Class NUMERIC-TENSOR

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

Slots on this class:

Documentation:

A numeric-valued tensor. Its components expressed in any basis are numeric or non-dimensional.

Instance-Of: Class

Subclass-Of: Dimensionless-quantity, Tensor-quantity

Other Related Axioms:

(Forall (?U)
        (=> (And (Unit-Of-Measure ?U)
                 (= (Quantity.Dimension ?U) (Quantity.Dimension ?V)))
            (Numeric-Tensor (Magnitude ?V ?U))))

(<=> (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))))))

(Forall (?U)
        (=> (And (Unit-Of-Measure ?U)
                 (= (Quantity.Dimension ?U) (Quantity.Dimension ?D)))
            (Numeric-Tensor (Magnitude ?D ?U))))

(<=> (Dyad ?D)
     (And (Constant-Quantity ?D)
          (Tensor-Quantity ?D)
          (= (Tensor-Order ?D) 2)
          (Forall (?B ?I ?J)
                  (=> (And (Orthonormal-Basis ?B)
                           (= (Basis.Dimension ?B)
                              (Spatial.Dimension ?D))
                           (Positive-Integer ?I)
                           (=< ?I (Spatial.Dimension ?D))
                           (Positive-Integer ?J)
                           (=< ?J (Spatial.Dimension ?D)))
                      (And (Defined (Dyad-Component ?D ?I ?J ?B))
                           (= (Quantity.Dimension (Dyad-Component ?D
                                                                  ?I
                                                                  ?J
                                                                  ?B))
                              (Quantity.Dimension ?D)))))
          (Forall (?U)
                  (=> (And (Unit-Of-Measure ?U)
                           (= (Quantity.Dimension ?U)
                              (Quantity.Dimension ?D)))
                      (Numeric-Tensor (Magnitude ?D ?U))))))