identify the vector character of an expression in the context of the Physics[Vectors] subpackage's conventions - Maple Programming Help

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Physics[Vectors][Identify] - identify the vector character of an expression in the context of the Physics[Vectors] subpackage's conventions

Calling Sequence

Identify(A)

Parameters

A

-

any algebraic (vectorial or scalar) expression

Description

• 

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 _phi 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:

(_i,_j,_k)

=

cartesian unit vectors,

(_rho,_phi,_k)

=

cylindrical unit vectors,

(_r,_theta,_phi)

=

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:

(x,y,z)

=

cartesian coordinates,

(rho,phi,z)

=

cylindrical coordinates,

(r,theta,phi)

=

spherical coordinates

  

NOTE: these variables x, y, z, rho,phi,r, and theta, as well as _i, _j, _k, _rho,_phi,_r, and _theta, 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, by entering Physics[Setup](mathematicalnotation = true), 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 from the Options Dialog: go to Tools > Options, select the Display tab, and set the Typesetting level to Extended.

Examples

withPhysics[Vectors]

&x,`+`,`.`,ChangeBasis,ChangeCoordinates,Component,Curl,DirectionalDiff,Divergence,Gradient,Identify,Laplacian,Nabla,Norm,Setup,diff

(1)

Setupmathematicalnotation=true

mathematicalnotation=true

(2)

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.

IdentifyA

0

(3)

IdentifyA_

5

(4)

A cartesian Vector.

Identifyx_i+y_j+z_k

1

(5)

A cylindrical Vector.

Identifyρ_ρ+z_k

2

(6)

A spherical Vector.

Identify_r+fr,θ_φ

3

(7)

A cartesian or cylindrical Vector.

Identify_k

6

(8)

A cylindrical or spherical Vector.

Identify_φ

7

(9)

The divergence of a Vector is a scalar.

Identify∇·A_x,y,z

0

(10)

The curl of a Vector is a Vector.

Identify∇×A_x,y,z

5

(11)

The Laplacian of a Vector is a Vector.

IdentifyLaplacianA_x,y,z

5

(12)

See Also

&x, +, ., ChangeBasis, Component, Curl, diff, DirectionalDiff, Divergence, Gradient, Laplacian, Nabla, Norm, Physics, Physics conventions, Physics examples, Physics[Vectors]


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