0 (of a calculation) giving the same result whatever order the values are in
1 of a calculation, giving the same result whatever order the values are in
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.
