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0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }{PSTYLE "" 0 260 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 
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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
258 "" 0 "" {TEXT -1 52 "Copyright (c) Pierre L. Douillet <douillet@cn
am.fr>\n" }}{PARA 259 "" 0 "" {TEXT -1 282 "libre reproduction pour un
 usage universitaire sous reserve d'une copie compl\350te,\navec repro
duction du programme source dont, en particulier, la pr\351sente menti
on\n\naucune garantie de fiabilit\351. en particulier, toute utilisati
on dans un contexte industriel est vivement d\351conseill\351e\n " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "restart; gc( ); " }}}{EXCHG 
{PARA 18 "" 0 "" {TEXT -1 13 "Ndiff_(V5.15)" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 45 "interface(verboseproc=1); ever_load:=  NULL :" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "# ndiff[]:= 'readlib'(`ndiff
/`) : savelib(`ndiff/`, `ndiff/.m`) : \n# mod\350le de d\351claration
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 
0 "" {TEXT -1 22 "Routines pr\351paratoires" }}{SECT 0 {PARA 4 "" 0 "
" {TEXT -1 28 "Cr\351ation de la liste savelib" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 891 "unprotect (savelib) : ssavelib:= NULL:  \nsavel
ib:= proc() local filename, values, library, pathname, f; \nglobal sav
elibname, ssavelib;\n  if not assigned(savelibname) then savelibname :
= op(1, [libname]) fi;\n  filename := args[nargs];\n  if not type(file
name, \{symbol,string\}) then \n     ERROR(`last argument (filename) m
ust be a symbol/string`) fi;\n  values := args[1 .. nargs - 1];\n  if \+
not type([values], list(\{symbol, string\})) then \n     ERROR(`argume
nts must be symbol/string`) fi;\n  if not type([savelibname], list(str
ing)) then \n     ERROR(`savelibname assigned improperly`) fi;\nssavel
ib:= ssavelib, values;\n    for library in [savelibname] do\n        p
athname := cat(library, '`/`', filename);\n        f := subs('T' = (va
lues, pathname), proc() save T end);\n        if traperror(f()) <> las
terror then RETURN() fi\n    od;\n    ERROR(`unable to save `.filename
.` in`, savelibname)\nend :" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 4 "i
nit" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "system(dater): fd:= f
open(\"c:/windows/date.txt\", READ):\ndate_string:= readline(fd): fclo
se(fd):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "message = \"ndiff  ;  a
uthor : <douillet@cnam.fr>  ;  last modif (V5) : \".\n (substring(date
_string, 22..35)):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "`ndiff/init`
:= subs(% , proc( ) option `Copyright Pierre L. Douillet`; \nunprotect
(gamma);\nprint(convert(message, symbol)) end ) : %();" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#%eondiff~~;~~author~:~<douillet@cnam.fr>~~;~~last~
