Dear Hans, Thank you for new methods! It would take some time for me to understand them fully. Learning Lua, metafun, lmtx, wiki is always a challenge for me. I also wonder where is the boundary of ConTeXt. I hope that you and all members in this list are well from COVID-19. Thank you again. Best regards, Dalyoung

2020. 7. 20. 오후 5:36, Hans Hagen 작성:

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 -----------------------------------------------------------------

Hello, I am making progress and I almost get what I want to achieve but I still have two problems : how to color cells not containing numbers with the same color as the others ? how to color in salmon, for example, cells 1 2 ? 3 Thank you Fabrice \usecolors[X11] \startuseMPgraphic{DiagonalRule} rulethickness := \frameddimension{rulethickness}; drawoptions( withpen pencircle scaled rulethickness withcolor \MPcolor{\framedparameter{framecolor}}); pair leftcorner, rightcorner; leftcorner := (rulethickness, \overlayheight-rulethickness); rightcorner := (\overlaywidth-rulethickness, rulethickness); draw leftcorner -- rightcorner; \stopuseMPgraphic \defineoverlay [DiagonalRule] [\useMPgraphic{DiagonalRule}] \define[2]\DiagonalLabel{% \setuptabulate [after={\blank[\frameddimension{offset}]}] \starttabulate [|p|r|] \NC \NC #2 \NC\NR \NC #1 \NC \NC\NR \stoptabulate } \starttext \startluacode function Binom(n,k) if k > n then return "" elseif (n == 0 or k == 0) then return 1 else return math.round((n*Binom(n-1,k-1))/k) end end context.startxtable({"align={middle,lohi}, width=1cm,offset=0.8ex,bodyfont=9pt,framecolor=cyan"}) context.startxrow() context.startxcell({"background=DiagonalRule,background=color,backgroundcolor=thistle2"}) context("\\DiagonalLabel{\\m{n}}{\\m{k}}") context.stopxcell() for j = 0, 7 do context.startxcell({"background=color,backgroundcolor=thistle2"}) context(j) context.stopxcell() end context.startxcell({"background=color,backgroundcolor=thistle2"}) context("\\dots") context.stopxcell() context.stopxrow() for i = 0, 7 do context.startxrow() context.startxcell({"background=color,backgroundcolor=thistle2"}) context(i) context.stopxcell() for j = 0, 8 do context.startxcell() context(Binom(i,j)) context.stopxcell() end context.stopxrow() end context.startxrow() context.startxcell({"background=color,backgroundcolor=thistle2"}) context("\\dots") context.stopxcell() for i = 0, 8 do context.startxcell({"background=color,backgroundcolor=thistle2"}) context("") context.stopxcell() end context.stopxrow() context.stopxtable() \stopluacode \stoptext Le lun. 20 juil. 2020 à 14:55, Hans Hagen a écrit :

On 7/20/2020 2:40 PM, Jeong Dal wrote:

...

I also wonder where is the boundary of ConTeXt. The boundaries are set and shift by users (the mailing list) and curiosity (personal).

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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