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First define a manifold M with local coordinates and define a (covariant) metric on
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M >
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| (2.1) |
Example 1.
Compute the inner product of two vectors.
M >
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| (2.2) |
M >
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| (2.3) |
M >
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| (2.4) |
Example 2.
Compute the inner product of two 1-forms.
M >
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| (2.5) |
M >
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| (2.6) |
M >
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| (2.7) |
Example 3.
Compute the inner product of two 2-forms.
M >
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| (2.8) |
M >
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| (2.9) |
M >
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| (2.10) |
Example 4.
Compute the inner product of two rank-3 tensors.
M >
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| (2.11) |
M >
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| (2.12) |
M >
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Partial contractions of T and S can be computed.
M >
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| (2.14) |
M >
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| (2.15) |
Example 5.
Compute the inner product of two lists of rank-1 tensors (1-forms). In this case the efficiency of the command is improved if the keyword argument inversemetric is given.
M >
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| (2.16) |
| (2.17) |
M >
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| (2.18) |
M >
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