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Overview of the Tools package

Description

 • The DifferentialGeometry:-Tools subpackage contains a number of utility procedures which are used primarily in the development of new DifferentialGeometry applications.
 • Each of the commands in the DifferentialGeometry:-Tools package can only be accessed by first executing with(DifferentialGeometry) and with(Tools), in that order or by using the long form of the command DifferentialGeometry:-Tools:-Command(...).

List of the Tools commands

The following is a list of available commands.

A brief description of the package's commands is as follows.

 • &MatrixMinus: subtract two Matrices or Vectors of vector fields, differential forms, or tensors.
 • &MatrixMult: multiply a Matrix of vectors, differential forms or tensors by a scalar or by a Matrix of scalars.
 • &MatrixPlus: add two Matrices or Vectors of vector fields, differential forms, or tensors.
 • &MatrixWedge: calculate the Matrix wedge product of two Matrices/Vectors of differential forms.
 • CalculationHistory: a module to store and retrieve important intermediate computations.
 • CanonicalBasis: calculate a standard basis for a subspace of vectors, forms, or tensors.
 • DGbiform: create a monomial bi-form.
 • DGform: create a monomial form.
 • DGinfo: obtain information about a DifferentialGeometry object.
 • DGmain: a module containing fast versions of some DifferentialGeometry procedures.
 • DGmap: apply a procedure to the coefficients of a vector, differential form or tensor.
 • DGscalar: create a degree 0 differential form or a rank 0 tensor.
 • DGsimplify: simplify a vector, differential form, or tensor.
 • DGtensor: create a monomial tensor.
 • DGvector: create a monomial vector.
 • DGvolume: create a top degree differential form.
 • DGzero: create a zero vector, differential form, or tensor.
 • Divergence: calculate the divergence of a vector field.
 • DGequal: test if two DifferentialGeometry objects are equal.
 • GenerateForms: create a list of differential forms.
 • IdentityTransformation: define the identity transformation on a manifold.