DefManifold.nb_1.html

Further Examples

Load the packages:

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Define a simple manifold:

Define a 3d manifold M.The correspondint tangent vbundle TangentM is also defined:

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This is all the information associated to the manifold:

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Global`M

ManifoldQ[M]^=True

SubmanifoldsOfManifold[M]^={}

Info[M]^={manifold,}

PrintAs[M]^=M

DimOfManifold[M]^=3

TangentBundleOfManifold[M]^=TangentM

ServantsOf[M]^={TangentM}

Currently we only have one manifold:

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It can be undefined, also removing the associated tangent vbundle:

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Now define a manifold with symbolic dimension and using reserved symbols as indices:

Define a constant symbol:

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Then we can define a manifold MC with unspecified dimension. Note that we use the Mathematica symbols C and D. The symbol E cannot be used because it has numeric value:

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The symbol C has been overloaded:

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Attributes[C]={NHoldAll,Protected}

AbstractIndexQ[C]^=True

PrintAs[C]^=C

VBundleOfIndex[C]^=TangentMC

TangentMC`Q[C]^=True

DaggerIndex[C]^=C

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Undefine the manifold:

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Now the additional definitions for C have been removed:

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Attributes[C]={NHoldAll,Protected}

Created by Mathematica (May 16, 2008)