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<Startup-Code startupcode="########################################################### INIT #####################################################################\012restart:\012AnimationII := module()                                                                                     \012\012  uses     plots, LinearAlgebra; \012  export   V_V, V_F, F_V, F_F, A_R, A_L, B_R, B_L, C_NN, C_NR, U_NN, U_NR, I_01, I_02, I_03,\012            b_0, b_1, B_0, B_1, B_00, B_01, B_10, B_11, B_000, B_100, B_010, B_001, B_110, \012            B_101, B_011, B_111, EP2D, EP3D, VO, VOp, D_2, OPT3D, VOE2D, VOE3D, VOF2D, VOF3D, \012           n2L, n2l, n2c, DER, BOOL, t2i, i2t, i2i, T2I, FCPM, fcpm, LAB, lab, col, COLV, NB, stdRG, \012            stdINT, M2L, L2M, I2R, V2L, C2V, RElist1, RElist2,\012            LengthTable, Indices, Tab, Purger, SearchAllInTable, MergeTable, DeleteAllInList,\012            Echanger, Ordonner_d, Ordonner,\012                                                                                                            \012           nw_point, nw_line, nw_polygon, nw_rectangle, nw_circle, nw_disk, nw_arrow, nw_coords, \012            nw_curvcar, nw_curvpar, nw_fieldplot,\012            NW_arrow, NWD_arrow, NWE_arrow, NW_point, NW_line, NWD_line, NWE_line, NW_polygon, \012            NWE_curvcar, NWE_curvpar, NWD_curvcar, NWD_curvpar, NWC_curvcar, NWC_curvpar, \012           nw_point3d, nw_line3d, nw_polygon3d, nw_parallelepiped3d, nw_arrow3d, nw_coords3d, \012            nw_surfcar3d, nw_surfcar3d_domx, nw_surfcar3d_domy, \012            nw_surfcyl3d, nw_surfcyl3d_domr, nw_surfcyl3d_domt, nw_surfpar3d, \012            nw_curvpar3d, \012            NW_arrow3d, NW_point3d, NW_line3d, NW_polygon3d,\012            NWC_curvpar3d,\012            nw_surfparXd, \012                                                                                                            \012           Code, nbA, nbS, nbV, isinPC, iA, iP, DOS, GRS, ATS, NIS, nbIS, nbIE, nbIF, DOSt, ATSt, doSt,\012           P_pc, P_bkg, P_mode, P_view, P_dim, P_jeu, P_lit, P_tpc, P_opt, P_nbi, \012           F_film, F_set, F_jeu, F_out,\012                                                                                                            \012           null2d, nwpoint, nwline, nwpolygon, nwrectangle, nwcircle, nwdisk, nwarrow, nwcoords, \012            nwcurvcar, nwcurvpar, nwfieldplot, nwcurvcar_t, nwcurvpar_t,\012            NWarrow, NWDarrow, NWEarrow, NWpoint, NWline, NWDline, NWEline, NWpolygon,\012            NWEcurvcar, NWEcurvpar, NWDcurvcar, NWDcurvpar, NWCcurvcar, NWCcurvpar, \012            NWDcurvcar_t, NWDcurvpar_t, NWCcurvcar_t, NWCcurvpar_t,\012           null3d, nwpoint3d, nwline3d, nwpolygon3d, nwparallelepiped3d, nwcoords3d, nwarrow3d, \012            nwsurfcar3d, nwsurfcar3d_domx, nwsurfcar3d_domy, \012            nwsurfcyl3d, nwsurfcyl3d_domr, nwsurfcyl3d_domt, nwsurfpar3d, \012            