The Normal command replaces products expressed with the * operator by simplified, unnested and sorted ones. The sorting procedure has the purpose of rewriting products expressed with the * operator of Physics, perhaps with different appearance but the same mathematical contents, in a unique manner here called "canonical form". In turn, this allows you to take advantage of the simplification commands of the Maple Standard Library since, after calling Normal, "equivalent" products can be recognized as such by the system. To set the identifiers for type/noncommutative and type/anticommutative variables see Setup.

Normal is automatically used by the Physics product operator * with all its options using their default values but for sortnoncommutative.

The canonical form for products expressed with the * operator of Physics is built as follows:

The sequence of operands of $*$ is split into two sequences: s1 and s2, containing the commutative and not commutative (anticommutative and noncommutative) operands, respectively.

The elements of s1 are sorted by using machine ordering (table(symmetric)), resulting in sorted_s1.

Each subsequence of anticommutative elements of s2 is sorted using machine ordering (table(antisymmetric)), resulting in sorted_s2.

Both sorted_s1 and sorted_s2 are normalized by using normal.

A result is built and returned as the normalized form of sorted_s1 times sorted_s2.

To simplify in general these products that involve noncommutative objects, taking into account the same commutation rules taken into account by Normal and in addition other simplification rules, use Simplify. To expand these generalized products over sums, use expand (will expand mathematical functions as well) or Expand (will expand only noncommutative products and related functions of the Physics package as for instance Commutators).

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

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

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

$\mathrm{Setup}\left(\mathrm{noncommutativeprefix}=Z\,\mathrm{\%Commutator}\left(\mathrm{Z1}\,\mathrm{Z2}\right)=0\right)$

$\left[\mathrm{algebrarules}=\left\{{\left[\mathrm{Z1},\mathrm{Z2}\right]}_{-}=0\right\}\,\mathrm{noncommutativeprefix}=\left\{Z\right\}\right]$

$\mathrm{Z1}\mathrm{Z2}-\mathrm{Z2}\mathrm{Z1}$

$0$

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

$0$