Theory TENSOR-QUANTITIES

• Last modified: Wednesday, 21 September 1994
• Source code: tensor-quantities.lisp
• List of other known theories

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:

• (c) 1993, 1994 Gregory R. Olsen and Thomas R. Gruber
  
• See-Also: The EngMath paper on line
  

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:

• =< defined as a relation in theory Kif-Numbers
• Abelian-Group defined as a relation in theory Abstract-Algebra
• Arity defined as a function in theory Frame-Ontology
• Class defined as a class in theory Frame-Ontology
• Column-Dimension defined as a function in theory Basic-Matrix-Algebra
• Constant-Quantity defined as a class in theory Physical-Quantities
• Defined defined as a class in theory Kif-Extensions
• Dimensionless-Quantity defined as a class in theory Physical-Quantities
• Distributes defined as a relation in theory Abstract-Algebra
• Documentation defined as a relation in theory Frame-Ontology
• Domain defined as a relation in theory Frame-Ontology
• Function defined as a class in theory Kif-Relations
• Identity-Dimension defined as a object in theory Physical-Quantities
• Identity-Matrix defined as a class in theory Basic-Matrix-Algebra
• Magnitude defined as a function in theory Physical-Quantities
• Matrix defined as a class in theory Basic-Matrix-Algebra
• Member defined as a relation in theory Kif-Sets
• Non-Negative-Integer defined as a class in theory Kif-Extensions
• Nth-Domain defined as a relation in theory Frame-Ontology
• Physical-Dimension defined as a class in theory Physical-Quantities
• Physical-Quantity defined as a class in theory Physical-Quantities
• Positive-Integer defined as a class in theory Kif-Extensions
• Quantity.Dimension defined as a function in theory Physical-Quantities
• Range defined as a relation in theory Frame-Ontology
• Row-Dimension defined as a function in theory Basic-Matrix-Algebra
• Row-Matrix defined as a class in theory Basic-Matrix-Algebra
• Scalar-Quantity defined as a class in theory Scalar-Quantities
• Size defined as a function in theory Basic-Matrix-Algebra
• Square-Matrix defined as a class in theory Basic-Matrix-Algebra
• Subclass-Of defined as a relation in theory Frame-Ontology
• Summation defined as a function in theory Physical-Quantities
• Superclass-Of defined as a relation in theory Frame-Ontology
• The-Zero-Scalar-For-Dimension defined as a function in theory Scalar-Quantities
• Transpose defined as a function in theory Basic-Matrix-Algebra
• Unit-Of-Measure defined as a class in theory Physical-Quantities
• Value defined as a function in theory Kif-Relations
• Value-Cardinality defined as a function in theory Frame-Ontology
• Value-Type defined as a relation in theory Frame-Ontology

All constants that were mentioned were defined.