{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 12 0 0 255 1 0 2 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 1 14 128 0 0 1 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 1 14 0 0 128 1 0 0 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 16 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 6 6 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 " Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 4 4 1 0 1 0 2 2 0 1 } {PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Text Output" -1 6 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 2 1 3 1 } 1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE " " -1 -1 "Times" 1 16 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 16 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 \+ Font 0" -1 256 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 12 128 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 258 1 {CSTYLE "" -1 -1 "Times " 1 16 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Title" -1 259 1 {CSTYLE "" -1 -1 "Times" 1 36 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 12 12 3 0 3 0 2 2 19 1 }{PSTYLE "Normal" -1 260 1 {CSTYLE "" -1 -1 "Times" 1 18 255 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 528 "restart: if kernelo pts(platform)=\"unix\" \n then unix:= true; win98:= false; \n date_st ring:= convert(substring(ssystem(\"date \"\"+%a %d/%m/%Y\"\" \")[2], 1 ..-2), symbol)\n else unix:= false; win98:= evalb(ssystem(\"win\")[2][ 1..13]=\"Vous utilisez\"); \n if win98 then tmp:= ssystem(\"date\")[2 ]; searchtext(\":\", tmp); \n tmp:= cat(substring(tmp, 1..%-2), \" \+ \", substring(tmp, %+1..-1));\n date_string:= substring(tmp, 22.. 35);\n else date_string:= ssystem(\"date /t\")[2][1..-2];\n fi: fi: ' unix'=unix, 'win98'=win98, 'date'= date_string;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%/%%unixG%&falseG/%&win98G%%trueG/%%dateGQ/Mer~14/09/200 56\"" }}}{EXCHG {PARA 260 "" 0 "" {TEXT -1 56 "sous win98, taper [entr \351e] pour sortir de la fenetre DOS" }}{PAGEBK }{PARA 260 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 259 "" 0 "" {TEXT -1 16 "Splines (v68-12 )" }}}{EXCHG {PARA 258 "" 0 "" {TEXT -1 64 "Copyright (c) 1999-2005 Pi erre L. Douillet \n" }}{PARA 258 "" 0 "" {TEXT -1 11 "licence GPL" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT -1 195 "libre reproduction pour un usage universitaire sous rese rve d'une copie compl\350te,\navec reproduction du programme source do nt, en particulier, la pr\351sente mention\n \n\naucune garantie de fi abilit\351. " }}{PARA 258 "" 0 "" {TEXT -1 89 "en particulier, toute u tilisation dans un contexte industriel est vivement d\351conseill\351e \n " }}}{EXCHG {PARA 260 "" 0 "" {TEXT -1 40 "chargement par la comman de with(splines)" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 15 "Initialisati ons" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "gc( ); kernelopts(AS SERT=true):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 465 "[libname][- 1]: racine:= %[1..-4]:\ndo loc:= searchtext(\"\\\\\",racine); if loc = 0 then break fi;\nracine:= cat(substring(racine,1..loc-1),\"/\", subs tring(racine,loc+1..-1)); od:\ndo loc:= searchtext(\"\\\\\",racine); i f loc = 0 then break fi;\nracine:= cat(substring(racine,1..loc-1),\"/ \", substring(racine,loc+1..-1)); od:\nloc:= searchtext(\"MAPLE\", rac ine): if loc <> 0 then\nracine:= cat(substring(racine,1..loc-1),\"Mapl e\", substring(racine,loc+5..