Function DYAD-COMPONENT

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

Slots on this function:

Documentation:

Function to generate the i,j th scalar component for a dyad in a particular basis. The i,j scalar component of dyad T is equal to bi*T*bj (basis vector i dot T dot basis vector j.

Arity: 5

Axioms:

(Nth-Domain Dyad-Component 5 Scalar-Quantity)

(Nth-Domain Dyad-Component 4 Orthonormal-Basis)

(Nth-Domain Dyad-Component 3 Positive-Integer)

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

(Nth-Domain Dyad-Component 1 Dyad)

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