If we have a graded algebra $A$, and $D$ is a homogeneous linear map of grade $d = deg(D)$ on $A$ then $D$ is a homogeneous derivation if $$D(ab)=D(a)b+\epsilon^{deg(a)\cdot deg(D)}aD(b)$$ $\epsilon\in\{-1,1\}$ acting on homogeneous elements of $A$. A graded derivation is a sum of homogeneous derivations with the same $\epsilon$. If $\epsilon = 1$, this definition reduces to the Leibniz rule. If $\epsilon = -1$, then $D(ab)=D(a)b+(-1)^{|a|}aD(b)$, for odd $|D|$. The notion of graded derivations of odd degree is sometimes called *antiderivation* or *anti-derivation* or *integration*. Examples of anti-derivations include the [[exterior derivative]] and the [[interior product]] acting on [[differential form]]s.