-1)); fi: \n'racine'=racine; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%'racineGQ,C:/MapleV6/6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "kernelopts(version): Version:= substring( %, 1..searchtext(\",\", %)-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(V ersionG%(Maple~6G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 77 "Test if \"pl dx\" is preloaded, as required for this library to operate properly" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 206 "try read( cat(racine, \"update/ch eck.m\"));\nprint(`The usual 'update' directory stil exists, as requie red`);\ncatch: print (` An 'update' repertory MUST be created, using ' pldx' package`);;\nend try; print(``);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%WThe~usual~'update'~directory~stil~exists,~as~requieredG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%!G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Biblioth\350que compl\351mentaire" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1147 "ssavelib:= NULL:\nunprotect(savelib); savelib:= pro c() error \"savelib is gone\" end :\nxsavelib:= proc() local filename, values, library, pathname, f;\nglobal ssavelib, libname; option `Copy right Pld`;\nif assigned(libname) then library := op(1, eval([libname] , 1))\n else error \"the global variable `libname' must be assigned\" \nend if;\nif nargs < 2 then error \"no names specified to save\" end \+ if;\nfilename := args[nargs];\nvalues := args[1 .. nargs - 1] ;\nif no t type(filename, '\{string, symbol\}') \n then error \"last argument (filename) must be a string\" end if;\nif not searchtext(\".m\", file name, -2 .. -1) = 1 \n then error \"last argument (filename) must be \+ a *.m string\" end if;\n if not type([values], 'list(\{symbol, string \})') \n then f := remove(type, [values], \{symbol,string\}); \n er ror \"all arguments must be symbols, cannot save these %1\", f\n end i f;\n pathname := cat(library, \"/\", filename);\n f := subs('T' = ( \+ (op@map)(convert, [values], symbol), pathname), \n proc() save T en d proc);\n try f(); ssavelib:= ssavelib, values; return; \n catch: \+ print(lasterror); \n end try;\nerror \"unable to save %1 in %2\", [ values], library\nend proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "tzx:=\"\": xsavelib('tzx', `splines.m`); " }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 36 "ssavelib:= NULL: ever_load:= NULL :" }}} {SECT 0 {PARA 4 "" 0 "" {TEXT -1 4 "init" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 218 "\"splines v68-12 ; author : ; last modif (v6) : \"\n || (date_string):\n`splines/init`:= \n subs( message=%, proc() option `Copyright Pierre L. Douillet`;\n print(conv ert(message, symbol)) end): %();" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%_ psplines~v68-12~;~~author~:~~~;~~last~modif~(v6)~: ~Mer~14/09/2005G" }}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 74 "Usuels (arrdim, pie2mat, mat2pie, lin2mat, val_mat, clin, clin_a, mat_plo)" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "arrdim" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 254 "unprotect(ar rdim);\narrdim:= proc(ar) option `Copyright Pierre L. Douillet`;\n if type(ar, matrix) then linalg['rowdim'](ar) \nelif type(ar, Matrix) th en LinearAlgebra['RowDimension'](ar) \nelse op(2, eval(ar)); rhs((proc (u) u end proc)(%)) end if\nend proc;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'arrdimGR6#%#arG6\"6#%=Copyright~Pierre~L.~DouilletGF(@'-%%typeG6 $9$%'matrixG-&%'linalgG6#.%'rowdimG6#F/-F-6$F/%'MatrixG-&%.LinearAlgeb raG6#.%-RowDimensionGF7C$-%#opG6$\"\"#-%%evalGF7-%$rhsG6#-R6#%\"uGF(F( F(F/F(F(F(6#%\"%GF(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "pie2mat " }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 306 "pie2mat:= p roc(fb1) option `Copyright Pierre L. Douillet`; \nglobal x, z; \nif n args=2 then fb1 else convert(fb1,piecewise); fi; [op(%)]; \n[seq( [ %[ 2*z-1],%[2*z]], z=1..ceil(nops(%)/2)-1), [x%(pie2matGR6# %$fb1G6\"6#%=Copyright~Pierre~L.~DouilletGF(C(@%/9#\"\"#9$-%(convertG6 $F0%*piecewiseG7#-%#opG6#%\"%G7$-%$seqG6$7$&F96#,&%\"zGF/\"\"\"!