Physics[Vectors][Identify] - identify the vector character of an expression in the context of the Physics[Vectors] subpackage's conventions
any algebraic (vectorial or scalar) expression
Identify returns a number between 0 and 7, related to the vector classification of its argument: 0 = scalar, 1 = cartesian-vector, 2 = cylindrical-vector, 3 = spherical-vector, 5 = non-projected vector, 6 = can be cartesian or cylindrical (projected over the z axis), 7 = can be cylindrical or spherical (projected over the _φ direction). This command is used by the commands of the Physics[Vectors] subpackage before proceeding with the computations; it can be used to check how is the package interpreting an expression or as tool in the context of other programs using Physics[Vectors].
The %Identify is the inert form of Identify, that is: it represents the same mathematical operation while holding the operation unperformed. To activate the operation use value.
Note that the representation for a vector implemented in the Physics[Vectors] subpackage is not a matrix (list of components), but an algebraic expression, as either a first degree polynomial in the unit vectors with no independent term, or a symbol with a predefined postfix: the underscore, _ (to change this default postfix see Physics/Setup). The classification of a projected vector in this context is made taking into account the following conventions:
cartesian unit vectors,
cylindrical unit vectors,
spherical unit vectors
The classification of a non-projected vector or vector function depends entirely on its name, i.e., on whether it ends with _(a mimicry of the arrow over a letter), as in f_ or f_⁡x,y,z
Concerning the coordinates, the conventions are:
NOTE: these variables x, y, z, ρ,φ,r, and θ, as well as _i, _j, _k, _ρ,_φ,_r, and _θ, respectively used to represent the coordinates and the unit vectors, are automatically protected when the Physics[Vectors] subpackage is loaded.
Mathematical vector notation: When the Physics[Vectors] subpackage is loaded in the Standard Graphical User Interface, and the Typesetting level is set to Extended (the default), non-projected vectors and unit vectors are respectively displayed with an arrow and a hat on top and the differential operators (Nabla, Laplacian, etc.) with an upside down triangle as in textbooks. You can also set this notation by entering Physics[Setup](mathematicalnotation = true). You can also set this notation from the Options Dialog: go to Tools > Options, select the Display tab, and set the Typesetting level to Extended.
The input for Identify is an algebraic (vectorial or scalar) expression. The output is a related number.
"A" is a scalar and "A_" is a non-projected Vector.
A cartesian Vector.
A cylindrical Vector.
A spherical Vector.
A cartesian or cylindrical Vector.
A cylindrical or spherical Vector.
The divergence of a Vector is a scalar.
The curl of a Vector is a Vector.
The Laplacian of a Vector is a Vector.
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