Theory TENSOR-QUANTITIES

Theory documentation:

This theory is used to represent vectors of n spatial dimensions which are physical quantities with physical dimensions, such as 'the velocity of particle p'. The theory supports arbitrary numbers of basis vector sets and hence vectors are not isomorphic to n-tuples as is the case in some textbook representations of vectors (Note: Multi-basis vector spaces are essential to many theories such as kinematics). Standard vector operations such as vector addition, scalar multiplication, and scalar or dot product are supported. Operators on vector-quantities must take into account the associated units and dimensions.

The theory now also include higher-order tensors.


Notes:


Cross Reference Report:

Theories included by Tensor-Quantities:

  Basic-Matrix-Algebra
  Scalar-Quantities

Theories that include Tensor-Quantities:

  3d-Tensor-Quantities

8 classes defined:

    Matrix-Quantity
       Numeric-Matrix
    Orthonormal-Basis
    Tensor-Quantity
       Vector-Quantity
          Unit-Vec
       Dyad
       Numeric-Tensor

No relations defined.


17 functions defined:

  *
  +
  -
  Basis.Dimension
  Basis.Vec
  Dot
  Dyad-Component
  Dyad-Of-Dimensions
  Spatial.Dimension
  Tensor-Order
  Tensor-To-Matrix
  The-Dyad
  The-Vector-Quantity
  The-Zero-Dyad-Of-Type
  The-Zero-Vector-Of-Type
  Vector-Component
  Vector-Quantities-Of-Dimensions

No instances defined.


The following constants were used from included theories:

All constants that were mentioned were defined.


This document was generated using Ontolingua.
Formatting and translation code was written by
François Gerbaux and Tom Gruber