The DifferentialGeometry:-Tools sub-package 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(...).

&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.