nwcurvpar3d, \012            NWarrow3d, NWpoint3d, NWline3d, NWpolygon3d,\012            nwsurfcar3d_t, nwsurfcar3d_domx_t, nwsurfcar3d_domy_t,\012            nwsurfcyl3d_t, nwsurfcyl3d_domr_t, nwsurfcyl3d_domt_t, nwsurfpar3d_t,\012            nwcurvpar3d_t, \012            NWCcurvpar3d, NWCcurvpar3d_t,\012            nwsurfparXd, nwsurfparXd_t,\012                                                                                                            \012           selection, selectionA, selectionE, selectionF, tempo, tempoA, tempoE, tempoF, filtre, filtreA, \012            filtreE, filtreF,\012           image, voir, animerS, animerEF, vue, plan, FondS, FondSA, FondA, FondP, Fond, \012            Scene, PieceMS, PieceME, PieceMF, PieceM, PieceAS, PieceAE, PieceAF, PieceA, Piece, \012            SelTimeInFilm, SelRangInFilm, VoirS, VoirEF, DefilerS, DefilerEF, AnimerS, AnimerEF, Seance,\012            Calculs,\012                                                                                                            \012           slider2d, Curseur, VIDE2D, VIDE3D, FILMVIDE2D, FILMVIDE3D;\012  local   Paragraphe;\012  global  SPEED, SLIDER;\012  option package;\012\012Paragraphe := &quot;Constantes &amp; Variables globales&quot;:                                                            \012\012V_V := [true,true]: V_F := [true,false]: F_V := [false,true]: F_F := [false,false]:\012A_R := [above,right]: A_L := [above,left]: B_R := [below,right]: B_L := [below,left]:\012C_NN := [constrained,none]:   C_NR := [constrained,normal]: \012U_NN := [unconstrained,none]: U_NR := [unconstrained,normal]:\012I_01 := [0,1]: I_02 := [[0,1],[0,1]]: I_03 := [[0,1],[0,1],[0,1]]: b_0 := false: b_1 := true: \012B_0 := [b_0]: B_1 := [b_1]: B_00 := [b_0,b_0]: B_10 := [b_1,b_0]: B_01 := [b_0,b_1]: B_11 := [b_1,b_1]:\012B_000 := [b_0,b_0,b_0]: B_100 := [b_1,b_0,b_0]: B_010 := [b_0,b_1,b_0]: B_001 := [b_0,b_0,b_1]: \012B_110 := [b_1,b_1,b_0]: B_101 := [b_1,b_0,b_1]: B_011 := [b_0,b_1,b_1]: B_111 := [b_1,b_1,b_1]:\012EP2D := pointplot([0,0],color=white,axes=none): EP3D := pointplot3d([0,0,0],color=white,axes=none):\012D_2 := [2,nul]: OPT3D := [none,0]: VO := table(): VOp := p -&gt; [seq( VO, k=1..p )]: \012VOE2D := table([ &quot;b&quot;=F_F,&quot;v&quot;=default,&quot;m&quot;=C_NR,&quot;d&quot;=D_2,&quot;j&quot;=&quot;E&quot; ]):\012VOE3D := table([ &quot;b&quot;=F_F,&quot;v&quot;=default,&quot;m&quot;=C_NR,&quot;d&quot;=[3,[45,45]],&quot;j&quot;=&quot;E&quot;,&quot;l&quot;=light1,&quot;t&quot;=0 ]):\012VOF2D := table([ &quot;b&quot;=F_F,&quot;v&quot;=default,&quot;m&quot;=C_NR,&quot;d&quot;=D_2,&quot;j&quot;=&quot;F&quot; ]):\012VOF3D := table([ &quot;b&quot;=F_F,&quot;v&quot;=default,&quot;m&quot;=C_NR,&quot;d&quot;=[3,[45,45]],&quot;j&quot;=&quot;F&quot;,&quot;l&quot;=light1,&quot;t&quot;=0 ]):\012\012Paragraphe := &quot;Routines&quot;:                                                                                   \012\012n2L    := n_                 -&gt; convert(StringTools[Char](65+n_),name):\012n2l    := n_                 -&gt; convert(StringTools[Char](32+n_),name):\012n2c    := n_                 -&gt; convert(StringTools[Char](48+n_),name):\012DER    := L_                 -&gt; L_[nops(L_)]:\012BOOL   := b_                 -&gt; ceil(evalhf(b_)):\012t2i    := (I_,t_)            -&gt; (I_[2]-I_[1])*t_+I_[1]:\012i2t    := (I_,t_)            -&gt; if I_[1]=I_[2] then 0 else (t_-I_[1])/(I_[2]-I_[1]) end if:\012i2i    := (I1_,I2_,t_)       -&gt; t2i(I2_,i2t(I1_,t_)):\012T2I    := (II_,T_)           -&gt; [seq(t2i(II_[k__],T_[k__]),k__=1..nops(II_))]:\012FCPM   := (t_,a_,b_,c_)      -&gt; a_*(1-ceil(t_))+b_*(-floor(t_)+ceil(t_))+c_*floor(t_):\012fcpm   := (I_,t_,a_,b_,c_)   -&gt; FCPM(i2t(I_,t_),a_,b_,c_):\012LAB    := (I_,t_,f_,o_)      -&gt; fcpm(I_,t_,f_(I_[1]),f_(o_),f_(I_[2])):\012lab    := (I1_,I2_,t_,f_,o_) -&gt; fcpm(I1_,t_,f_(I2_[1]),f_(o_),f_(I2_[2])):\012col    := (n_,k_)            -&gt; COLOR(RGB,(k_ mod n_)/n_,(k_+1 mod n_)/n_,(k_+2 mod n_)/n_):\012COLV    := (n_,V_)           -&gt; COLOR(RGB,(floor(V_[1]) mod n_)/n_,(floor(V_[2]) mod n_)/n_,(floor(V_[3]) mod n_)/n_):\012NB     := name_              -&gt; convert(StringTools[Select](StringTools[IsDigit],name_),decimal,10):\012stdRG  := (d_,v_)            -&gt; [seq(-v_..v_,k__=1..d_)]:\012stdINT := (d_,v_)            -&gt; if d_=1 then [-v_,v_] else [seq([-v_,v_],k__=1..d_)] end if:\012M2L    := A_                 -&gt; [seq( Column(A_,j__) , j__=1..ColumnDimension(A_) )]:\012L2M    := LL_                -&gt; convert(LL_,Matrix)^%T:\012I2R    := II_                -&gt; \012 if type(II_,listlist) then [seq(II_[k__][1]..II_[k__][2],k__=1..nops(II_))]\012                       else II_[1]..II_[2]\012                       end if:\012V2L    := V_                 -&gt; convert(V_,list):\012C2V    := z                  -&gt; &lt;Re(z),Im(z)&gt;:\012                                                                                                            \012LengthTable := tab -&gt; nops([indices(tab)]):\012Indices := proc(T_) local ind__,k__,T__:\012 if type(T_,list) then T__ := convert(T_,table) else T__ := T_ end if:\012 ind__ := []:\012 for k__ in indices(T__) do \012  if nops(k__)=1 then ind__ := [op(ind__),op(k__)] \012                 else ind__ := [op(ind__),k__] \012  end if end do:\012 ind__:\012 end proc:\012Tab := proc(T_,l_:=NULL,k_:=NULL,ij_:=NULL) local res__:\012 res__ := T_:\012 if ((type(T_,'table') or type(T_,Matrix)) or (type(T_,Vector) or type(T_,list)))\012  then  if ij_&lt;&gt;NULL then res__ := T_[op(l_)][op(k_)][op(ij_)] \012   else if k_&lt;&gt;NULL  then res__ := T_[op(l_)][op(k_)] \012   else if l_&lt;&gt;NULL  then res__ := T_[op(l_)] \012   end if end if end if\012  end if:\012 res__:\012 end proc:\012Purger := proc(II_,symb_) local II__,k__:\012 II__ := []:\012 for k__ from 1 to nops(II_) do\012  if II_[k__][1]&lt;&gt;symb_  then