Function VECTOR-COMPONENT

• Defined in theory: Tensor-quantities
• Source code: tensor-quantities.lisp

Slots on this function:

Documentation:

Function to generate the ith scalar component for a vector-quantity in a particular basis. The ith scalar component is the dot (inner) product of the vector-quantity with the ith basis vector of the given basis.

Arity: 4

Axioms:

(Nth-Domain Vector-Component 4 Scalar-Quantity)

(Nth-Domain Vector-Component 3 Orthonormal-Basis)

(Nth-Domain Vector-Component 2 Positive-Integer)

(Nth-Domain Vector-Component 1 Vector-Quantity)

(<=> (Vector-Component ?V ?I ?B ?S)
     (And (Vector-Quantity ?V)
          (Positive-Integer ?I)
          (Orthonormal-Basis ?B)
          (Scalar-Quantity ?S)
          (= (Quantity.Dimension ?S) (Quantity.Dimension ?V))
          (= (Spatial.Dimension ?V) (Basis.Dimension ?B))
          (=< ?I (Spatial.Dimension ?V))
          (= ?S (Dot ?V (Basis.Vec ?B ?I)))))