\"\"&F 96#,$FBF//FB;FC,&-%%ceilG6#,$-%%nopsGF8#FCF/FCFCFD7$2%\"xG%)infinityG- F76$FDF9-%'removeG6%%%typeGF97$%\"=G%)anythingG-%$mapG6$R6#FBF(F(F(7$- %$rhsG6#&F06#FC&F06#F/F(F(F(F9-%'MatrixGF8F(6$FTFBF(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "mat2pie" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 182 "mat2pie:= proc(fun) option `Copyright Pierre L. Doui llet`; \nconvert(fun, listlist); map(proc(u) global x; [x<=u[1], u[2]] end, %); convert((piecewise@op@map)(op,%), piecewise); end ;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%(mat2pieGR6#%$funG6\"6#%=Copyright~P ierre~L.~DouilletGF(C%-%(convertG6$9$%)listlistG-%$mapG6$R6#%\"uGF(F(F (7$1%\"xG&F/6#\"\"\"&F/6#\"\"#F(6#F9F(%\"%G-F-6$--%\"@G6$-FF6$%*piecew iseG%#opGF26$FKFAFJF(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "lin2m at" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 270 "lin2mat:= proc() option `Copyright Pierre L. Douillet`; global x; local k, mat; \nmat:= matrix(1+nargs/2,2,[args,infinity,0]); \nfor k from 2 to narg s/2 do mat[k,2]:= (args[2*k-2]*(args[2*k-1]-x)+ args[2*k]*(x-args[2*k- 3]))/(args[2*k-1]-args[2*k-3]) od;\nMatrix(mat); end ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(lin2matGR6\"6$%\"kG%$matG6#%=Copyright~Pierre~L .~DouilletGF&C%>8%-%'matrixG6%,&\"\"\"F3*&#F3\"\"#F39#F3F3F67%9\"%)inf inityG\"\"!?(8$F6F3,$F7F5%%trueG>&F.6$F=F6*&,&*&&F96#,&F=F6F6!\"\"F3,& &F96#,&F=F6F3FIF3%\"xGFIF3F3*&&F96#,$F=F6F3,&FNF3&F96#,&F=F6\"\"$FIFIF 3F3F3,&FKF3FTFIFI-%'MatrixG6#F.F&6#FNF&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "val_mat" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 189 "val_mat:= proc(mat, xx::numeric) option `Copyright Pierre L. \+ Douillet`; \nglobal x; local k; \nfor k from 1 to arrdim(mat)-1 do if \+ xx< mat[k,1] \nthen break fi; od; subs(x=xx, mat[k,2]); end ;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%(val_matGR6$%$matG'%#xxG%(numericG6# %\"kG6#%=Copyright~Pierre~L.~DouilletG6\"C$?(8$\"\"\"F3,&-%'arrdimG6#9 $F3F3!\"\"%%trueG@$29%&F86$F2F3[-%%subsG6$/%\"xGF=&F86$F2\"\"#F/6#FEF/ " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "clin" }{MPLTEXT 1 0 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "smaller_clin:= proc(tx,ty); (ty=inf inity) or is(tx " 0 "" {MPLTEXT 1 0 519 "clin := proc(c1,f1,c2,f2) option `Copyright Pierre L. Douillet`; \nglobal s maller_clin; local mxj, mxk, j,k, rl; \nmxj:= arrdim(f1); mxk:= arrdim (f2); j:=1; k:= 1 ; rl:= NULL; \nwhile (j< mxj) or (k%%clinGR6&%#c1G%#f1G%#c2G%#f2G6'%$mxjG%$mxkG%\"jG%\"kG%#rlG6#%=Copy right~Pierre~L.~DouilletG6\"C*>8$-%'arrdimG6#9%>8%-F86#9'>8&\"\"\">8'F B>8(%%NULLG?(F3FBFBF352FAF62FDF<@'/&F:6$FAFB&F?6$FDFBC%>FF6$FF7$FN,&*& 9$FB&F:6$FA\"\"#FBFB*&9&FB&F?6$FDFenFBFB>FA,&FAFBFBFB>FD,&FDFBFBFB-%-s maller_clinG6$FNFPC$>FFFT>FAF[oC$>FF6$FF7$FPFV>FDF]o7$FF7$%)infinityG, &*&FXFB&F:6$F6FenFBFB*&FgnFB&F?6$F " 0 "" {MPLTEXT 1 0 737 "clin_a:= proc(c1, ff1, c 2, ff2, ff3) option `Copyright Pierre L. Douillet`;\nglobal smaller_cl in; \nlocal mx1, mx2, j1, j2, j3; \nmx1:= arrdim(ff1); mx2:= arrdim(f f2); j1:=1; j2:= 1; j3:=1; \nassign(ff3, Matrix(mx1+mx2-1, 2, array) \+ ); userinfo(5, 'pie', mx1, mx2, eval(ff3)); \nwhile (j1< mx1) or (j2%'clin _aGR6'%#c1G%$ff1G%#c2G%$ff2G%$ff3G6'%$mx1G%$mx2G%#j1G%#j2G%#j3G6#%=Cop yright~Pierre~L.~DouilletG6\"C.>8$-%'arrdimG6#9%>8%-F96#9'>8&\"\"\">8' FC>8(FC-%'assignG6$9(-%'MatrixG6%,(F7FCF=FCFC!\"\"\"\"#%&arrayG-%)user infoG6'\"\"&.%$pieGF7F=-%%evalG6#FK?(F4FCFCF452FBF72FEF=C%>&FK6$FGFQ,& *&9$FC&F;6$FBFQFCFC*&9&FC&F@6$FEFQFCFC>FG,&FGFCFCFC@'/&F;6$FBFC&F@6$FE FCC%>&FK6$,&FGFCFCFPFCF[p>FB,&FBFCFCFC>FE,&FEFCFCFC-%-smaller_clinG6$F [pF]pC$>FapF[p>FBFepC$>FapF]p>FEFgp>&FK6$FGFC%)infinityG>F\\o,&*&F`oFC &F;6$F7FQFCFC*&FdoFC&F@6$F=FQFCFC@$2FGFOC$>FK-&%.LinearAlgebraG6#.