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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeAug 27th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexcreated [[gradient]]

   created gradient

2. • CommentRowNumber2.
   • CommentAuthordomenico_fiorenza
   • CommentTimeAug 31st 2011
   • (edited Aug 31st 2011)
   • PermaLink
   Author: domenico_fiorenza
   Format: MarkdownItexcreated stubs for [[curl]] and [[divergence]]

   created stubs for curl and divergence

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeAug 31st 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks! I have added more links and a TOC.

   Thanks!

   I have added more links and a TOC.

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeAug 31st 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownItexI added redirect [[rotation of a vector field]] to the more cryptic anglosaxon alternative [[curl]] (and which I could prefer to be a title in fact, wikipedia givee 2.1 mil hits, for curl of a vactor field 320 thousand hits).

   I added redirect rotation of a vector field to the more cryptic anglosaxon alternative curl (and which I could prefer to be a title in fact, wikipedia givee 2.1 mil hits, for curl of a vactor field 320 thousand hits).

5. • CommentRowNumber5.
   • CommentAuthordomenico_fiorenza
   • CommentTimeAug 31st 2011
   • PermaLink
   Author: domenico_fiorenza
   Format: MarkdownItexadded a link to and created a stub for [[symplectic gradient]]. By trhe way, I notice now that [[moment map]] is still very stubby; i hope to be able to expand that soon.

   added a link to and created a stub for symplectic gradient. By trhe way, I notice now that moment map is still very stubby; i hope to be able to expand that soon.

6. • CommentRowNumber6.
   • CommentAuthorTobyBartels
   • CommentTimeAug 31st 2011
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexPeople are forgetting that you need an orientation, not just a metric, to do Hodge duals (and thus, for example, to define the curl of a vector field as a vector field on a Riemannian $3$-fold).

   People are forgetting that you need an orientation, not just a metric, to do Hodge duals (and thus, for example, to define the curl of a vector field as a vector field on a Riemannian $3$-fold).

7. • CommentRowNumber7.
   • CommentAuthorzskoda
   • CommentTimeAug 31st 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownItexgo on, jump in, I seem not to have time these days to reconcentrate on this topic, which I started

   go on, jump in, I seem not to have time these days to reconcentrate on this topic, which I started

8. • CommentRowNumber8.
   • CommentAuthorzskoda
   • CommentTimeSep 1st 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownItexAnyway, I did expand [[moment map]] following Joel Robbin's notes (well, I think I have learned the first steps into the subject from my advisor, so I follow his notes). Still not much there but at least the basic reasoning leading to the definition is produced (and the literature).

   Anyway, I did expand moment map following Joel Robbin’s notes (well, I think I have learned the first steps into the subject from my advisor, so I follow his notes). Still not much there but at least the basic reasoning leading to the definition is produced (and the literature).

9. • CommentRowNumber9.
   • CommentAuthorTobyBartels
   • CommentTimeSep 2nd 2011
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexUnhappy that we had the [[curl]] only in the classical $3$ dimensions, I discussed its relation to the [[cross product]] and described nonclassical cross products. The latter page is now massively general!

   Unhappy that we had the curl only in the classical $3$ dimensions, I discussed its relation to the cross product and described nonclassical cross products. The latter page is now massively general!

10. • CommentRowNumber10.
    • CommentAuthorzskoda
    • CommentTimeSep 2nd 2011
    • PermaLink
    Author: zskoda
    Format: MarkdownItexWell, a further justification should go from the Stokes theorem. I mean, there is a limit of an integral formula for the rotation of the vector field, similar to the one for the divergence.

    Well, a further justification should go from the Stokes theorem. I mean, there is a limit of an integral formula for the rotation of the vector field, similar to the one for the divergence.

11. • CommentRowNumber11.
    • CommentAuthorzskoda
    • CommentTimeSep 2nd 2011
    • (edited Sep 2nd 2011)
    • PermaLink
    Author: zskoda
    Format: MarkdownItexI mean $$ rot \vec\mathcal{A} = lim_{vol D\to 0} \frac{1}{vol D} \oint_{\partial D} \vec{n}\times \vec\mathcal{A} d S $$ $$ div \vec\mathcal{A} = lim_{vol D\to 0} \frac{1}{vol D} \oint_{\partial D} \vec{n}\cdot \vec\mathcal{A} d S $$ where $D$ runs over the domains with smooth boundary containing point $x$ at which the rotation or the divergence of the vector field is calculated. These formulas are invariant.

    I mean

    $$rot \vec\mathcal{A} = lim_{vol D\to 0} \frac{1}{vol D} \oint_{\partial D} \vec{n}\times \vec\mathcal{A} d S$$ $$div \vec\mathcal{A} = lim_{vol D\to 0} \frac{1}{vol D} \oint_{\partial D} \vec{n}\cdot \vec\mathcal{A} d S$$

    where $D$ runs over the domains with smooth boundary containing point $x$ at which the rotation or the divergence of the vector field is calculated. These formulas are invariant.

12. • CommentRowNumber12.
    • CommentAuthorzskoda
    • CommentTimeSep 2nd 2011
    • PermaLink
    Author: zskoda
    Format: MarkdownItexI added the above remarks in the case of [[divergence]] (in which case this works in any dimension).

    I added the above remarks in the case of divergence (in which case this works in any dimension).

13. • CommentRowNumber13.
    • CommentAuthorzskoda
    • CommentTimeSep 2nd 2011
    • PermaLink
    Author: zskoda
    Format: MarkdownItexNew entry [[nabla]] and additions to [[rotation of a vector field]].

    New entry nabla and additions to rotation of a vector field.

14. • CommentRowNumber14.
    • CommentAuthorTobyBartels
    • CommentTimeSep 5th 2011
    • PermaLink
    Author: TobyBartels
    Format: MarkdownItexI've generalised [[nabla]] to discuss all applications of the operator, defined using the integral formula in a very general way, and moved the formula originally there (for the gradient only) to [[gradient]].

    I’ve generalised nabla to discuss all applications of the operator, defined using the integral formula in a very general way, and moved the formula originally there (for the gradient only) to gradient.

15. • CommentRowNumber15.
    • CommentAuthorzskoda
    • CommentTimeSep 5th 2011
    • PermaLink
    Author: zskoda
    Format: MarkdownItexRight, I have left it in a rudimentary form, planning something similar and I am happy with your way of finishing the job!

    Right, I have left it in a rudimentary form, planning something similar and I am happy with your way of finishing the job!

16. • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeSep 5th 2011
    • PermaLink
    Author: Urs
    Format: MarkdownItexThere is something funny going on with the rendering: at least on my system that \nabla \odot T in the entry sometimes (such as in the big displayed formula) comes out as "$\nabla box T$".

    There is something funny going on with the rendering: at least on my system that

      \nabla \odot T
    

    in the entry sometimes (such as in the big displayed formula) comes out as “$\nabla box T$”.

17. • CommentRowNumber17.
    • CommentAuthorTobyBartels
    • CommentTimeSep 5th 2011
    • PermaLink
    Author: TobyBartels
    Format: MarkdownItexYou probably caught this while I was in the midst of editing for itex's capabilities. Reload the page and check again.

    You probably caught this while I was in the midst of editing for itex’s capabilities. Reload the page and check again.

18. • CommentRowNumber18.
    • CommentAuthorUrs
    • CommentTimeSep 5th 2011
    • PermaLink
    Author: Urs
    Format: MarkdownItexAh, right, now it dsiplays correctly.

    Ah, right, now it dsiplays correctly.