modif~(V5)~:~Sam~09/12/2000G" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 8 "
xreadlib" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 249 "xreadlib:= proc
(qui::uneval) option `Copyright Pierre L. Douillet` ; local qui2, ou ;
 \nqui2:= eval(qui,1); to 10 do ou:= searchtext('`/`', qui2); if ou = \+
0 then break fi;\nqui2:= substring(qui2, ou+1..-1): assign(qui2, readl
ib(qui)); od; qui2 ;\n end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)xrea
dlibGR6#'%$quiG%'unevalG6$%%qui2G%#ouG6#%=Copyright~Pierre~L.~Douillet
G6\"C%>8$-%%evalG6$9$\"\"\"?(F/F7F7\"#5%%trueGC&>8%-%+searchtextG6$.%
\"/GF2@$/F=\"\"!%&breakG>F2-%*substringG6$F2;,&F=F7F7F7!\"\"-%'assignG
6$F2-%(readlibG6#F6F2F/F/F/" }}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 92 "Package Ndiff (xdiff, x
push, xleibniz, diff/Xdiff, int/Xdiff, combine/Xdiff, simplify/Xdiff)
" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "# une procedure explicitement \+
lineaire" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 471 "Xdi
ff := proc(quoi,qui, nb) option remember, `Copyright Pierre L. Douille
t, 1996`; \nlocal quoi1, qui1, nb1; \nif quoi=0 then 0\nelif nb=0 then
 quoi \nelif type(quoi,`*`)  and remove(has, quoi, qui) <> 1\n  then r
emove(has,quoi,qui)* 'Xdiff' (select(has,quoi,qui), qui,nb) \nelif typ
ematch(quoi, 'Xdiff'(quoi1::anything, qui1::name, nb1::anything)) and \+
\n     qui1=qui then procname(quoi1, qui, nb+nb1) \nelif type(quoi,`+`
) then map(procname, args) \nelse 'Xdiff'(args) fi end ; " }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%&XdiffGR6%%%quoiG%$quiG%#nbG6%%&quoi1G%%qui1G
%$nb1G6$%)rememberG%CCopyright~Pierre~L.~Douillet,~1996G6\"@-/9$\"\"!F
5/9&F5F43-%%typeG6$F4%\"*G0-%'removeG6%%$hasGF49%\"\"\"*&F>FC-.F$6%-%'
selectGF@FBF7FC3-%*typematchG6$F4-FF6%'8$%)anythingG'8%%%nameG'8&FR/FT
FB-9!6%FQFB,&F7FCFWFC-F:6$F4%\"+G-%$mapG6$FZ9\"-FF6#F]oF1F1F1" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "# procedure xpush" }{MPLTEXT 1 0 
0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 267 "xpush :=proc(expr) options \+
`Copyright Pierre L. Douillet, 1996`; \nif type (expr,  'Xdiff' (anyth
ing $3)) then \n Xdiff ( combine( diff(op(1,expr),op(2,expr)) , 'power
') , op(2,expr), op(3,expr)-1) \nelif has(expr, 'Xdiff') then map(proc
name, args) else expr fi; \nend;  " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%&xpushGR6#%%exprG6\"6#%CCopyright~Pierre~L.~Douillet,~1996GF(@'-%%ty
peG6$9$-.%&XdiffG6#-%\"$G6$%)anythingG\"\"$-F26%-%(combineG6$-%%diffG6
$-%#opG6$\"\"\"F/-FB6$\"\"#F/.%&powerGFE,&-FB6$F8F/FD!\"\"FD-%$hasG6$F
/F1-%$mapG6$9!9\"F/F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "#pro
cedure xleibniz" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 517 "xleibniz:= proc
(expr, fact::polynom) option `Copyright Pierre L. Douillet, 1996`;\nlo
cal exp1, exp2, xx, nn, k;\n  if fact=0 then ERROR()\n  elif typematch
(expr, 'Xdiff'(exp1::anything, xx::name, nn::algebraic)) then\n    k:=
'k': exp2 := combine(normal(exp1/fact), power);\n    fact *Xdiff(exp2,
