#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):
Replying to [comment:20 vbraun]:
> Doctest coverage: `sage -coverage src/sage/tensor/`
OK I see: most private methods appear to have no doctest because their
doctests have been put in the docstring of the class itself: this is the
only way for them to appear in the generated html documentation. This is
particularly true for the `__init__` methods (there are actually a lot of
doctests for them). Shall the doctests be repeated in the docstring of the
private methods ? What is the general policy for this ?
> I don't think the string notation is very user friendly,
`A['^{ab}_{cd}']*B['^d_a']` looks more like line noise. How about
recognizing symbolic variables and the built-in function `any` as special:
>
> sage: var('a, d')
> sage: A[a, any, any, d] * B[d, a]
>
Your suggestion for `any` is quite compeling, thanks. Note that, in the
present version, it is already possible to replace unrelevant indices with
dots, which decreases the noise:
sage: S = A['^{a.}_{.d}']*B['^d_a']
> Or, perhaps better in the long run: Define your own index class that
knows about whether indices are upper or lower. Then we can also check
that you don't contract two upper indices, and/or automatically insert the
metric there:
>
> sage: a, b, c, d = A.indices()
> sage: a
> Upper index
> sage: A[a, b, c, d] * B[d, a]
You are right: in the long run, we should probably introduce an indice
class to get rid of the strings. The only advantage of the present
notation is that we do not have to spoil some variable names to denote
indices: they can be set on the fly, to denote an operation like
contraction where index notation is more clear, most operations being
performed in an index-free setting.
--
Ticket URL: <http://trac.sagemath.org/ticket/15916#comment:21>
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