Overview of the Tools package - Maple Help

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Overview of the Tools package

Description

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The DifferentialGeometry:-Tools sub-package contains a number of utility procedures which are used primarily in the development of new DifferentialGeometry applications.

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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.

&MatrixMinus

&MatrixMult

&MatrixPlus

&MatrixWedge

CalculationHistory

CanonicalBasis

DGbiform

DGform

DGinfo

DGmain

DGmap

DGscalar

DGsimplify

DGtensor

DGvector

DGvolume

DGzero

Divergence

DGequal

GenerateForms

IdentityTransformation

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

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&MatrixMinus: subtract two Matrices or Vectors of vector fields, differential forms, or tensors.

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&MatrixMult: multiply a Matrix of vectors, differential forms or tensors by a scalar or by a Matrix of scalars.

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&MatrixPlus: add two Matrices or Vectors of vector fields, differential forms, or tensors.

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&MatrixWedge: calculate the Matrix wedge product of two Matrices/Vectors of differential forms.

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CalculationHistory: a module to store and retrieve important intermediate computations.

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CanonicalBasis: calculate a standard basis for a subspace of vectors, forms, or tensors.

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DGbiform: create a monomial bi-form.

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DGform: create a monomial form.

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DGinfo: obtain information about a DifferentialGeometry object.

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DGmain: a module containing fast versions of some DifferentialGeometry procedures.

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DGmap: apply a procedure to the coefficients of a vector, differential form or tensor.

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DGscalar: create a degree 0 differential form or a rank 0 tensor.

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DGsimplify: simplify a vector, differential form, or tensor.

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DGtensor: create a monomial tensor.

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DGvector: create a monomial vector.

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DGvolume: create a top degree differential form.

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DGzero: create a zero vector, differential form, or tensor.

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Divergence: calculate the divergence of a vector field.

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DGequal: test if two DifferentialGeometry objects are equal.

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GenerateForms: create a list of differential forms.

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IdentityTransformation: define the identity transformation on a manifold.

See Also

DifferentialGeometry, GroupActions, JetCalculus, Library, LieAlgebras, Tensor


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