Class VECTOR-QUANTITY

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

Slots on this class:

Documentation:

The class of quantities which are n-dimensional vectors (first order tensor-quantities). Each vector has an associated spatial dimension and an associated physical dimension. Each vector-quantity can be decomposed into scalar components for a given orthonormal basis of the proper dimension. The physical-dimension of a scalar component of the vector-quantity is equivalent to the physical-dimension of the vector-quantity.

Subclass-Of: Constant-quantity, Tensor-quantity

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Slots on instances of this class:

Tensor-Order: 1

Axioms:

(<=> (Vector-Quantity ?V)
     (And (Constant-Quantity ?V)
          (Tensor-Quantity ?V)
          (= (Tensor-Order ?V) 1)
          (Forall (?B ?I)
                  (=> (And (Orthonormal-Basis ?B)
                           (= (Basis.Dimension ?B)
                              (Spatial.Dimension ?V))
                           (Positive-Integer ?I)
                           (=< ?I (Spatial.Dimension ?V)))
                      (And (Defined (Vector-Component ?V ?I ?B))
                           (= (Quantity.Dimension (Vector-Component ?V
                                                                    ?I
                                                                    ?B))
                              (Quantity.Dimension ?V)))))
          (Forall (?U)
                  (=> (And (Unit-Of-Measure ?U)
                           (= (Quantity.Dimension ?U)
                              (Quantity.Dimension ?V)))
                      (Numeric-Tensor (Magnitude ?V ?U))))))