Re: [fricas-devel] DeRhamComplex

Am 06.04.2016 um 00:21 schrieb Waldek Hebisch: > Kurt Pagani wrote: >> >> I'd like to suggest a slightly modified version of DeRhamComplex for the >> following reasons: >> >> A) in the current version we cannot use non-atomic symbols: >> >> (1) -> X:=DERHAM(INT,[x[i] for i in 1..4]) >> >>(1) D

Re: [fricas-devel] DeRhamComplex

Kurt Pagani wrote: > > I'd like to suggest a slightly modified version of DeRhamComplex for the > following reasons: > > A) in the current version we cannot use non-atomic symbols: > > (1) -> X:=DERHAM(INT,[x[i] for i in 1..4]) > >(1) DeRhamComplex(Integer,[x[1],x[2],x[3],x[4]]) >

Re: [fricas-devel] DeRhamComplex

Hello Waldek I'd like to suggest a slightly modified version of DeRhamComplex for the following reasons: A) in the current version we cannot use non-atomic symbols: (1) -> X:=DERHAM(INT,[x[i] for i in 1..4]) (1) DeRhamComplex(Integer,[x[1],x[2],x[3],x[4]])

Re: [fricas-devel] DeRhamComplex

On 12 October 2014 21:26, Waldek Hebisch wrote: > Bill Page wrote: >> >> There is some unpleasant code in DERHAM that presumes knowledge of the >> Rep of AntiSymm: >> >> terms : % -> List Record(k: EAB, c: R) >> terms(a) == >> -- it is the case that there are at least two terms

Re: [fricas-devel] DeRhamComplex

Bill Page wrote: > > There is some unpleasant code in DERHAM that presumes knowledge of the > Rep of AntiSymm: > > terms : % -> List Record(k: EAB, c: R) > terms(a) == > -- it is the case that there are at least two terms in a > a pretend List Record(k: EAB, c: R) > >

Re: [fricas-devel] DeRhamComplex

Kurt Pagani wrote: > > On Sunday, 12 October 2014 20:32:50 UTC+2, Waldek Hebisch wrote: > > > > Kurt Pagani wrote: > > > > > > It was indeed not very difficult. A simplex can be represented most > > > favourably as a matrix (rows = points of F) and FreeAbelianGroup will > do > > > the rest. > > >

Re: [fricas-devel] DeRhamComplex

Meanwhile I have rather realized what you mean: citation: http://en.wikipedia.org/wiki/Abstract_simplicial_complex <<< an *abstract simplicial complex* is a purely combinatorial description of the geometric notion of a simplicial complex , consist

Re: [fricas-devel] DeRhamComplex

On Sunday, 12 October 2014 20:32:50 UTC+2, Waldek Hebisch wrote: > > Kurt Pagani wrote: > > > > It was indeed not very difficult. A simplex can be represented most > > favourably as a matrix (rows = points of F) and FreeAbelianGroup will do > > the rest. > > I admit that I got lost in this t

Re: [fricas-devel] DeRhamComplex

Kurt Pagani wrote: > > It was indeed not very difficult. A simplex can be represented most > favourably as a matrix (rows = points of F) and FreeAbelianGroup will do > the rest. I admit that I got lost in this thread. However, what you do looks strange so I wonder if you really want this. Nam

[fricas-devel] DeRhamComplex

> Wouldn't that be easy? > > http://fricas.github.io/api/MonoidRing.html > > Maybe you'd have to implement k-chains as well with the help of > > http://fricas.github.io/api/FreeGroup.html > > It doesn't

Re: [fricas-devel] DeRhamComplex

On 10/09/2014 02:20 AM, Bill Page wrote: >> In fact, I wonder whether this isn't already in FriCAS. > I was wondering where in FriCAS you thought we might look. Oh. Sorry... that was just a guess of mine. There are many gems in FriCAS, one only has to find and learn about them. But maybe this part

Re: [fricas-devel] DeRhamComplex

> We need a mapping between manifolds, e.g. between the set of > independent variables of one DFORM into the independent variables of > another DFORM. > > My first thought is that maybe pullback and pushforward should be > exports of a package that is parameterized by a list of expressions.

