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Stock Compensation Plans and Stock Based Compensation (Details 1) - USD ($) $ in Thousands	12 Months Ended
	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Stock based compensation expense and allocation by cost
Stock-based compensation	$ 210,090	$ 197,268	$ 181,547
Cost of product and maintenance [Member]
Stock based compensation expense and allocation by cost
Stock-based compensation	4,161	2,922	2,759
Cost of services [Member]
Stock based compensation expense and allocation by cost
Stock-based compensation	3,375	3,720	3,510
Marketing and sales [Member]
Stock based compensation expense and allocation by cost
Stock-based compensation	43,264	42,096	39,088
Research and development [Member]
Stock based compensation expense and allocation by cost
Stock-based compensation	131,247	124,999	114,656
General and administrative [Member]
Stock based compensation expense and allocation by cost
Stock-based compensation	$ 28,043	$ 23,531	$ 21,534

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- Definition

Stock based compensation expense and allocation by cost.

+ References

No definition available.

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- Definition

Amount of noncash expense for share-based payment arrangement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=123570139&loc=d3e3602-108585

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