Cadabra manual: Distribute

distribute

Distribute factors over sums.

Rewrite a product of sums as a sum of products, as in

$\begin{equation*} a\,(b+c) \rightarrow a\,b + a\,c\, . \end{equation*}$ This would read

ex:=a (b+c); distribute(_);

$\displaystyle{}a \left(b+c\right)$

$\displaystyle{}a b+a c$

The algorithm in fact works on all objects which carry the Distributable property,

Op{#}::Distributable; ex:=Op(A+B); distribute(_);

$\displaystyle{}\text{Attached property Distributable to }Op\left(\#\right).$

$\displaystyle{}Op\left(A+B\right)$

$\displaystyle{}Op\left(A\right)+Op\left(B\right)$

The primary example of a property which inherits the Distributable property is PartialDerivative. The distribute algorithm thus also automatically writes out partial derivatives of sums as sums of partial derivatives,

\partial{#}::PartialDerivative; ex:=\partial_{m}{A + B + C}; distribute(_);

$\displaystyle{}\text{Attached property PartialDerivative to }\partial{\#}.$

$\displaystyle{}\partial_{m}\left(A+B+C\right)$

$\displaystyle{}\partial_{m}{A}+\partial_{m}{B}+\partial_{m}{C}$