linguistic:translation, linguistic:paraphrasing, linguistic:voice_change
Integer functions and formal sums

The elements of Z (B) {\displaystyle \mathbb {Z} ^{(B)}} may also be written as formal sums, expressions in the form of a sum of finitely many terms, where each term is written as the product of a nonzero integer with a distinct member of B {\displaystyle B}. These expressions are considered equivalent when they have the same terms, regardless of the ordering of terms, and they may be added by forming the union of the terms, adding the integer coefficients to combine terms with the same basis element, and removing terms for which this combination produces a zero coefficient. They may also be interpreted as the signed multisets of finitely many elements of B {\displaystyle B}.