 xx, nn ) +\n    sum(diff(fact, xx $ k)*Xdiff(exp2, xx, nn - k)*binomi
al(nn, k), k = 1 .. degree(fact));\n    collect(%, Xdiff, z -> ``(xfac
tor(expand(z))))\n  elif has(expr, 'Xdiff') then map(procname, args)\n
  else expr\n  fi\nend;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)xleibniz
GR6$%%exprG'%%factG%(polynomG6'%%exp1G%%exp2G%#xxG%#nnG%\"kG6#%CCopyri
ght~Pierre~L.~Douillet,~1996G6\"@)/9%\"\"!-%&ERRORGF3-%*typematchG6$9$
-.%&XdiffG6%'8$%)anythingG'8&%%nameG'8'%*algebraicGC&>8(.FM>8%-%(combi
neG6$-%'normalG6#*&FC\"\"\"F6!\"\"%&powerG,&*&F6\"\"\"-F@6%FPFFFIFgnFg
n-%$sumG6$*(-%%diffG6$F6-%\"$G6$FFFMFgn-F@6%FPFF,&FIFgnFM!\"\"Fgn-%)bi
nomialG6$FIFMFgn/FM;Fgn-%'degreeG6#F6Fgn-%(collectG6%%\"%GF@R6#%\"zGF3
6$%)operatorG%&arrowGF3-%!G6#-%(xfactorG6#-%'expandG6#F=F3F3F3-%$hasG6
$F=F?-%$mapG6$9!9\"F=F3F3F3" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "# \+
d\351rivation  " }{MPLTEXT 1 0 1 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
161 "`diff/Xdiff`:= proc(uu,xx,nb,yy) options `Copyright Pierre L. Dou
illet, 1996`;  \nif yy <> xx then Xdiff( diff(uu,yy), xx, nb) else Xdi
ff(uu, xx, nb+1); fi; end; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+diff
/XdiffGR6&%#uuG%#xxG%#nbG%#yyG6\"6#%CCopyright~Pierre~L.~Douillet,~199
6GF+@%09'9%-%&XdiffG6%-%%diffG6$9$F0F19&-F36%F8F1,&F9\"\"\"F=F=F+F+F+
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "# int\351gration" }{MPLTEXT 
1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 191 "`int/Xdiff`:= proc(xxdi
ff) options `Copyright Pierre L. Douillet, 1996`; \nif op(2,xxdiff)= _
X then subsop(3=op(3,xxdiff)-1, xxdiff); \nelse subsop( 1=int(op(1, xx
diff), _X),  xxdiff) fi ; end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*i
nt/XdiffGR6#%'xxdiffG6\"6#%CCopyright~Pierre~L.~Douillet,~1996GF(@%/-%
#opG6$\"\"#9$%#_XG-%'subsopG6$/\"\"$,&-F.6$F7F1\"\"\"!\"\"F;F1-F46$/F;
-%$intG6$-F.6$F;F1F2F1F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "#
 combine  : juste pour etre connu de combine" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 80 "`combine/Xdiff`:= proc(z) options `Copyright Pierre L
. Douillet, 1996`; \nz; end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%.com
bine/XdiffGR6#%\"zG6\"6#%CCopyright~Pierre~L.~Douillet,~1996GF(9$F(F(F
(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "# simplify" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 539 "`simplify/Xdiff`:=proc(expr) option `Copyright \+
Pierre L. Douillet, 1996`; \nlocal quoi, qui, qui1, nb, nb1, return; \+
\nglobal xfactor;\nreturn:= expr; \nif typematch(expr, 'Xdiff'(quoi::a
nything, qui::name, nb::anything)) then\n  if type(nb, integer) then r
eturn:= (expand@diff)(quoi, qui $ nb) \n  elif typematch(quoi, (qui1::
name)^(nb1::anything)) and qui1 = qui \n       then return:= qui^(nb1 \+
- nb)*nb1!/(nb1 - nb)!\nfi elif has(expr, 'Xdiff') then return:= map(p
rocname, args)\nfi; if nargs=1 then return else (xfactor@simplify)(ret
