Normal - Maple Help

Physics[Normal] - The Normal tensor

 Calling Sequence Normal(f, option=value, ...)

Parameters

 f - algebraic expression, or relation between them, or a set or list of them producttopower - optional - can be true (default) or false, to express products of the same object as a power reprocesscommutativeproducts - optional - can be true (default) or false, to reprocess commutative products identifying and normalizing anticommutative and noncommutative operands operands sortnoncommutative - optional - can be true (default) or false, to sort noncommutative operands in products using into account commutation rules for them unnest - optional - can be true (default) or false, to unnest given nested products flattening the nested operations into only one

Description

 • 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:
 1 The sequence of operands of $*$ is split into two sequences: s1 and s2, containing the commutative and not commutative (anticommutative and noncommutative) operands, respectively.
 2 The elements of s1 are sorted by using machine ordering (table(symmetric)), resulting in sorted_s1.
 3 Each subsequence of anticommutative elements of s2 is sorted using machine ordering (table(antisymmetric)), resulting in sorted_s2.
 4 Both sorted_s1 and sorted_s2 are normalized by using normal.
 5 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).

Examples

 > $\mathrm{with}\left(\mathrm{Physics}\right):$
 > $\mathrm{Setup}\left(\mathrm{mathematicalnotation}=\mathrm{true}\right)$
 $\left[{\mathrm{mathematicalnotation}}{=}{\mathrm{true}}\right]$ (1)

Set first some identifiers to work with type/anticommutative and type/noncommutative variables and a related algebra

 > $\mathrm{Setup}\left(\mathrm{noncommutativeprefix}=Z,\mathrm{%Commutator}\left(\mathrm{Z1},\mathrm{Z2}\right)=0\right)$
 $\left[{\mathrm{algebrarules}}{=}\left\{{\mathrm{%Commutator}}{}\left({\mathrm{Z1}}{,}{\mathrm{Z2}}\right){=}{0}\right\}{,}{\mathrm{noncommutativeprefix}}{=}\left\{{Z}\right\}\right]$ (2)
 > $\mathrm{Z1}\mathrm{Z2}-\mathrm{Z2}\mathrm{Z1}$
 ${0}$ (3)
 > $\mathrm{Normal}\left(\right)$
 ${0}$ (4)
 > 

Compatibility

 • The Physics[Normal] command was introduced in Maple 16.
 • For more information on Maple 16 changes, see Updates in Maple 16.