Actually, we are currently working at removing strings. If you download the
latest version from the git server (see the instructions on the web page;
it should become version 0.4 soon), you would notice that the new syntax is
X.<x,y,z> = M.chart('x y z')
The string 'xyz', which was used as a chart identifier, has disappeared.
Indeed, the charts have been made hashable and are now used directely as
keys in internal dictionaries (like the dictionary of the various
coordinate expressions of a given scalar field), instead of their string
"identifier".
Le mercredi 18 décembre 2013 13:34:18 UTC+1, maldun a écrit :
>
> Good Job!
>
> But I have to agree with Volker, using strings is not a good idea.
> Why not using functions as input instead?
>
> e.g. in your example from the tutorial:
>
> X.<x,y,z> = M.chart('x y z', 'xyz')
>
> I would use something like
> var('x y z')
> charti = x*y*z
>
> X = M.chart(vars = [x,y,z], map = charti)
>
>
> On Sunday, November 24, 2013 10:32:45 PM UTC+1, Eric Gourgoulhon wrote:
>>
>> Hi,
>>
>> We have just posted a new version (0.3) of SageManifolds at
>> http://sagemanifolds.obspm.fr
>> SageManifolds is an attempt to include differential geometry and tensor
>> calculus in Sage (cf. the initial
>> post<https://groups.google.com/forum/#!topic/sage-devel/RjqMIWjSC-0>,
>> the v0.2
>> post<https://groups.google.com/forum/#!topic/sage-devel/j1zfFSFwsjg>
>> and trac
>> 14865<http://www.google.com/url?q=http%3A%2F%2Ftrac.sagemath.org%2Fticket%2F14865&sa=D&sntz=1&usg=AFQjCNGzTrK0EbxxuoTmTNi55FE3PHB8aA>).
>>
>> It is still in some preliminary stage but following the comments made on
>> this list and during meetings of Paris Sage group (thanks to all!), we have
>> worked towards a better integration into Sage. In particular:
>>
>> - Parent / Element scheme is now used for Manifold / Point
>> - The instantiation of most objects is now performed via factory
>> methods, so that there is no need to have the class name in the global
>> namespace and tab completion can be used to guess the method to employ.
>> - The coordinates associated with a chart are no longer put by
>> default in the global namespace; to do so, one has to use the preparser
>> tool <x,y,...> during the chart instantiation.
>>
>> For example, the sphere S^2, along with the two charts associated with
>> stereographic projections from two poles, is set up as follows:
>>
>> sage: M = Manifold(2, 'S^2') # 2 = dimension of the manifold
>> sage: U = M.open_domain('U') # the complement of the North pole
>> sage: stereoN.<x,y> = U.chart('x y', 'stereoN') # (x,y) = stereographic
>> coord. from the North pole
>> sage: V = M.open_domain('V') # the complement of the South pole
>> sage: stereoS.<u,v> = V.chart('u v', 'stereoS') # (u,v) = stereographic
>> coord. from the South pole
>> sage: phi = stereoN.transition_map(stereoS, (x/(x^2+y^2), y/(x^2+y^2)), \
>> ....: intersection_name='W', \
>> ....: chart1_name='stereoN_W', restrictions1=[x^2+y^2!=
>> 0], \
>> ....: chart2_name='stereoS_W', restrictions2=[u^2+v^2!=
>> 0])
>> sage: phi(x,y)
>> (x/(x^2 + y^2), y/(x^2 + y^2))
>> sage: M.domains['W'] is U.intersection(V)
>> True
>> sage: M.atlas
>> {'stereoN': chart 'stereoN' (U, (x, y)),
>> 'stereoN_W': chart 'stereoN_W' (W, (x, y)),
>> 'stereoS': chart 'stereoS' (V, (u, v)),
>> 'stereoS_W': chart 'stereoS_W' (W, (u, v))}
>> sage: M.frames
>> {'stereoN_W_b': coordinate basis 'stereoN_W_b' (d/dx,d/dy),
>> 'stereoN_b': coordinate basis 'stereoN_b' (d/dx,d/dy),
>> 'stereoS_W_b': coordinate basis 'stereoS_W_b' (d/du,d/dv),
>> 'stereoS_b': coordinate basis 'stereoS_b' (d/du,d/dv)}
>>
>>
>> The sphere example is detailed on
>> http://sagemanifolds.obspm.fr/examples.html (embedding into R^3, induced
>> metric, curvature, spherical coordinates).
>>
>> Many things remain to be done. People interested in contributing are
>> welcome! We have set up a git repository (
>> https://gitroc.obspm.fr/gitweb/SageManifolds.git) for this (see the
>> instructions here), as well as a mailing list.
>>
>> Eric Gourgoulhon & Michal Bejger.
>>
>>
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