[fricas-devel] Re: Order in algebra

2009-05-16 Thread Waldek Hebisch
Ralf Hemmecke wrote: > > Waldek, > > I think with your explanation, I can give my OK for the patch. > But don't you think it would be a good idea do develop that idea with > properly fixing the <-problem on a branch. It looks as if that could > take quite a while to do it right. > > But anywa

[fricas-devel] Re: Order in algebra

2009-05-15 Thread Ralf Hemmecke
Waldek, I think with your explanation, I can give my OK for the patch. But don't you think it would be a good idea do develop that idea with properly fixing the <-problem on a branch. It looks as if that could take quite a while to do it right. But anyway, since your patch will probably not br

[fricas-devel] Re: Order in algebra

2009-05-15 Thread Waldek Hebisch
Ralf Hemmecke wrote: > > Anyway, I look through your patch and found something that troubles me > (see below). > > In particular, I don't think that > > -d > 0 => > +smaller?(0, d) => > alpha:F := sqrt d > > makes sense. > > If I see correctly, the d is of type

[fricas-devel] Re: Order in algebra

2009-05-15 Thread Waldek Hebisch
Ralf Hemmecke wrote: > > Hi Waldek, > > I must admit, I only have a vague idea of what problem you want to > solve. Up to now I only guess that it has to do with having a unique > order that is used, for example, for printing or in other places where > an order of the elements is needed, the

[fricas-devel] Re: Order in algebra

2009-05-15 Thread Ralf Hemmecke
> http://www.math.uni.wroc.pl/~hebisch/fricas/o2b.diff The following patch is in some sense understandable, but otherwise also strange. Understandable, because it seems to have to do with what "smaller?" was intended for. Strange, because, here appears a redefinition of "negConstant". "neg" i

[fricas-devel] Re: Order in algebra

2009-05-15 Thread Ralf Hemmecke
Dear Waldek, On 05/15/2009 01:23 AM, Waldek Hebisch wrote: > I have now a patch which separates internal order needed for > technical reasons and for printing from mathematical order, > that is OrderedSet. The patch is at: > > http://www.math.uni.wroc.pl/~hebisch/fricas/o2b.diff Let me first s

[fricas-devel] Re: Order in algebra

2009-05-15 Thread Ralf Hemmecke
Hi Waldek, I must admit, I only have a vague idea of what problem you want to solve. Up to now I only guess that it has to do with having a unique order that is used, for example, for printing or in other places where an order of the elements is needed, the domain itself, however, does not pr

[fricas-devel] Re: Order in algebra

2009-05-15 Thread Martin Rubey
Waldek Hebisch writes: > I am not aware of resonable mathematical definition. Above > I used "natural" in informal way. Yes, I know, and I'd be surprised if there was a "mathematical" definition. But it would be good to find something that's at least close to a definition. I have to digest t

[fricas-devel] Re: Order in algebra

2009-05-15 Thread Ralf Hemmecke
> PS: one final personal thing: I strongly prefer > > Expression(R: Comparable): Exports +1 > > over > > Expression(R : Comparable): Exports -1 Ralf --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "

[fricas-devel] Re: Order in algebra

2009-05-15 Thread Waldek Hebisch
Martin Rubey wrote: > > Waldek Hebisch writes: > > > Martin Rubey wrote: > >> > >> I have a request: please document the difference between > >> > >> \section{category COMPAR Comparable} > >> <>= > >> )abbrev category COMPAR Comparable > >> > >> and > >> > >> \section{category ORDSET Order

[fricas-devel] Re: Order in algebra

2009-05-15 Thread Martin Rubey
Waldek Hebisch writes: > Martin Rubey wrote: >> >> I have a request: please document the difference between >> >> \section{category COMPAR Comparable} >> <>= >> )abbrev category COMPAR Comparable >> >> and >> >> \section{category ORDSET OrderedSet} >> <>= >> )abbrev category ORDSET OrderedS

[fricas-devel] Re: Order in algebra

2009-05-15 Thread Waldek Hebisch
Martin Rubey wrote: > > I have a request: please document the difference between > > \section{category COMPAR Comparable} > <>= > )abbrev category COMPAR Comparable > > and > > \section{category ORDSET OrderedSet} > <>= > )abbrev category ORDSET OrderedSet OrderedSet should be a natural orde

[fricas-devel] Re: Order in algebra

2009-05-15 Thread Waldek Hebisch
Ralf Hemmecke wrote: > > Hi Waldek, > > +Comparable(): Category == SetCategory with > + --operations > +smaller?: (%,%) -> Boolean > + ++ smaller?(x, y) is a strict total ordering on the elements of > the set. > > Just out of curiosity... > Is there any reason making Comparable inher

[fricas-devel] Re: Order in algebra

2009-05-15 Thread Ralf Hemmecke
> I guess it is roughly that OrderedSet respects "=" and "+", i.e., > > a < b, b = c => a < c and a + d < b + d I agree that OrderedSet might say something about a relation between < an =, but certainly, compatibility of < with + is a property that belongs to OrderedAbelianSemiGroup and no

[fricas-devel] Re: Order in algebra

2009-05-15 Thread Martin Rubey
Waldek Hebisch writes: > I have now a patch which separates internal order needed for > technical reasons and for printing from mathematical order, > that is OrderedSet. The patch is at: > > http://www.math.uni.wroc.pl/~hebisch/fricas/o2b.diff super! > I am still testing the patch, but unless

[fricas-devel] Re: Order in algebra

2009-05-15 Thread Ralf Hemmecke
Hi Waldek, +Comparable(): Category == SetCategory with + --operations +smaller?: (%,%) -> Boolean + ++ smaller?(x, y) is a strict total ordering on the elements of the set. Just out of curiosity... Is there any reason making Comparable inherit from SetCategory? I don't have a concrete

[fricas-devel] Re: Order in algebra

2009-05-14 Thread Gabriel Dos Reis
Waldek Hebisch writes: | I have now a patch which separates internal order needed for | technical reasons and for printing from mathematical order, | that is OrderedSet. The patch is at: > | http://www.math.uni.wroc.pl/~hebisch/fricas/o2b.diff Interesting enough, I was working on similar patch