| 词汇 | commutative |
| 释义 | commutative adjective mathematics specializeduk /kəˈmjuː.təˌtɪv/ us /kəˈmjuː.t̬əˌtɪv/ (of a calculation) giving the same result whatever order the values are in可交换的（计算） Calculations & calculating algebraic algebraically algo algorithmic amount calculate guesstimate interpolation inverse function linear equation mathematical matrix miscalculate miscalculation miscount operator sum sum total triangulate work something out commutative | American Dictionarycommutative adjective us/kəˈmjuː·t̬əˌtɪv/ mathematics of a calculation, giving the same result whatever order the values are in Examples of commutativecommutative The principle is very useful, since closed nets do not need commutative conversions. This raises some intriguing issues, since in general (for arbitrary finite metric spaces) such enlargements are neither commutative nor associative. In this paper we provide tools for deciding whether a knotted commutative calculus admits reductive cut elimination and for automating cut-elimination proofs in these calculi. This operator is commutative and is defined whenever no components are defined on both sides. In reductions, we introduce an associative (and commutative) operator to combine a set of values. The defined conditions (reductivity and weak substitutivity) are recalled below and applied to knotted commutative calculi. In this particular example, the binary operation is not only associative but also commutative, but this need not be the case in general. Both and are clearly also commutative, and almost as clearly associative. Nevertheless, the actual bootstraps will require different arguments since the non-commutativity will prevent some of the rearrangements that we did in the commutative case. Additionally, we integrate into our setting a method for the annotation of hypergraphs with an algebraic structure (in our case, a commutative monoid). We can now characterize those monads with commutative strength as follows. These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. |
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