%*Su bmatrixG6%FK;FCFG;FCFQ%%NULLGFKF46#FipF4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1014 "mat_plo := proc(fun1) option `Copyright Pierre L. D ouillet`; \nglobal x, val_mat, xoption, k, p; \nlocal opt, kmax, k_max , pmax, fun, xti, yti, mem, x_max ; \nopt := [args[2..-1]] ; \n Digit s:= xoption(opt, 'digits', Digits) ; \n fun := Matrix(fun1) : kmax := arrdim(fun) ; \n x_max:= xoption(opt, 'xmax', fun[kmax-1,1]*1.3) ;\n for k_max from 1 to kmax-1 while fun[k_max,1] < x_max do od; \n fun [k_max,1] := x_max; \n k:= 'k': p:='p': seq(fun[k,1], k=1..k_max) ; xti := evalf([%],3) :\n map2(val_mat, fun, xti ): yti := evalf(%, 3) : \n pmax := xoption(opt, 'numpoints', '10') ; \n if (fun[1,1]>0) an d (fun[1,2]=0) then mem := [0,0], [fun[1,1], 0] else mem := NULL fi : \n mem, seq( (op@map)(subs, [seq(x=fun[k,1]+(fun[k+1,1]-fun[k,1])*p/p max, p= 0..pmax )], \n [x, fun[k+1,2]]), k= 1..k_max-1) ;\n plot( [%] , 'font' = ['TIMES', 'ROMAN', 16], 'labelfont' = ['TIMES', 'ROMAN' , 16], \n 'axesfont' = ['TIMES', 'ROMAN', 16], 'xtickmarks'= xti, 'yt ickmarks'= yti, \n 'axes'='framed', 'color'='black', op(opt)) : end ; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(mat_ploGR6#%%fun1G6+%$optG%%kma xG%&k_maxG%%pmaxG%$funG%$xtiG%$ytiG%$memG%&x_maxG6#%=Copyright~Pierre~ L.~DouilletG6\"C3>8$7#&9\"6#;\"\"#!\"\">%'DigitsG-%(xoptionG6%F7.%'dig itsGF@>8(-%'MatrixG6#9$>8%-%'arrdimG6#FG>8,-FB6%F7.%%xmaxG,$&FG6$,&FM \"\"\"FenF>Fen$\"#8F>?(8&FenFenFZ2&FG6$FinFenFRF4>F[oFR>%\"kG.F_o>%\"p G.Fbo-%$seqG6$&FG6$F_oFen/F_o;FenFin>8)-%&evalfG6$7#%\"%G\"\"$-%%map2G 6%%(val_matGFGF\\p>8*-F^p6$FapFbp>8'-FB6%F7.%*numpointsG.\"#5@%32\"\"! &FG6$FenFen/&FG6$FenF=Ffq>8+6$7$FfqFfq7$FgqFfq>F]r%%NULLG6$F]r-Feo6$-- %\"@G6$%#opG%$mapG6%%%subsG7#-Feo6$/%\"xG,&FgoFen*&*&,&&FG6$,&F_oFenFe nFenFenFenFgoF>FenFboFenFenF\\qF>Fen/Fbo;FfqF\\q7$Fbs&FG6$FisF=/F_o;Fe n,&FinFenFenF>-%%plotG6+F`p/.%%fontG7%.%&TIMESG.%&ROMANG\"#;/.%*labelf ontGFht/.%)axesfontGFht/.%+xtickmarksGF\\p/.%+ytickmarksGFhp/.%%axesG. %'framedG/.%&colorG.%&blackG-Fjr6#F7F46'FbsFfpFBF_oFboF4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "ever_load:= ever_load, arrdim, pie 2mat, mat2pie, lin2mat, val_mat, smaller_clin, clin, clin_a, mat_plo; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*ever_loadG6+%'arrdimG%(pie2matG %(mat2pieG%(lin2matG%(val_matG%-smaller_clinG%%clinG%'clin_aG%(mat_plo G" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 59 "Int\351gration (mat_primi, mat_int, mat_esp, mat_var, mat_lap)" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "mat_primi" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 322 "mat_primi:= proc (fun, var) option `Copyright Pierre L. Douillet` ;\nlocal k, res, u; u:= 'u': res := copy(fun); \nres[1,2] := int(subs( var = u, fun[1,2]),u = 0 .. var); \nfor k from 2 to arrdim(fun) do in t(subs(var = u,fun[k,2]),u = fun[k-1,1] .. var);\nres[k,2] := %+ subs( var = fun[k-1,1], res[k-1,2]) od; Matrix(res) end ;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%*mat_primiGR6$%$funG%$varG6%%\"kG%$resG%\"uG6#%=Cop yright~Pierre~L.~DouilletG6\"C'>8&.F2>8%-%%copyG6#9$>&F56$\"\"\"\"\"#- %$intG6$-%%subsG6$/9%F2&F9FF=-%'arrdimGF8%%trueGC$-F @6$-FC6$FE&F96$FLF>/F2;&F96$,&FLF=F=!\"\"F=FF>&F5FV,&%\"%GF=-FC6$/FFFY &F56$FenF>F=-%'MatrixG6#F5F/F/F/" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "mat_int" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 222 "` splines/mat_int` := proc() option `Copyright Pierre L. Douillet`; \ngl obal mat_primi; local tmp; tmp:= mat_primi(args);\nif tmp[-1,1]=infini ty then limit(tmp[-1,2], args[2]=infinity) else (sort@expand)( tmp[-1, 2]) fi; end ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%0splines/mat_intGR6 \"6#%$tmpG6#%=Copyright~Pierre~L.~DouilletGF&C$>8$-%*mat_primiG6#9\"@% /&F-6$!