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 $\mathrm{\_\φ}$ 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:

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 $\mathrm{f\_}$ or $\mathrm{f\_}\left(x\,y\,z\right)$

Concerning the coordinates, the conventions are:

NOTE: these variables x, y, z, $\mathrm{\rho },\mathrm{\phi },r$, and $\mathrm{\theta }$, as well as _i, _j, _k, $\mathrm{\_\ρ},\mathrm{\_\φ},\mathrm{\_r}$, and $\mathrm{\_\θ}$, 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.

$\mathrm{with}\left(\mathrm{Physics}\left[\mathrm{Vectors}\right]\right)$

$\left[\mathrm{\&x}\,\mathrm{`+`}\,\mathrm{`.`}\,\mathrm{Assume}\,\mathrm{ChangeBasis}\,\mathrm{ChangeCoordinates}\,\mathrm{CompactDisplay}\,\mathrm{Component}\,\mathrm{Curl}\,\mathrm{DirectionalDiff}\,\mathrm{Divergence}\,\mathrm{Gradient}\,\mathrm{Identify}\,\mathrm{Laplacian}\,\nabla \,\mathrm{Norm}\,\mathrm{ParametrizeCurve}\,\mathrm{ParametrizeSurface}\,\mathrm{ParametrizeVolume}\,\mathrm{Setup}\,\mathrm{Simplify}\,\mathrm{`^`}\,\mathrm{diff}\,\mathrm{int}\right]$

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

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

$\mathrm{Identify}\left(A\right)$

$0$

$\mathrm{Identify}\left(\mathrm{A\_}\right)$

$5$

$\mathrm{Identify}\left(x\mathrm{\_i}+y\mathrm{\_j}+z\mathrm{\_k}\right)$

$1$

$\mathrm{Identify}\left(\mathrm{\rho }\mathrm{\_\ρ}+z\mathrm{\_k}\right)$

$2$

$\mathrm{Identify}\left(\mathrm{\_r}+f\left(r\,\mathrm{\theta }\right)\mathrm{\_\φ}\right)$

$3$

$\mathrm{Identify}\left(\mathrm{\_k}\right)$

$6$

$\mathrm{Identify}\left(\mathrm{\_\φ}\right)$

$7$

$\mathrm{Identify}\left(\mathrm{Divergence}\left(\mathrm{A\_}\left(x\,y\,z\right)\right)\right)$

$0$

$\mathrm{Identify}\left(\mathrm{Curl}\left(\mathrm{A\_}\left(x\,y\,z\right)\right)\right)$

$5$

$\mathrm{Identify}\left(\mathrm{Laplacian}\left(\mathrm{A\_}\left(x\,y\,z\right)\right)\right)$

$5$