urn) fi end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%/simplify/XdiffGR6#%
%exprG6(%%quoiG%$quiG%%qui1G%#nbG%$nb1G%'returnG6#%CCopyright~Pierre~L
.~Douillet,~1996G6\"C%>8)9$@&-%*typematchG6$F5-.%&XdiffG6%'8$%)anythin
gG'8%%%nameG'8'F@@&-%%typeG6$FE%(integerG>F4--%\"@G6$%'expandG%%diffG6
$F?-%\"$G6$FBFE3-F86$F?)'8&FC'8(F@/FenFB>F4*&*&)FB,&Fgn\"\"\"FE!\"\"F^
o-%*factorialG6#FgnF^o\"\"\"-Fao6#F]o!\"\"-%$hasG6$F5F;>F4-%$mapG6$9!9
\"@%/9#F^oF4--FN6$%(xfactorG%)simplifyG6#F4F16#FfpF1" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 58 "xsimplify:= proc(expr); simplify(expr, Xd
iff, delay); end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*xsimplifyGR6#%
%exprG6\"F(F(-%)simplifyG6%9$%&XdiffG%&delayGF(F(F(" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 32 
"Routines matricielles (xschmidt)" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
50 "# Routine xschmidt, elimination de Gauss-Schmidt \n" }{MPLTEXT 1 
0 326 "xschmidt:= proc(gr)  options `Copyright Pierre L. Douillet, 199
6`;  \nlocal k, gr1, piv0, phi0; \ngr1:= copy(gr); phi0:=&*(); for k t
o linalg['rowdim'](gr) - 1 do piv0:= xmk_piv(gr1,k);\ngr1:= evalm(tran
spose(piv0) &* gr1 &* piv0); phi0:= evalm(phi0 &* piv0) od;\nif nargs=
2 then assign(args[2], evalm(gr1)) fi; evalm(phi0) ; end;" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%)xschmidtGR6#%#grG6&%\"kG%$gr1G%%piv0G%%phi0G
6#%CCopyright~Pierre~L.~Douillet,~1996G6\"C'>8%-%%copyG6#9$>8'-%#&*GF/
?(8$\"\"\"F=,&-&%'linalgG6#.%'rowdimGF5F=!\"\"F=%%trueGC%>8&-%(xmk_piv
G6$F2F<>F2-%&evalmG6#-F:6$-F:6$-%*transposeG6#FIF2FI>F8-FO6#-F:6$F8FI@
$/9#\"\"#-%'assignG6$&9\"6#Fjn-FO6#F2-FO6#F8F/F/F/" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 42 "F
aire joli (xradic, xfrac, xfactor, xdiff)" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 35 "# xfrac (bouger le signe moins ...)" }{MPLTEXT 1 0 1 " " 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 334 "xfrac:=proc(z) option `Copyright
 Pierre L. Douillet, 1996`;\n if type(z, `=`) then map(procname, args)
 else expand(-numer(z))/expand(-denom(z))  fi ;end;\nxfrac2:=  ``@nume
r/denom;\nxfraq:= proc(z) option `Copyright Pierre L. Douillet, 1996`;
\n    if type(z, `=`) then map(procname, args) else (expand@numer)(z)/
(expand@denom)(z) fi; end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&xfrac
GR6#%\"zG6\"6#%CCopyright~Pierre~L.~Douillet,~1996GF(@%-%%typeG6$9$%\"
=G-%$mapG6$9!9\"*&-%'expandG6#,$-%&numerG6#F/!\"\"\"\"\"-F86#,$-%&deno
mGF=F>!\"\"F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'xfrac2G*&-%\"@
G6$%!G%&numerG\"\"\"%&denomG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%&xfraqGR6#%\"zG6\"6#%CCopyright~Pierre~L.~Douillet,~1996GF(@%-%%typeG
6$9$%\"=G-%$mapG6$9!9\"*&--%\"@G6$%'expandG%&numerG6#F/\"\"\"--F96$F;%
&denomGF=!\"\"F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "# xradic \+
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 366 "xradic:= proc(z) local sel, co
