The Expand command expands powers and distributes products over sums, where the products can be expressed with the * and ^ operators in the Physics package, or with the commutative (:-*, :-^) or inert (%*, %^) versions of them. Expand also expands the Commutator and AntiCommutator functions of the Physics package, Brackets and Inverse of products. The products resulting from these expansions are all returned normalized using Normal.

After the Physics package has been loaded, the functionality provided by Expand is also automatically provided through the standard expand command. However expand additionally expands mathematical functions, something that Expand does not do.

Note: For the conventions adopted to represent noncommutative and anticommutative objects, see Setup and the types anticommutative and noncommutative.

$\mathrm{with}\left(\mathrm{Physics}\right)\:$

$\mathrm{Setup}\left(\mathrm{mathematicalnotation}=\mathrm{true}\right)$

$\left[\mathrm{mathematicalnotation}=\mathrm{true}\right]$

$\mathrm{Setup}\left(\mathrm{anticommutativeprefix}=\left\{Q\,\mathrm{\theta }\right\}\,\mathrm{noncommutativeprefix}=Z\right)$

$\left[\mathrm{anticommutativeprefix}=\left\{Q\,\mathrm{\theta }\right\}\,\mathrm{noncommutativeprefix}=\left\{Z\right\}\right]$

$\mathrm{Q1}\left(\mathrm{Q1}+\mathrm{Q3}\left(\mathrm{Q4}+\mathrm{Q5}\right)\right)\mathrm{Q6}$

$\mathrm{Q1}\left(\mathrm{Q1}+\mathrm{Q3}\left(\mathrm{Q4}+\mathrm{Q5}\right)\right)\mathrm{Q6}$

$\mathrm{Expand}\left(\right)$

$\mathrm{Q1}\mathrm{Q3}\mathrm{Q4}\mathrm{Q6}+\mathrm{Q1}\mathrm{Q3}\mathrm{Q5}\mathrm{Q6}$

$a\left(h\left(\mathrm{\theta }\right)+b\right)\mathrm{Q1}\mathrm{Z1}\mathrm{Q2}\mathrm{Q4}+\mathrm{Z3}\mathrm{Q5}c\left(\mathrm{Q3}-\mathrm{Q6}\right)f\left(\mathrm{\theta }\right)$

$a\left(h\left(\mathrm{\theta }\right)+b\right)\mathrm{Q1}\mathrm{Q2}\mathrm{Q4}\mathrm{Z1}+cf\left(\mathrm{\theta }\right)\mathrm{Q5}\left(\mathrm{Q3}-\mathrm{Q6}\right)\mathrm{Z3}$

$\mathrm{Expand}\left(\right)$

$h\left(\mathrm{\theta }\right)\mathrm{Q1}\mathrm{Q2}\mathrm{Q4}\mathrm{Z1}a+b\mathrm{Q1}\mathrm{Q2}\mathrm{Q4}\mathrm{Z1}a-f\left(\mathrm{\theta }\right)\mathrm{Q3}\mathrm{Q5}\mathrm{Z3}c-f\left(\mathrm{\theta }\right)\mathrm{Q5}\mathrm{Q6}\mathrm{Z3}c$

$\mathrm{convert}\left(\,\mathrm{horner}\right)$

$\left(h\left(\mathrm{\theta }\right)\mathrm{Q1}\mathrm{Q2}\mathrm{Q4}\mathrm{Z1}+b\mathrm{Q1}\mathrm{Q2}\mathrm{Q4}\mathrm{Z1}\right)a+\left(-f\left(\mathrm{\theta }\right)\mathrm{Q3}\mathrm{Q5}\mathrm{Z3}-f\left(\mathrm{\theta }\right)\mathrm{Q5}\mathrm{Q6}\mathrm{Z3}\right)c$

$\mathrm{Z3}\mathrm{Q5}c\left(\mathrm{Q3}-\mathrm{Q6}\right)\cos \left(a+b\right)$

$c\cos \left(a+b\right)\mathrm{Q5}\left(\mathrm{Q3}-\mathrm{Q6}\right)\mathrm{Z3}$

$\mathrm{Expand}\left(\right)$

$-c\cos \left(a+b\right)\mathrm{Q3}\mathrm{Q5}\mathrm{Z3}-c\cos \left(a+b\right)\mathrm{Q5}\mathrm{Q6}\mathrm{Z3}$

$\mathrm{expand}\left(\right)$

$-c\cos \left(a\right)\cos \left(b\right)\mathrm{Q3}\mathrm{Q5}\mathrm{Z3}-c\cos \left(a\right)\cos \left(b\right)\mathrm{Q5}\mathrm{Q6}\mathrm{Z3}+c\sin \left(a\right)\sin \left(b\right)\mathrm{Q3}\mathrm{Q5}\mathrm{Z3}+c\sin \left(a\right)\sin \left(b\right)\mathrm{Q5}\mathrm{Q6}\mathrm{Z3}$

$\mathrm{Setup}\left(\mathrm{quantumoperators}=\left\{A\,B\right\}\right)$

$\left[\mathrm{quantumoperators}=\left\{A\,B\right\}\right]$

$\mathrm{\%Bracket}\left(\mathrm{Bra}\left(\mathrm{\phi }\right)\,aA+bB+c\,\mathrm{Ket}\left(\mathrm{\psi }\right)\right)$

$⟨\mathrm{\phi }\left|aA+bB+c\right|\mathrm{\psi }⟩$

$\mathrm{Expand}\left(\right)$

$a⟨\mathrm{\phi }\left|A\right|\mathrm{\psi }⟩+b⟨\mathrm{\phi }\left|B\right|\mathrm{\psi }⟩+c⟨\mathrm{\phi }|\mathrm{\psi }⟩$