\"\"\"\"\"%)infinityG-%&limitG6$&F-6$F6\"\"#/&F16#F>F8--%\"@G6$ %%sortG%'expandG6#F " 0 "" {MPLTEXT 1 0 131 "mat_esp := proc (ma) option `Copyright Pierre L. Douillet`; globa l x;\nmat_int(LinearAlgebra['ColumnOperation'](ma, 2, x), x); end ;" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 244 "mat_var := proc (ma) option `Cop yright Pierre L. Douillet`, remember; \nlocal esp; global x;\nesp:= ma t_int(LinearAlgebra['ColumnOperation'](ma, 2, x ), x); \n mat_int (LinearAlgebra['ColumnOperation'](ma, 2, x^2), x) - esp^2; \nesp, %; e nd ; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(mat_espGR6#%#maG6\"6#%=Cop yright~Pierre~L.~DouilletGF(-%(mat_intG6$-&%.LinearAlgebraG6#.%0Column OperationG6%9$\"\"#%\"xGF7F(6#F7F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%(mat_varGR6#%#maG6#%$espG6$%=Copyright~Pierre~L.~DouilletG%)remember G6\"C%>8$-%(mat_intG6$-&%.LinearAlgebraG6#.%0ColumnOperationG6%9$\"\"# %\"xGF=,&-F26$-F56%F;F<*$)F=F<\"\"\"F=FE*$)F0F " 0 "" {MPLTEXT 1 0 100 "mat_lap := proc (ma) global x;\nm at_int(LinearAlgebra['ColumnOperation'](ma, 2, exp(-z*x) ), x);\nend: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 127 "splines[mat_int]:= `sp lines/mat_int`; \nxsavelib(`splines/mat_int`, mat_primi, mat_esp, mat_ var, mat_lap, `splines/mat_int.m`) :" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>&%(splinesG6#%(mat_intG%0splines/mat_intG" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "xdiffer" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 647 "`splines/xdif fer`:= proc(f1,f2) option `Copyright Pierre L. Douillet`; \nglobal x, \+ smaller_clin; local mxj, mxk, j,k, rl; \nmxj:= arrdim(f1); mxk:= arrdi m(f2); if (mxj>mxk) then RETURN(procname(f2,f1)) fi; \nj:=1; k:= 1 ; r l:= NULL; \nwhile (j< mxj) or (k " 0 "" {MPLTEXT 1 0 92 "splines[xdiffer]:= `splines/xdiffer` : \n xsavelib(`splines/xdiffer`, `splines/xdiffer. m`) :" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%0splines/xdifferGR6$%#f1G%# f2G6'%$mxjG%$mxkG%\"jG%\"kG%#rlG6#%=Copyright~Pierre~L.~DouilletG6\"C- >8$-%'arrdimG6#9$>8%-F66#9%@$2F:F4-%'RETURNG6#-9!6$F=F8>8&\"\"\">8'FH> 8(%%NULLG?(F1FHFHF152FGF42FJF:@'/&F86$FGFH&F=6$FJFHC%>FL6$FL7$FT*&&F86 $FG\"\"#FH),&FgnFH&F=6$FJFin!\"\"FinFH>FG,&FGFHFHFH>FJ,&FJFHFHFH-%-sma ller_clinG6$FTFVC$>FLFZ>FGF`oC$>FL6$FL7$FVFfn>FJFbo7$FL7$%)infinityG*& &F86$F4FinFH),&FbpFH&F=6$F:FinF^oFinFH-%'matrixG6#%\"%G-%(mat_intG6$F[ q%\"xG-%%sqrtG6#-%&evalfG6$-%'expandGFjp\"#IF16$F_qFdoF1" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 24 "convol, version diverses" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 35 " Troisi\350me version (\340 travers xplif)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 329 "`convol/smaller` := proc(a,b) local rep, ou_ca; \nif b=infinity then RETURN(true) fi; \nif a=infinity then RETURN(false) f i;\nrep:= is(ax)=addressof, ou_ca)); fi;\nre p end:" }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 10 "tri fusion" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 547 "`convol/fus` := proc(la::list, lb: :list) global `convol/smaller`; \nlocal lc, pa,pb,pc, mxa, mxb; \nmxa: = nops(la); mxb:= nops(lb); pa:=1; pb:=1; pc:=1; lc:= array(1..mxa+mxb );\nwhile (pa<=mxa) and (pb<=mxb) do if `convol/smaller`(la[pa],lb[pb] ) \nthen lc[pc]:=la[pa]; pa:=pa+1; else lc[pc]:=lb[pb]; pb:=pb+1;fi;\n pc:=pc+1; od;\nwhile (pa<=mxa) do lc[pc]:=la[pa]; pa:=pa+1; pc:=pc+1; \+ od;\nwhile (pb<=mxb) do lc[pc]:=lb[pb]; pb:=pb+1; pc:=pc+1; od; \nconv ert(lc,list); end :\n`value/Fus`:= proc(x) global `convol/fus`; `convo l/fus`(op(value([op(x)]))) end ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% *value/FusGR6#%\"xG6\"F(F(-%+convol/fusG6#-%#opG6#-%&valueG6#7#-F-6#9$ F(6#F*F(" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 10 "tri Maple " }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 258 "`convol/tri` := proc(li) gl obal `convol/smaller`; local infi; \n# print(` tri : `, args); \nif ha s (li, infinity) then infi:= true; remove(has, li, infinity) \nelse