Physics[Vectors][Component] - the component (first, second, or third) of a vector
an algebraic vector
a name or one of 1, 2, 3, or an algebraic expression representing these numbers
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.
An explicit algebraic vector in cartesian coordinates
R ≔ a⁡x,y,z⁢_i+b⁡x,y,z⁢_j+c⁡x,y,z⁢_k
The first and third components
The "nth" component returns unevaluated
Substituting n by something concrete, the component is obtained
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:
The second component
When A_ is replaced by a projected vector, the selection of the component is performed
It is also possible to work all abstract; this is the "nth" component of a non-projected vector
Component admits as argument a generic algebraic vectorial expression, for instance
Note however that when the expression passed to Component is not a vector, the computation is interrupted with an error message
Error, (in Physics:-Vectors:-Component) first argument is not a vector
Physics, Physics conventions, Physics examples, Physics Updates, Tensors - a complete guide, Mini-Course Computer Algebra for Physicists, Physics/Vectors, Vectors,operations, Vectors/Identify
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