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Business Combinations	12 Months Ended
Business Combinations	Oct. 31, 2021
Business Combinations [Abstract]
Business Combinations	Business Combinations Fiscal 2021 Acquisitions During fiscal 2021, the Company completed several acquisitions for an aggregate consideration of $298.9 million, net of cash acquired. The Company does not consider these acquisitions to be material, individually or in the aggregate, to the Company’s consolidated statements of income. The preliminary purchase allocations are $109.3 million of identifiable intangible assets and $204.5 million in goodwill, of which $158.8 million is attributable to the Semiconductor & System Design reporting segment and $45.7 million is attributable to the Software Integrity reporting segment. Approximately $34.0 million of the goodwill related to the fiscal 2021 acquisitions will be deductible for tax purposes. Fiscal 2020 Acquisitions During fiscal 2020, the Company completed several acquisitions for an aggregate consideration of $238.3 million, net of cash acquired. The Company does not consider these acquisitions to be material, individually or in the aggregate, to the Company's consolidated statements of income. The preliminary purchase allocations are $65.3 million of identifiable intangible assets, and $173.7 million in goodwill, of which $160.4 million is attributable to the Semiconductor & System Design reporting segment and $13.3 million is attributable to the Software Integrity reporting segment. The preliminary fair value estimates for the assets acquired and liabilities assumed for all acquisitions completed within 12 months from the applicable acquisition date are not yet finalized and may change as additional information becomes available during the respective measurement periods. The primary areas of those preliminary estimates relate to certain tangible assets and liabilities, identifiable intangible assets, and income taxes. Acquisition-Related Transaction Costs Transaction costs were $15.4 million and $14.1 million during fiscal 2021 and 2020, respectively. These costs consist of professional fees and administrative costs and were expensed as incurred in the Company’s consolidated statements of income.