in fi:= false; li fi; \nsort(%, `convol/smaller`); if infi then [op(%), i nfinity] else % fi; end :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 " `value/Tri`:= proc(li::list) global `convol/tri`; `convol/tri`(va lue(li)) end ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*value/TriGR6#'%#l iG%%listG6\"F*F*-%+convol/triG6#-%&valueG6#9$F*6#F,F*" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 225 "`convol/add_li` := proc (ang_f, an g_g) global glob_assu, Tri, xplif ; \nmap(proc(c,li) (op@map)(proc(a,b ) a+b end, li, c) end, ang_f, ang_g) ;\nxplif( Tri(convert(convert(%,s et), list)), [glob_assu]) ; [op(%), infinity] ; end :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1358 "`splines/convol`:= proc(ff, gg) option `Copyright P ierre L. Douillet`;\nglobal glob_assu, t, x, Tri, xplif, `convol/add_l i`, kk;\nlocal mxf, mxg, sq_ang_f, sq_ang_g, sq_g_ang, x_li, \n mxr, t_tri, jj, _res, somme, nu, pg, vg, pf, vf ;\n mxf := arrdim(ff); sq _ang_f := seq(ff[kk,1], kk=1..mxf-1);\n mxg := arrdim(gg); sq_ang_g \+ := seq(gg[kk,1], kk=1..mxg-1);\n x_li := `convol/add_li`([sq_ang_f], \+ [sq_ang_g]); ## ajoute infinity final\n mxr := nops(x_li);\n _res := M atrix(map(z -> [z, 0], x_li));\n userinfo(5, 'pie', 'x_li' = convert(% ,listlist));\n sq_g_ang := seq(x - sq_ang_g[mxg - kk], kk = 1 .. mxg - 1);\n kk := 'kk';\n for jj to mxr - 1 do\n userinfo(5, 'pie', 'x' = \+ x_li[jj] .. x_li[jj + 1]);\n t_tri := xplif( Tri([sq_ang_f, sq_g_ang, infinity]), \n [glob_assu, x, 'RealRange'('Open'(x_li[jj]), 'Open '(x_li[jj + 1]))]);\n userinfo(5, 'pie', 't_tri' = %);\n somme := 0; nu := 0; \n pg := mxg; vg := subs(x = x - t, gg[pg, 2]);\n pf := 1 ; vf := subs(x = t, ff[pf, 2]);\n while 1 < pg or pf < mxf do\n n u := nu + 1;\n userinfo(5, 'pie', nu, 'pf' = pf, vf, 'pg' = pg, vg); \n if has(t_tri[nu], x) \n then pg := pg - 1; vg := subs(x = x - t, gg[pg, 2])\n else pf := pf + 1; vf := subs(x = t, ff[pf, 2])\n end if;\n somme := somme + int(vg*vf, t = t_tri[nu] .. t_tri[nu + 1])\n end do;\n _res[jj + 1, 2] := somme\n end do;\n Matrix(_res)\n end proc;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%/splines/convolGR6$%#ff G%#ggG62%$mxfG%$mxgG%)sq_ang_fG%)sq_ang_gG%)sq_g_angG%%x_liG%$mxrG%&t_ triG%#jjG%%_resG%&sommeG%#nuG%#pgG%#vgG%#pfG%#vfG6#%=Copyright~Pierre~ L.~DouilletG6\"C.>8$-%'arrdimG6#9$>8&-%$seqG6$&FC6$%#kkG\"\"\"/FK;FL,& F?FLFL!\"\">8%-FA6#9%>8'-FG6$&FUFJ/FK;FL,&FRFLFLFP>8)-%.convol/add_liG 6$7#FE7#FW>8*-%%nopsG6#Fin>8--%'MatrixG6#-%$mapG6$R6#%\"zGF<6$%)operat orG%&arrowGF<7$FC\"\"!F8(-FG6$,&%\"xGFL&FW6#,&FRFLFKFPFPFen>FK.FK?(8,FL FL,&F`oFLFLFP%%trueGC--Fep6%FgpFhp/.Ffq;&Fin6#F]r&Fin6#,&F]rFLFLFL>8+- %&xplifG6$-%$TriG6#7%FEFbq%)infinityG7%%*glob_assuGFfq-.%*RealRangeG6$ -.%%OpenG6#Ffr-F\\t6#Fhr-Fep6%FgpFhp/.F\\sF_q>8.Fcp>8/Fcp>80FR>81-%%su bsG6$/Ffq,&FfqFL%\"tGFP&FU6$Fjt\"\"#>82FL>83-F^u6$/FfqFbu&FC6$FguFeu?( FFht,&FhtFLFLFL-Fep6)FgpFhpFht/.FguFguFiu/.FjtF jtF\\u@%-%$hasG6$&F\\s6#FhtFfqC$>Fjt,&FjtFLFLFP>F\\uF]uC$>Fgu,&FguFLFL FL>FiuFju>Fft,&FftFL-%$intG6$*&F\\uFLFiuFL/Fbu;F`w&F\\s6#FevFL>&Feo6$F jrFeuFft-Fgo6#FeoF<6)FfsFbuFfqFasF^sF[oFKF<" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "spli nes[convol]:= `splines/convol` : " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 138 "xsavelib(`splines/convol`, `convol/add_li`, `convol/tri`, `convol /fus`, `convol/smaller`, `value/Tri`, `value/Fus`, `splines/convol.m` ) ;" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 60 "Version acc\351l\351r\351e (impl\351mentation ' array' et pas 'listlist')" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 566 "`convol_a/fus` :=proc(la::array, lb::array, lc::symbol) global x, adrx; \nlocal pa,pb,pc, mxa, mxb; \nassume(args[4..