Re: [Maxima-discuss] continued fraction display improvement

[Eduardo O. <edu...@gm...>]

Hi Jerry,

Here's a beginner's approach to building a Maxima object corresponding
to your figure at the bottom left of the page:

  texput(ldots, "\\ldots");
  o : lambda([], b[0]+a[1]/(b[1]+a[2]/(b[2]+ldots)));
  simp : false;
  o();
  tex(o())$

The last two lines yield this:

  (%i4) o();
                                          a
                                           1
  (%o4)                        b  + ---------------
                                0            a
                                              2
                                    b  + ----------
                                     1   b  + ldots
                                          2
  (%i5) tex(o())$
  $$b_{0}+{{a_{1}}\over{b_{1}+{{a_{2}}\over{b_{2}+\ldots}}}}$$
  (%i6)

When I was asking for help to write this -

  http://angg.twu.net/eev-maxima.html#luatree

Robert Dodier sent this idea,

  https://sourceforge.net/p/maxima/mailman/message/37690570/

that should be easy to adapt to your case, but I haven't tried that...

  Cheers,
    Eduardo Ochs
    http://angg.twu.net/eev-maxima.html


On Fri, 26 Aug 2022 at 05:17, Jerry <wj...@gm...> wrote:

> I have worked on continued fractions for over 40 years and have many
> unpublished works.  It would be of great help to put an option in funmake
> so that it does not simplify the representation into a mess.   The Macsyma
> company that is now defunct did this so that continued fractions could be
> easily displayed in the traditional form.
> [image: image.png]
> They produced funmake_no_simp which does not simplify so that one can take
> numerators and denominators to produce a continued fraction rather than a
> strictly Regular continued fraction.  In this simple example for e^x, the
> numerators are the same, but suppose I have a symbolic list such as
> [b[0], b[1], b[2],...] that I want to put in the numerators, I cannot seem
> to display it.
>
> eg
> makecf(nums,dens,%,[last]):=block([],negsumdispflag:false,
>   last:if last=[] then "."["."["."]] else first(last),
>   for i:1 thru % do
>    last:funmake_no_simp("+",[apply(nums,[%-i+1])/last,apply(dens,[%-i])]),
>   last);
>
> then
> makeit(nn):= makecf(lambda([n],x-x0),lambda([n],(a[n])),nn)
> Where all the numerators are x-x0 for an expansion around x0 and a[n] are
> the denominators with a[0] the separate additive term.
>
> Maxima produces for e^x a rather non-satisfying representation:
>
>
>        --------------------------------------- + 1
>
>                            x
>
>           ----------------------------------- + 1
>
>                          x
>
>           ------------------------------- - 2
>
>                        x
>
>           --------------------------- - 3
>
>                      x
>
>           ----------------------- + 2
>
>                    x
>
>           ------------------- + 5
>
>                  x
>
>           --------------- - 2
>
>                x
>
>           ----------- - 7
>
>              x
>
>           ------- + 2
>
>            x
>
>           --- + 9
>
>           .
>
>            .
>
>             .
> It is a great deal of difficulty to take arrays or lists and put them into
> an equation editor than to just paste the result as previously.
>
> To pique your interest, I attach one of my whiz bang results
> (unpublished).  I have hundreds of cf programs for Macsyma that I could
> share.  The bottom left corner is what I need in Maxima.
>
> Thank you.
> WJ Lentz
> mar...@gm...
> 831 601 2120
>
> _______________________________________________
> Maxima-discuss mailing list
> Max...@li...
> https://lists.sourceforge.net/lists/listinfo/maxima-discuss
>