#15916: Tensors on free modules of finite rank
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Reporter: egourgoulhon | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: linear algebra | Resolution:
Keywords: free module, | Merged in:
tensor, tensor product | Reviewers:
Authors: Eric Gourgoulhon, | Work issues:
Michal Bejger | Commit:
Report Upstream: N/A | d8f518ff48c8be2ea73f2b51e067af9e6c87b4bf
Branch: | Stopgaps:
u/egourgoulhon/tensor_modules |
Dependencies: |
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Comment (by egourgoulhon):
The ticket has been updated to coincide with the pure algebraic part of
[http://sagemanifolds.obspm.fr/ SageManifolds v0.6]. Changes are:
1/ The possibility to use index notations for denoting tensor contractions
or symmetrizations: the indices have to be passed in LaTeX notations
(possibly without {}) as a string inside the square bracket operator, e.g.
{{{
sage: S = A['^{ab}_{cd}']*B['^d_a'] # equivalent to S = A.contract(0, 3,
B, 1, 0)
}}}
to denote the tensor S^b^,,c,, = A^ab^,,cd,, B^d^,,a,, ,
{{{
sage: S = A['^{(ab)}_{cd}'] # equivalent to S = A.symmetrize(0,1)
}}}
to denote the tensor S^ab^,,cd,, = A^(ab)^,,cd,,, and
{{{
sage: S = A['^{ab}_{[cd]}'] # equivalent to S = A.antisymmetrize(2,3)
}}}
to denote the tensor S^ab^,,cd,, = A^ab^,,[cd],,.
See
[http://sagemanifolds.obspm.fr/doc/tensors_free_module/tensor_with_indices.html
this page] and
[http://sagemanifolds.obspm.fr/doc/tensors_free_module/free_module_tensor.html#sage.tensor.modules.free_module_tensor.FreeModuleTensor.contract
this one] for more details.
2/ The code for tensor contractions has been completely rewritten; it is
more efficient and allows now for multiple contractions (as in the first
example above).
3/ The argument of methods `symmetrize()` and `antisymmetrize()` in the
`FreeModuleTensor` class is now directly a sequence of index positions
(and no longer a single list/tuple encapsulating such a sequence).
Besides, new examples have been provided on
http://sagemanifolds.obspm.fr/examples.html; two of them are directly
relevant to this ticket:
* [http://sagemanifolds.obspm.fr/examples/html/SM_tensors_modules.html
tensors on free modules of finite rank] (tutorial)
* [http://sagemanifolds.obspm.fr/examples/html/SM_vector_fields_S2.html
vector-field modules on the 2-sphere] (a concrete example of use)
--
Ticket URL: <http://trac.sagemath.org/ticket/15916#comment:19>
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