-1]); adrx:= addr essof(x); # la variable qualifi\351e \nmxa:= arrdim(la); mxb:= arrdim( lb); pa:=1; pb:=1; pc:=1; lc:= array(1..mxa+mxb);\nwhile (pa<=mxa) and (pb<=mxb) do if `convol/smaller`(la[pa],lb[pb]) \nthen lc[pc]:=la[pa] ; pa:=pa+1; else lc[pc]:=lb[pb]; pb:=pb+1;fi;\npc:=pc+1; od;\nwhile (p a<=mxa) do lc[pc]:=la[pa]; pa:=pa+1; pc:=pc+1; od; while (pb<=mxb) do \+ lc[pc]:=lb[pb]; pb:=pb+1; pc:=pc+1; od;\nx:='x': lc:= map2(subs, point to(adrx)=x, lc); end: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 173 " `convol_a/add_li` := proc (ang_f::list, ang_g:: list); \n map(proc(c, li) (op@map)(proc(a,b) a+b end, li, c) end, ang_f, ang_g );\nconvert(c onvert(%,set), list); sort(%); end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 197 "jime:= 0: \njnt:= proc(expr, _v1, _v2) global jime, \+ _X, `int/indef`; \n local stamp; stamp:=time();\n `int/indef`(expr); subs(_X=_v2,%)-subs(_X=_v1,%); expand(%); \njime:=jime+time()-stamp; \+ %%; end :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1511 "`splines/con vol_a`:= proc(ff::array, gg::array, _res::name) \nglobal x, _X, infole vel, `int/indef`, `convol_a/add_li`,`convol_a/fus`, kk, jnt;\nlocal ff t, ggt, mxf, mxg, ang_g, x_li, mxr, jj, somme, nu, pg, vg, pf, vf, ang _f, g_ang, t_tri;\nt_tri:= 't_tri'; kk:= 'kk': mxf:= arrdim(ff); mxg:= arrdim(gg); # xtime(debut); \nang_f:= [seq(ff[kk,1], kk=1..mxf-1)]; \+ \nang_g:= [seq(gg[kk,1], kk=1..mxg-1)]; # !!! infinity !!!\n\nx_li:= ` convol_a/add_li`(ang_f, ang_g); userinfo(5, 'pie', 'x_li' = %); \nmxr: = nops(x_li)+1; \n_res:= matrix(mxr,2, array); for kk to mxr-1 do _res [kk,1]:= x_li[kk] od; \n_res[mxr,1]:= infinity; _res[1,2]:= 0;\ng_ang: = array([seq(x-ang_g[mxg-kk], kk=1..mxg-1)]); ang_f:= array([op(ang_f) , infinity]);\nfft:= map2(subs,x=_X,ff); ggt:= map2(subs,x=x-_X,gg); \+ \n\nfor jj from 1 to mxr-1 do jj; # xres_run([\", xtime(\")]);\n forg et(`int/indef`, 'reinitialize' = false);\n if jj=88 then infolevel['pi e']:=10 else infolevel['pie']:=1; fi; \n if jj=mxr-1 then x_li[jj]1) or (pf " 0 "" {MPLTEXT 1 0 158 "splines[convol_a]:= `spline s/convol_a`;\nxsavelib(`splines/convol_a`, 'jime', jnt, `convol_a/add_ li`, `convol_a/fus`, `convol/smaller`, `splines/convol_a.m`) :" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>&%(splinesG6#%)convol_aG%1splines/con vol_aG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 11 "Information " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 156 "subs(readlib= _readlib, eval(splines)): \nsort(op(%), proc(a,b) lexorder(lhs(a) , lhs(b)) end ): \n'elements' = Vector(%), 'ever_loaded' = Vector([ever_load]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$/%)elementsG-%'RTABLEG6$\"(;'es-%'MATR IXG6#7&7#/%'convolG%/splines/convolG7#/%)convol_aG%1splines/convol_aG7 #/%(mat_intG%0splines/mat_intG7#/%(xdifferG%0splines/xdifferG/%,ever_l oadedG-F&6$\"(c'es-F*6#7+7#%'arrdimG7#%(pie2matG7#%(mat2pieG7#%(lin2ma tG7#%(val_matG7#%-smaller_clinG7#%%clinG7#%'clin_aG7#%(mat_ploG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 121 "ever_load:= op(\{ever_load \}):\never_load_list:= map(proc(z) cat(` `,z) end, sort([ever_load])): \nsplines['ever_loaded']:= %;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%(s plinesG6#%,ever_loadedG7+%(~arrdimG%&~clinG%(~clin_aG%)~lin2matG%)~mat 2pieG%)~mat_ploG%)~pie2matG%.~smaller_clinG%)~val_matG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "xsavelib('splines', `splines/init`, ever_load, `splines.m`);" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 8 "Contr\364le" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "select(type, \{ssavelib\}, procedur e): liste:= sort(convert(%, list));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6 #>%&listeG7=%'arrdimG%%clinG%'clin_aG%.convol/add_liG%+convol/fusG%/co nvol/smallerG%+convol/triG%0convol_a/add_liG%-convol_a/fusG%$jntG%(lin 2matG%(mat2pieG%(mat_espG%(mat_lapG%(mat_ploG%*mat_primiG%(mat_varG%(p