Hi all,
Thank you for your contributions, it allows me to progress.
@Hans and Deal
The code is impressive but does not correspond to the shape of the triangle


that I have to make (by convention).
Fabrice

Le lun. 20 juil. 2020 à 10:36, Hans Hagen <j.hagen@xs4all.nl> a écrit :

> On 7/20/2020 7:56 AM, Jeong Dal wrote:
> > Dear Fabrice,
> >
> > You may split Binom(n,k) function into two functions as following:
> >
>  > see original mail
>  >
> > Dalyoung
> Best stay in a protected namespace ...
>
> \startluacode
>
>      local function fact (n)
>          if n <= 0 then
>              return 1
>          else
>              return n * fact(n-1)
>          end
>      end
>
>      local function ncr(n,r)
>          return fact(n)/(fact(r)*fact(n-r))
>      end
>
>      userdata.P = {
>          fact = fact,
>          ncr  = ncr,
>      }
>
>      function MP.pascal_ncr(n, r)
>          mp.print(ncr(n,r))
>      end
>
> \stopluacode
>
> Watch the last definition. This permits
>
>        % tt := lua("mp.print(userdata.P.ncr(" & decimal n & "," &
> decimal r & " ))");
>
> replaced by
>
>          tt := lua.MP.pascal_ncr(n,r);
>
> which looks nicer.
>
> \startbuffer[pt1]
>      numeric n, r, s, u, dx, dy, tt;
>      path p, q;
>      pair A, B, start, now;
>      u := 1.8cm;
>      A := dir(210)*u;
>      B := dir(-30)*u;
>      dy := sind(30)*u;
>      dx := 2*cosd(30)*u;
>      for n=0 upto 4:
>          start := n*dir(210)*u;
>          for r=0 upto n:
>              s := n-r;
>            % tt := lua("mp.print(userdata.P.ncr(" & decimal n & "," &
> decimal r & " ))");
>            tt := lua.MP.pascal_ncr(n,r);
>              now := start+r*right*dx;
>              dotlabel.top(textext("$\displaystyle {" & decimal n &
> "\choose" & decimal r & "} = "& decimal tt & "$"),now);
>              draw (now+A) -- now -- (now+B);
>          endfor;
>      endfor;
> \stopbuffer
>
> Now, in context lmtx we can have a different kind of abstraction. We can
> do this:
>
>      function MP.pascal_ncr_x()
>          mp.print(ncr(mp.scan.pair()))
>      end
>
> and then use:
>
>      tt := runscript("MP.pascal_ncr_x()") (n,r) ;
>
> Of course one can decide to pick to two numerics instead, like
>
>      tt := runscript("MP.pascal_ncr_x()") n r ;
>
> but i leave that as exercise.
>
>            % tt := runscript mp_pascal_ncr (n,r) ;
>              tt := pascal_ncr (n,r) ;
>
> However, we still have the rather verbose runscript here, so we go
> further, we register pascal as script:
>
> \startluacode
>      metapost.registerscript("pascal_ncr",MP.pascal_ncr_x)
> \stopluacode
>
> And then define an alias at the metafun end:
>
> \startMPextensions
>      newinternal mp_pascal_ncr ; mp_pascal_ncr := scriptindex "pascal_ncr"
> ;
>
>      def pascal_ncr =
>          runscript mp_pascal_ncr
>      enddef ;
> \stopMPextensions
>
> The internal permits this:
>
>     tt := runscript mp_pascal_ncr (n,r) ;
>
> while the additional def permits
>
>              tt := pascal_ncr (n,r) ;
>
> Now watch out, because we define pascal_ncr here, something
> lua.MP.pascal_ncr(n,r) won't work because the last part gets expanded
> because that is what mp does (i'll probably cook something for that some
> day).
>
> Now, to come back to
>
>     "I couldn’t wikify it at that time because I don’t know
>      how to.  I’ll do it soon."
>
> looks like you suddenly have an additional challenge,
>
> Hans
>
>
>
> -----------------------------------------------------------------
>                                            Hans Hagen | PRAGMA ADE
>                Ridderstraat 27 | 8061 GH Hasselt | The Netherlands
>         tel: 038 477 53 69 | www.pragma-ade.nl | www.pragma-pod.nl
> -----------------------------------------------------------------
>
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