [Member] Contract with Customer, Liability, Current Deferred revenue Core technology. Core Technology [Member] Core Technology [Member] Corporate Debt Securities [Member] Corporate Bonds [Member] Cost, Amortization Cost of revenue Cost of Revenue Cost of revenue Cost of Sales [Member] Cost of Revenue [Member] Cost of Sales, Policy [Policy Text Block] Cost of Revenue Cover page. Cover page. Credit Facility [Axis] Credit Facility [Axis] Credit Facility [Domain] Credit Facility [Domain] Cumulative Effect of New Accounting Principle in Period of Adoption Cumulative effect adjustment Cumulative Effect on Retained Earnings, Net of Tax Increase in retained earnings Cumulative Effect on Retained Earnings, Tax Decrease in retained earnings Current Fiscal Year End Date Current Fiscal Year End Date Current Income Tax Expense (Benefit) Current Customer Concentration Risk [Member] Customer [Member] Customer Relationships [Member] Customer Relationships [Member] Debt Disclosure [Abstract] Debt Disclosure [Abstract] Debt Disclosure [Text Block] Financing Arrangements Debt instrument maturity month year extended. Debt Instrument Maturity Month Year Extended Revolving credit facility, maturity period Debt Instrument, Term Revolving credit facility, maturity term Debt Securities, Available-for-sale, Realized Gain (Loss) Loss from short-term interest-bearing investments Deferred Foreign Income Tax Expense (Benefit) Net (benefit) provisional expense from release of valuation allowances on deferred tax assets Deferred Income Tax Assets, Net Net deferred tax assets Deferred Income Taxes and Other Tax Liabilities, Noncurrent Deferred income taxes and taxes payable Deferred Income Tax Expense (Benefit) Deferred Deferred income taxes Deferred Tax Liabilities, Gross Total deferred tax liabilities Deferred Revenue Total Deferred revenue Deferred Revenue, Current Deferred revenue (current) Deferred revenue (current) Deferred Revenue, Noncurrent Deferred revenue (non-current) Deferred Revenue, Revenue Recognized Deferred revenue recognized Deferred tax assets deductible tax credits net capital and operating loss carryforwards. Deferred Tax Assets Deductible Tax Credits Net Capital And Operating Loss Carryforwards Tax credits, net capital and operating loss carryforwards Deferred Tax Assets, Deferred Income Deferred revenue Deferred Tax Assets, Gross Total deferred tax assets Deferred tax assets intangible assets, computer software and intellectual property. Deferred Tax Assets Intangible Assets Computer Software And Intellectual Property Intangible assets, computer software and intellectual property Deferred Tax Assets, Net of Valuation Allowance Total deferred tax assets, net Deferred Tax Assets, Other Other Deferred Tax Assets, Tax Deferred Expense, Compensation and Benefits Employee compensation and benefits Deferred Tax Assets, Valuation Allowance Valuation allowances Valuation of write-downs of deferred tax assets charged against the allowance. Deferred Tax Assets Valuation Allowance Written Off Valuation allowances on deferred tax assets written off against the deferred tax assets Amount of deferred tax liability attributable to intangible assets, computer software and intellectual property. Deferred Tax Liabilities Intangible Assets Computer Software And Intellectual Property Intangible assets, computer software and intellectual property Deferred Tax Liabilities, Other Other Deferred Tax Liabilities, Undistributed Foreign Earnings Anticipated withholdings on subsidiaries' earnings Deposit Contracts, Assets Deposit with insurance companies Depreciation Depreciation expense Depreciation, Depletion and Amortization Depreciation and amortization Derivative Contract [Domain] Derivative Contract [Domain] Derivative Asset, Fair Value, Amount Not Offset Against Collateral Derivative Asset Derivative Liability, Fair Value, Amount Not Offset Against Collateral Derivative Liability Derivative, Fair Value, Net Derivative financial instruments, net Net fair value Derivative Instrument [Axis] Derivative Instrument [Axis] Derivative instruments. Derivative Instruments Derivative instruments Derivative Instruments and Hedging Activities Disclosure [Abstract] Derivative Instruments and Hedging Activities Disclosure [Abstract] Derivative Instruments and Hedging Activities Disclosure [Text Block] Derivative Financial Instruments Derivative Instruments, Gain (Loss) [Table] Derivative Instruments, Gain (Loss) [Table] Derivative Instruments, Gain (Loss) [Line Items] Derivative Instruments, (Loss) Gain [Line Items] Derivative Notional Amount 1 Derivative Notional Amount 1 Foreign exchange contracts Derivative, Remaining Maturity Maximum maturity period of significant portion of forward and option contracts outstanding Derivatives, Fair Value [Line Items] Derivatives, Fair Value [Line Items] Derivatives, Policy [Policy Text Block] Derivatives and Hedging A description of typical maturity period of other risk management derivatives. Description Of Maturity Period Of Other Risk Management Derivatives Typical maturity period of other risk management derivatives Designated as Hedging Instrument [Member] Derivatives Designated as Hedging Instruments [Member] Difference between Revenue Guidance in Effect before and after Topic 606 [Member] Adjustments due to ASC 606 [Member] Disaggregation of Revenue [Table Text Block] Revenue by Nature of Activities Disclosure of Compensation Related Costs, Share-based Payments [Abstract] Disclosure of Compensation Related Costs, Share-based Payments [Abstract] Disclosure of Compensation Related Costs, Share-based Payments [Text Block] Stock Option and Incentive Plan Disclosure Of Dividends Declared And Paid [Text Block] Disclosure Of Dividends Declared And Paid [Text Block] Dividends Dividend declaration date august seven two thousand nineteen. Dividend declaration date august seven two thousand nineteen [Member] Declaration Date, August 7, 2018 [Member] Dividend declaration date August 2, 2017. Dividend Declaration Date August Two Two Thousand Seventeen [Member] Declaration Date, August 2, 2017 [Member] Dividend declaration date february five two thousand nighteen Dividend declaration date february five two thousand nighteen [Member] Declaration Date, February 5, 2019 [Member] Dividend declaration date February 1, 2017. Dividend Declaration Date February One Two Thousand Seventeen [Member] Declaration Date, February 1, 2017 [Member] Dividend declaration date January 30, 2018. Dividend Declaration Date January Thirty Two Thousand Eighteen [Member] Declaration Date, January 30, 2018 [Member] Dividend declaration date July 31, 2018. Dividend Declaration Date July Thirty One Two Thousand Eighteen [Member] Declaration Date, July 31, 2018 [Member] Dividend declaration date may fourteen two thousand nineteen. Dividend declaration date may fourteen two thousand nineteen [Member] Declaration Date, May 14, 2019 [Member] Dividend declaration date May 9, 2017. Dividend Declaration Date May Nine Two Thousand Seventeen [Member] Declaration Date, May 9, 2017 [Member] Dividend declaration date May 10, 2018. Dividend Declaration Date May Ten Two Thousand Eighteen [Member] Declaration Date, May 10, 2018 [Member] Dividend declaration date November eight two thousand eighteen. Dividend Declaration Date November Eight Two Thousand Eighteen [Member] Declaration Date, November 8, 2018 [Member] Dividend declaration date November 8, 2017. Dividend Declaration Date November Eight Two Thousand Seventeen [Member] Declaration Date, November 8, 2017 [Member] Dividend declaration date November 8, 2016. Dividend Declaration Date November Eight Two Thousand Sixteen [Member] Declaration Date, November 8, 2016 [Member] Dividends Payable, Date to be Paid Cash dividend payable date Payment Date Dividends [Axis] Dividends [Axis] Dividends, Common Stock, Cash Cash dividends declared Dividends Declared [Table Text Block] Summary of Dividends Declared by Board of directors Dividends [Domain] Dividends [Domain] Dividends Payable, Amount Per Share Quarterly dividend payment per share Dividends Payable, Current Dividends payable Dividends Payable Total Amount Dividends Payable, Date Declared Declaration Date Dividends payable date declared Dividends Payable, Date of Record Record Date Dividends Payable, Date to be Paid, Year and Month Cash dividend anticipated payable date Dividends Payable [Line Items] Dividends Payable [Line Items] Dividends Payable [Table] Dividends Payable [Table] Document Annual Report Document Annual Report Document Fiscal Period Focus Document Fiscal Period Focus Document Fiscal Year Focus Document Fiscal Year Focus Document Information [Line Items] Document Information [Line Items] Document Information [Table] Document Information [Table] Document Period End Date Document Period End Date