mment; option `Copyright Pierre L. Douillet, 1996`;\nif nargs=1 then c
omment:=id else comment:= args[2] fi;\nif type(z, '`*`') then sel := s
elect(type, z, sqrt); \nsqrt(comment(sel^2)) * map(procname, remove(ty
pe, z, sqrt), comment); RETURN( % ) fi;\n    if type(z, \{`=`, functio
n, '`+`'\}) then RETURN(map(procname, z, comment)) fi; z end ;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'xradicGR6#%\"zG6$%$selG%(commentG6#
%CCopyright~Pierre~L.~Douillet,~1996G6\"C&@%/9#\"\"\">8%%#idG>F4&9\"6#
\"\"#@$-%%typeG6$9$.%\"*GC%>8$-%'selectG6%F=F?%%sqrtG*&-FH6#-F46#*$)FD
F:\"\"\"F2-%$mapG6%9!-%'removeGFGF4F2-%'RETURNG6#%\"%G@$-F=6$F?<%.%\"+
G%)functionG%\"=G-FX6#-FR6%FTF?F4F?F-F-F-" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 9 "# xfactor" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 331 "xfactor:= proc(expr) option `Copyright Pierre L. Dou
illet, 1996`;  \nlocal fact; global xcombipo, x, poly;\n  if nargs = 2
 then fact := args[2] else fact := poly fi; \n  if type(fact, numeric)
 or fact= x then (xcombipo@factor)(expr) else \n    algsubs(fact = _ZZ
(x), yjoli(expr) ); subs(_ZZ(x) = fact, (xcombipo@factor)(%)) fi;\n%; \+
end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(xfactorGR6#%%exprG6#%%factG
6#%CCopyright~Pierre~L.~Douillet,~1996G6\"C%@%/9#\"\"#>8$&9\"6#F1>F3%%
polyG@%5-%%typeG6$F3%(numericG/F3%\"xG--%\"@G6$%)xcombipoG%'factorG6#9
$C$-%(algsubsG6$/F3-%$_ZZG6#F@-%&yjoliGFG-%%subsG6$/FNF3-FB6#%\"%GFYF,
6%FEF@F8F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "# xdiff" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 134 "xdiff:= proc(expr) option `Copyright Pierre
 L. Douillet, 1996`; \n yjoli(expr); if nargs=1 then % else diff(%, ar
gs[2..nargs]) fi; end;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "`diff/`:=
 proc(a,b); diff(a,b) end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&xdiff
GR6#%%exprG6\"6#%CCopyright~Pierre~L.~Douillet,~1996GF(C$-%&yjoliG6#9$
@%/9#\"\"\"%\"%G-%%diffG6$F4&9\"6#;\"\"#F2F(F(F(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%&diff/GR6$%\"aG%\"bG6\"F)F)-%%diffG6$9$9%F)F)F)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 49 "Sucre syn
taxique (xintparts, xelim, xlimit, xvo )" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 11 "# xintparts" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 687 "xintparts:= proc(F, expr::algebraic) option `Copyrig
ht Pierre L. Douillet, 1996`;\nlocal f, x, r, u, up, v, vp, arglist;\n
global lasterror;\nif type(F, 'function') and member(op(0, F), \{'int'
, 'Int'\}) then\n  f := op(1, F); arglist := op(2 .. nops(F), F);\n  x
 := op(2, F); if type(x, `=`) then r := rhs(x); x := lhs(x) fi;\n  u :
= expr; vp := traperror(normal(f/u));\n  if vp = lasterror then ERROR(
u, \" not a factor of \", f) fi;\n  up := Xdiff(u, x,1); v := int(vp, \+
x);\n  if type(r, 'range') then\n    Limit(u*v, x= op(2, r), 'left') -
 Limit(u*v, x = op(1, r), 'right') - Int(up*v, arglist);\n  else u*v -
 Int(up*v, arglist) fi \nelif has(F, \{int, Int\}) then map(procname, \+
