Define is used to define a Maple object entering algebraic expressions, representing a mathematical object with tensorial properties in the context of the Physics package. You can include in that definition the object's structure and symmetry properties regarding permutation of its indices, if any.

If you define an object already defined, Define performs a check for consistency between the previous and the given definitions, and interrupts with an error if there are inconsistencies. To clear previous definitions, use the optional argument clear; if given alone, it will clear all the previous definitions, otherwise it will clear only the definitions of the objects specified. To redefine a previously defined object (that is, define it ignoring previous definitions), include the optional argument redo, together with the new definition.

The command Define() with no argument returns the definitions of objects known to the system at the time it is called.

After an object is defined through the Define command, each time a Physics command finds this object in a mathematical expression, the command operates with the object taking into account the sum rule for repeated indices, the symmetry properties defined for it, as well as its commutation rules, if any were defined.

Note that when an object is defined through the Define command, no assignment is made to the object itself; instead, the information is stored in a table, and made available to the different Physics commands, which automatically query this information, on background, to verify whether the objects found in the working expression were previously defined, what their properties are, if any, and whether they match their previous definitions regarding number of indices and dependency. If some inconsistency is detected, an error interruption pointing to the problem found occurs. In this way, Maple takes care of the typical mistakes that could happen while computing with more sophisticated notation.

When the dimension of the spacetime is changed in the middle of a session, all definitions previously made by using Define are automatically cleared.

Generally speaking, a Physics object can be defined as such in two different ways:

- By calling Define directly with all the information regarding the object, such as Define().

- By calling Define with only a basic piece of information, as in Define(A). Then, when a Physics command is called, an expression containing the command, such as , automatically calls Define to update the information on the number of indices and variables of objects previously defined.

The first approach tells from the beginning what will be correct in what follows. In the second approach, what will be correct is implicit the first time the object is entered with all the information; assuming there are no mistakes the first time, this approach is simpler.

antisymmetric and symmetric

To define symmetry properties for some or all of the indices of an object being defined with the Define command, use the following guidelines:

- To define the indices as totally symmetric or antisymmetric with respect to permutations, add the keyword symmetric or antisymmetric,respectively, to the calling sequence. For example, Define( , symmetric).

If many objects are being defined at once, the symmetry properties are assumed to hold for all of them.

- To define more detailed symmetry properties (for one Tensor at a time) use, for example, Define( , symmetric = ),

so that:  is symmetric with respect to the interchange of positions between the indices , and also between the indices . In the same way, you can simultaneously define symmetric and antisymmetric properties. For example, Define(, symmetric = , antisymmetric = ), so that for the commands in the Physics package,  .

clear

Clear previous definitions in the current session.

If given with no arguments, clear removes all definitions in the current session.

If given with objects , clear removes the specified definitions.

query

Query about previous definitions in the current session. For example, Define(query), where query is any of query, history, indices, functionality, and structure.

quiet

Proceed without displaying messages on the screen.

redo

To re-define an object that has already been defined, where the new definition is not the same as the old, use either the clear option and then define the object again, or do both in one step by using the redo option.

The redo option removes the previous definition, if any, and gives the object the new definition as specified.