Formal derivative

Let $𝑉$ be a vector space (or, in particular, a field) and $𝑉 {𝑧}$ denote formal sums over $𝑉$ . The formal derivative #m/def/fcalc

𝑑 𝑑 𝑧 : 𝑉 {𝑧} \to 𝑉 {𝑧}

is defined by extending the rules

𝑑 𝑑 𝑧 (𝑧 𝑛) = {0 𝑛 = 0 𝑛 𝑧 𝑛 - 1 𝑛 \neq 0

by linearity. The formal derivative therefore constitutes a derivation on the algebra of Laurent polynomials $𝕂 [𝑧, 𝑧 - 1]$ .

See also