args) \nelse F  fi  end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*xintpar
tsGR6$%\"FG'%%exprG%*algebraicG6*%\"fG%\"xG%\"rG%\"uG%#upG%\"vG%#vpG%(
arglistG6#%CCopyright~Pierre~L.~Douillet,~1996G6\"@'3-%%typeG6$9$.%)fu
nctionG-%'memberG6$-%#opG6$\"\"!F<<$.%$intG.%$IntGC,>8$-FC6$\"\"\"F<>8
+-FC6$;\"\"#-%%nopsG6#F<F<>8%-FC6$FVF<@$-F:6$Fen%\"=GC$>8&-%$rhsG6#Fen
>Fen-%$lhsGFao>8'9%>8*-%*traperrorG6#-%'normalG6#*&FM\"\"\"Ffo!\"\"@$/
Fio%*lasterrorG-%&ERRORG6%FfoQ2~not~a~factor~of~F6FM>8(-%&XdiffG6%FfoF
enFP>8)-FH6$FioFen@%-F:6$F^o.%&rangeG,(-%&LimitG6%*&FfoFPF`qFP/Fen-FC6
$FVF^o.%%leftGFP-Fjq6%F\\r/Fen-FC6$FPF^o.%&rightG!\"\"-FJ6$*&F[qFPF`qF
apFRFir,&F\\rFPFjrFir-%$hasG6$F<<$FJFH-%$mapG6$9!9\"F<F66#FepF6" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "# question/r\351ponse" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 129 "xvo:=proc(z::uneval) option `Copyright Pier
re L. Douillet, 1996`;  \ntraperror(value(eval(z))); print(eval(z,1)= \+
eval(%) ); end ;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xvoGR6#'%\"zG
%'unevalG6\"6#%CCopyright~Pierre~L.~Douillet,~1996GF*C$-%*traperrorG6#
-%&valueG6#-%%evalG6#9$-%&printG6#/-F56$F7\"\"\"-F56#%\"%GF*F*F*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 167 "xvo:= proc(z::uneval, comme
nt) option `Copyright Pierre L. Douillet, 1996`; \nif nargs=1 then eva
l(z) else traperror(comment(z)) fi; print(eval(z, 1) = eval(%));%; end
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$xvoGR6$'%\"zG%'unevalG%(commen
tG6\"6#%CCopyright~Pierre~L.~Douillet,~1996GF+C%@%/9#\"\"\"-%%evalG6#9
$-%*traperrorG6#-9%F5-%&printG6#/-F46$F6F2-F46#%\"%GFDF+F+F+" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "# limites a gauche et a droite" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "xlimit:=proc(f,x) local xx; xx:='x
x': \n[limit(f(xx), xx=x, 'left') , limit(f(xx), xx=x, 'right')] end ;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'xlimitGR6$%\"fG%\"xG6#%#xxG6\"F
+C$>8$.F.7$-%&limitG6%-9$6#F./F.9%.%%leftG-F26%F4F7.%&rightGF+F+F+" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "# `n
diff/init`() ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "ndiff['in
it']:=`ndiff/init`;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&ndiffG6#%%i
nitG%+ndiff/initG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 211 "ever_
load:= Xdiff, `combine/Xdiff`, `diff/`, `diff/Xdiff`, `int/Xdiff`, `si
mplify/Xdiff`, xdiff, xfactor, xfrac, ''xfrac2'', xfraq, xintparts, xl
eibniz, xlimit, xpush, xradic, xreadlib, xschmidt, xsimplify, xvo;" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*ever_loadG66%&XdiffG%.combine/Xdiff
G%&diff/G%+diff/XdiffG%*int/XdiffG%/simplify/XdiffG%&xdiffG%(xfactorG%
&xfracG.%'xfrac2G%&xfraqG%*xintpartsG%)xleibnizG%'xlimitG%&xpushG%'xra
dicG%)xreadlibG%)xschmidtG%*xsimplifyG%$xvoG" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "sa
velib('ndiff', `ndiff/init`, xreadlib, ever_load, `ndiff.m`);" }}}