ie2matG%-smaller_clinG%/splines/convolG%1splines/convol_aG%-splines/in itG%0splines/mat_intG%0splines/xdifferG%(val_matG%*value/FusG%*value/T riG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "protect(mat_int); pr otect(arrdim);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "lasterror := 'lasterror': _eps:= '_eps' : jime := 'jime' : \nfor _kkkk in liste \+ do xmint(_kkkk); od;" }}{PARA 6 "" 1 "" {TEXT -1 6 "arrdim" }}{PARA 6 "" 1 "" {TEXT -1 4 "clin" }}{PARA 6 "" 1 "" {TEXT -1 6 "clin_a" }} {PARA 6 "" 1 "" {TEXT -1 15 "`convol/add_li`" }}{PARA 6 "" 1 "" {TEXT -1 12 "`convol/fus`" }}{PARA 6 "" 1 "" {TEXT -1 16 "`convol/smaller`" }}{PARA 6 "" 1 "" {TEXT -1 12 "`convol/tri`" }}{PARA 6 "" 1 "" {TEXT -1 17 "`convol_a/add_li`" }}{PARA 6 "" 1 "" {TEXT -1 14 "`convol_a/fus `" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#QK--------------~convol_a/fus~--- -----------6\"" }}{PARA 6 "" 1 "" {TEXT -1 69 "Names used as global na mes, but not declared: : `convol/smaller`" }}{PARA 6 "" 1 "" {TEXT -1 3 "jnt" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#QB--------------~jn t~--------------6\"" }}{PARA 6 "" 1 "" {TEXT -1 55 "These global varia bles start with an '_': : _X" }}{PARA 6 "" 1 "" {TEXT -1 7 "l in2mat" }}{PARA 6 "" 1 "" {TEXT -1 7 "mat2pie" }}{PARA 6 "" 1 "" {TEXT -1 7 "mat_esp" }}{PARA 6 "" 1 "" {TEXT -1 7 "mat_lap" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#QF--------------~mat_lap~--------------6\"" }}{PARA 6 "" 1 "" {TEXT -1 54 "Names used as global names, but not dec lared: : z" }}{PARA 6 "" 1 "" {TEXT -1 7 "mat_plo" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#QF--------------~mat_plo~--------------6\"" }} {PARA 6 "" 1 "" {TEXT -1 55 "These constants cannot be assigned a valu e: : 10" }}{PARA 6 "" 1 "" {TEXT -1 55 "Names used as global na mes, but not declared: : 10" }}{PARA 6 "" 1 "" {TEXT -1 9 "mat_pr imi" }}{PARA 6 "" 1 "" {TEXT -1 7 "mat_var" }}{PARA 6 "" 1 "" {TEXT -1 7 "pie2mat" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#QF--------------~pie2 mat~--------------6\"" }}{PARA 6 "" 1 "" {TEXT -1 54 "Declared global \+ variables, but never used: : z" }}{PARA 6 "" 1 "" {TEXT -1 12 "smaller_clin" }}{PARA 6 "" 1 "" {TEXT -1 16 "`splines/convol`" }} {PARA 6 "" 1 "" {TEXT -1 18 "`splines/convol_a`" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#QO--------------~splines/convol_a~--------------6\"" }} {PARA 6 "" 1 "" {TEXT -1 55 "These global variables start with an '_': : _X" }}{PARA 6 "" 1 "" {TEXT -1 14 "`splines/init`" }} {PARA 6 "" 1 "" {TEXT -1 17 "`splines/mat_int`" }}{PARA 6 "" 1 "" {TEXT -1 17 "`splines/xdiffer`" }}{PARA 6 "" 1 "" {TEXT -1 7 "val_mat " }}{PARA 6 "" 1 "" {TEXT -1 11 "`value/Fus`" }}{PARA 6 "" 1 "" {TEXT -1 11 "`value/Tri`" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {EXCHG {PARA 258 "" 0 "" {TEXT -1 64 "Copyright (c) 1999-2005 Pierre L . Douillet \n" }}{PARA 258 "" 0 "" {TEXT -1 11 "li cence GPL" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT -1 195 "libre reproduction pour un usage universitaire sous reserve d' une copie compl\350te,\navec reproduction du programme source dont, en particulier, la pr\351sente mention\n \n\naucune garantie de fiabilit \351. " }}{PARA 258 "" 0 "" {TEXT -1 89 "en particulier, toute utilisa tion dans un contexte industriel est vivement d\351conseill\351e\n " } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}}{MARK "18 1" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 7258616 7258656 } {RTABLE M6R0 I4RTABLE_SAVE/7258616X*%)anythingG6"6"\[[[[[t%"%/%'convolG%/splines/convolG/%)c onvol_aG%1splines/convol_aG/%(mat_intG%0splines/mat_intG/%(xdifferG%0splines/xd ifferGF& } {RTABLE M6R0 I4RTABLE_SAVE/7258656X*%)anythingG6"6"\[[[[[t*"*%'arrdimG%(pie2matG%(mat2pieG%( lin2matG%(val_matG%-smaller_clinG%%clinG%'clin_aG%(mat_ploGF& }