the component (first, second, or third) of a vector - Maple Help

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Physics[Vectors][Component] - the component (first, second, or third) of a vector

Calling Sequence

Component(A, n)

Parameters

A

-

an algebraic vector

n

-

a name or one of 1, 2, 3, or an algebraic expression representing these numbers

Description

• 

Component(A, n) returns the nth. component of the vector A when A is a projected vector expression, or an unevaluated representation of the nth component when A is a non-projected vector or n is an unresolved name representing one of 1, 2 or 3. If A is not a vector then an error message is returned. Regarding how a vector is identified as such in the context of the Physics/Vectors package, see Identify and type, PhysicsVectors.

  

The %Component is the inert form of Component, that is: it represents the same mathematical operation while holding the operation unperformed. To activate the operation use value.

• 

When Component returns unevaluated, the display on the screen shows the vectorial expression between parentheses, and indexed (as usual when working by hand). This is done using a `print/Component` procedure.

Examples

withPhysics[Vectors]

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

(1)

Setupmathematicalnotation=true

mathematicalnotation=true

(2)

An explicit algebraic vector in cartesian coordinates

Rax,y,z_i+bx,y,z_j+cx,y,z_k

Rax,y,zi+bx,y,zj+cx,y,zk

(3)

The first and third components

ComponentR,1

ax,y,z

(4)

ComponentR,3

cx,y,z

(5)

The "nth" component returns unevaluated

ComponentR,n

ax,y,zi+bx,y,zj+cx,y,zkn

(6)

Substituting n by something concrete, the component is obtained

n=1|n=1

ax,y,z

(7)

Here A_ is an abstract non-projected vector; by default, in the framework of the Physics[Vectors] package, symbols ending with "_" represent non-projected vectors (to change this postfix see Setup:

typeA_,PhysicsVectors

true

(8)

The second component

ComponentA_,2

A2

(9)

When A_ is replaced by a projected vector, the selection of the component is performed

A_=R|A_=R

bx,y,z

(10)

It is also possible to work all abstract; this is the "nth" component of a non-projected vector

ComponentA_,n

An

(11)

Component admits as argument a generic algebraic vectorial expression, for instance

typeA_+B_,PhysicsVectors

true

(12)

ComponentA_+B_,n

A+Bn

(13)

Note however that when the expression passed to Component is not a vector, the computation is interrupted with an error message

typeA,PhysicsVectors

false

(14)

ComponentA,n

Error, (in Physics:-Vectors:-Component) first argument is not a vector

See Also

Physics, Physics conventions, Physics examples, Physics/Vectors, Vectors,operations, Vectors/Identify


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