{SECT 0 {PARA 3 "" 0 "" {TEXT -1 8 "Contr\364le" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 53 "liste:= select(type, [ssavelib], procedure): s
ort(%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#77%&XdiffG%.combine/XdiffG%
&diff/G%+diff/XdiffG%*int/XdiffG%+ndiff/initG%/simplify/XdiffG%&xdiffG
%(xfactorG%&xfracG%&xfraqG%*xintpartsG%)xleibnizG%'xlimitG%&xpushG%'xr
adicG%)xreadlibGF4%)xschmidtG%*xsimplifyG%$xvoG" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 56 "readlib(mmint): lasterror:= 'lasterror': _eps:
= '_eps': " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "lasterror:= 'lasterror': for _kkkk \+
in liste do lprint(_kkkk); \nmmint(_kkkk); od;" }}{PARA 6 "" 1 "" 
{TEXT -1 10 "ndiff/init" }}{PARA 6 "" 1 "" {TEXT -1 8 "xreadlib" }}
{PARA 6 "" 1 "" {TEXT -1 5 "Xdiff" }}{PARA 6 "" 1 "" {TEXT -1 13 "comb
ine/Xdiff" }}{PARA 6 "" 1 "" {TEXT -1 5 "diff/" }}{PARA 6 "" 1 "" 
{TEXT -1 10 "diff/Xdiff" }}{PARA 6 "" 1 "" {TEXT -1 9 "int/Xdiff" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#QH--------------~int/Xdiff~-----------
---6\"" }}{PARA 6 "" 1 "" {TEXT -1 55 "Names used as global names, but
 not declared:      : _X" }}{PARA 6 "" 1 "" {TEXT -1 14 "simplify/Xdif
f" }}{PARA 6 "" 1 "" {TEXT -1 5 "xdiff" }}{PARA 6 "" 1 "" {TEXT -1 7 "
xfactor" }}{PARA 6 "" 1 "" {TEXT -1 5 "xfrac" }}{PARA 6 "" 1 "" {TEXT 
-1 5 "xfraq" }}{PARA 6 "" 1 "" {TEXT -1 9 "xintparts" }}{PARA 6 "" 1 "
" {TEXT -1 8 "xleibniz" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#QG----------
----~xleibniz~--------------6\"" }}{PARA 6 "" 1 "" {TEXT -1 65 "Names \+
used as global names, but not declared:      : power, Xdiff" }}{PARA 
6 "" 1 "" {TEXT -1 6 "xlimit" }}{PARA 6 "" 1 "" {TEXT -1 5 "xpush" }}
{PARA 6 "" 1 "" {TEXT -1 6 "xradic" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
QE--------------~xradic~--------------6\"" }}{PARA 6 "" 1 "" {TEXT -1 
55 "Names used as global names, but not declared:      : id" }}{PARA 
6 "" 1 "" {TEXT -1 8 "xreadlib" }}{PARA 6 "" 1 "" {TEXT -1 8 "xschmidt
" }}{PARA 6 "" 1 "" {TEXT -1 9 "xsimplify" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#QH--------------~xsimplify~--------------6\"" }}{PARA 
6 "" 1 "" {TEXT -1 65 "Names used as global names, but not declared:  \+
    : Xdiff, delay" }}{PARA 6 "" 1 "" {TEXT -1 3 "xvo" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "# restart;" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 260 "" 0 "" {TEXT -1 52 "Copyright (c) Pierre L
. Douillet <douillet@cnam.fr>\n" }}{PARA 261 "" 0 "" {TEXT -1 283 "lib
re reproduction pour un usage universitaire sous reserve d'une copie c
ompl\350te,\navec reproduction du programme source dont, en particulie
r, la pr\351sente mention\n \naucune garantie de fiabilit\351. en part
iculier, toute utilisation dans un contexte industriel est vivement d
\351conseill\351e\n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
}{PARA 3 "" 0 "" {TEXT -1 0 "" }}}{MARK "19 4 29" 0 }{VIEWOPTS 1 1 0 
1 1 1803 }