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.ha...@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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