Overview of the Tools package
List of the Tools commands
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(...).
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.
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