commutatively การใช้

Thus, every context-free language is commutatively equivalent to some regular language.
Two languages are said to be " commutatively equivalent " if they have the same set of Parikh vectors.
If S is any semi-linear set, the language of words whose Parikh vectors are in S is commutatively equivalent to some regular language.
In simple terms, this is just the formal statement of the informal discussion given above : the letters in an alphabet \ Sigma _ k can be commutatively re-ordered past the letters in an alphabet \ Sigma _ j, unless they are letters that occur in both alphabets.
Because a weight is a map to a commutative ring, the map factors through the abelianization of the algebra \ mathcal { A } equivalently, it vanishes on the derived algebra in terms of matrices, if v is a common eigenvector of operators T and U, then T U v = U T v ( because in both cases it is just multiplication by scalars ), so common eigenvectors of an algebra must be in the set on which the algebra acts commutatively ( which is annihilated by the derived algebra ).