Re: [fricas-devel] DeRhamComplex

On 8 October 2014 20:26, Kurt Pagani wrote: > > Some more bricks ... > attached is a first draft of the functions which IMO should be sufficient. Thanks! > Pull-back/push-forward have to be presumably in a higher-level domain as we > need a mapping F:X -->Y between two DFORM domains (??) > We n

Re: [fricas-devel] DeRhamComplex

There is some unpleasant code in DERHAM that presumes knowledge of the Rep of AntiSymm: terms : % -> List Record(k: EAB, c: R) terms(a) == -- it is the case that there are at least two terms in a a pretend List Record(k: EAB, c: R) I recall that this sort of thing was

Re: [fricas-devel] DeRhamComplex

On 8 October 2014 17:43, Ralf Hemmecke wrote: > On 10/08/2014 04:07 PM, Bill Page wrote: > >> Where do you think we should look for a possible "boundary operator"? > > I don't quite get your question. If I look at Earlier you wrote: On 8 October 2014 03:31, Ralf Hemmecke wrote: > ... > It doesn

Re: [fricas-devel] DeRhamComplex

On 10/08/2014 04:07 PM, Bill Page wrote: > Ralf, > > I would be interested if you could elaborate on this idea. Yes, > MonoidRing looks like it should be relevant and I agree that in the > development of functionality in a new area like DifferentalGeometry > one should be aware of and integrate w

Re: [fricas-devel] DeRhamComplex

Ralf, I would be interested if you could elaborate on this idea. Yes, MonoidRing looks like it should be relevant and I agree that in the development of functionality in a new area like DifferentalGeometry one should be aware of and integrate where possible existing related domains, e.g. FriCAS a

Re: [fricas-devel] DeRhamComplex

On 10/07/2014 09:49 PM, Kurt Pagani wrote: > I'm glad to hear. Maybe you could think about (or more if time allows ;) > how to implement simplices in the spirit of > http://en.wikipedia.org/wiki/Simplicial_homology such that one has for > instance formal sums of simplexes with integer coefficien

Re: [fricas-devel] DeRhamComplex

On Tuesday, 7 October 2014 19:15:32 UTC+2, Bill Page wrote: > > On 7 October 2014 12:13, Kurt Pagani > > wrote: > > > > On Tuesday, 7 October 2014 05:36:26 UTC+2, Bill Page wrote: > >> ... > >> Your examples look good to me, except I would definitely prefer not to > >> have to pass a metric

Re: [fricas-devel] DeRhamComplex

Thank you for the links. I had a look into the tutorial, very impressive indeed and good to know so we can compare our results. I'm confident we'll get close to it without being too 'academic', rigor yes but keep it simple (apparently there are 20k+ loc, which can certainly be maintained by big

Re: [fricas-devel] DeRhamComplex

Here is an example of an ambitious development in Sage that overlaps some your objectives for FriCAS: http://sagemanifolds.obspm.fr/ http://trac.sagemath.org/ticket/14865 On 7 October 2014 13:15, Bill Page wrote: > On 7 October 2014 12:13, Kurt Pagani wrote: > ... >> What I have in mind is fi

Re: [fricas-devel] DeRhamComplex

On 7 October 2014 12:13, Kurt Pagani wrote: > > On Tuesday, 7 October 2014 05:36:26 UTC+2, Bill Page wrote: >> ... >> Your examples look good to me, except I would definitely prefer not to >> have to pass a metric for each function call. > > In the first place I had included the functions, > >

Re: [fricas-devel] DeRhamComplex

? > > > > Works for me. The subject is now: Re: [fricas-devel] DeRhamComplex > strange, it's still in 'New Release'. > > > > > Following your suggestion (before having read above) I renamed the > domain to > > DiffForms/DFORM for the m

Re: [fricas-devel] DeRhamComplex

On 6 October 2014 21:59, Kurt Pagani wrote: >> > I opened a new thread for 'not to be off-topic'. > > didn't work, obviously :( > Maybe someone can move this? > Works for me. The subject is now: Re: [fricas-devel] DeRhamComplex > > Following your sugge

Re: [fricas-devel] DeRhamComplex

On Monday, 6 October 2014 23:57:34 UTC+2, Ralf Hemmecke wrote: > > On 10/06/2014 10:56 PM, Kurt Pagani wrote: > > I don't oppose to create a new domain, however, it would certainly be > based > > on DERHAM as it contains 95% of the work necessary. > > I haven't looked too deeply into this sub

Re: [fricas-devel] DeRhamComplex

On 6 October 2014 16:56, Kurt Pagani wrote: > > I opened a new thread for 'not to be off-topic'. Thank you. > For the sake of clarity we should compare 'a' definition of DeRham complex > http://ncatlab.org/nlab/show/de+Rham+complex with the description given in > derham.spad: > > ++ Description:

Re: [fricas-devel] DeRhamComplex

On 10/06/2014 10:56 PM, Kurt Pagani wrote: > I don't oppose to create a new domain, however, it would certainly be based > on DERHAM as it contains 95% of the work necessary. I haven't looked too deeply into this subject, but for additional functionality, it might be an option to consider writing

[fricas-devel] DeRhamComplex

I opened a new thread for 'not to be off-topic'. For the sake of clarity we should compare 'a' definition of DeRham complex http://ncatlab.org/nlab/show/de+Rham+complex with the description given in derham.spad: ++ Description: The deRham complex of Euclidean space, that is, the ++ class of di