II__ := [op(II__),II_[k__]] end if:\012  end do:\012 II__:\012 end proc:\012SearchAllInTable := proc(elt_,L_) local Ind__,k__:\012 Ind__ := []:\012 for k__ in Indices(L_) do\012  if L_[op(k__)]=elt_ then Ind__ := [op(Ind__),k__] end if:\012  end do:\012 Ind__:\012 end proc:\012MergeTable  := proc(Vo_,Vs_) local tab__,k__:\012 tab__ := Vo_:\012 for k__ in Indices(Vs_) do tab__[op(k__)] := Vs_[op(k__)] end do:\012 op(tab__):\012 end proc:\012DeleteAllInList := proc(elt_,L_) local L__,k__:\012 L__ := []:\012 for k__ in L_ do\012  if k__&lt;&gt;elt_ then L__ := [op(L__),k__] end if:\012  end do:\012 L__:\012 end proc:\012Echanger := proc(L_,i_,j_) local tamp__,LL__:\012 LL__ := L_:\012 tamp__ := LL__[i_]: LL__[i_] := LL__[j_]: LL__[j_] := tamp__:\012 LL__:\012 end proc:\012Ordonner_d := proc(L_,i_) local j__,LL__:\012 LL__ := L_:\012 for j__ from i_ to nops(LL__) do \012  if LL__[j__][2]&gt;LL__[i_][2] then LL__ := Echanger(LL__,i_,j__) end if:\012  end do:\012 LL__:\012 end proc:\012Ordonner := proc(L_,sens_) local i__,LL__:\012 LL__ := L_:\012 for i__ from 1 to nops(LL__) do LL__ := Ordonner_d(LL__,i__) end do:\012 if sens_=&quot;c&quot; then LL__ := ListTools:-Reverse(LL__) end if:\012 LL__:\012 end proc:\012                                                                                                            \012RElist1 := MM_  -&gt; \012 if nops(MM_)=1 then [[MM_[1]],[MM_[1]]] \012                else [[seq( MM_[k__],k__=1..nops(MM_), 2)],[seq( MM_[k__+1],k__=1..nops(MM_), 2)]] \012                end if:\012RElist2 := MM_  -&gt; \012 if nops(MM_)=1 then [[MM_[1]],[MM_[1]]] \012                else [[seq( MM_[k__],k__=1..nops(MM_)-1) ],[seq( MM_[k__+1],k__=1..nops(MM_)-1)] ] \012                end if:\012\012Paragraphe := &quot;Outils Graphiques 2D&quot;:                                                                       \012\012nw_point     := (M_,AT_)  -&gt; \012plots[display]\012  ([ plots[pointplot](M_,symbol=AT_[4],color=AT_[1]),\012     plots[textplot]([M_[1],M_[2],(AT_[2])],align=AT_[3],color=AT_[1]) ]):\012nw_line      := (MN_,AT_) -&gt; \012 plots[display](plottools[line]  (V2L(MN_[1]),V2L(MN_[2]),color=AT_[1],linestyle=AT_[3],thickness=AT_[4])):\012nw_circle    := (Cr_,AT_) -&gt; \012 plots[display](plottools[circle](V2L(Cr_[1]),Cr_[2]     ,color=AT_[1],linestyle=AT_[3],thickness=AT_[4])):\012nw_polygon   := (MM_,AT_) -&gt; \012 plots[display](plottools[polygon]([seq(V2L(MM_[k]),k=1..nops(MM_))],\012                color=AT_[1],transparency=AT_[2],linestyle=AT[3],thickness=AT[4])):\012nw_rectangle := (MN_,AT_) -&gt; \012 plots[display](plottools[rectangle](MN_[1],MN_[2],\012                color=AT_[1],transparency=AT_[2],linestyle=AT[3],thickness=AT[4])):\012nw_disk      := (Cr_,AT_) -&gt;\012 plots[display](plottools[disk](V2L(Cr_[1]),Cr_[2],\012                color=AT_[1],transparency=AT_[2],linestyle=AT[3],thickness=AT[4])):\012nw_arrow     := (MV_,AT_) -&gt; \012 plots[display](plots[arrow](MV_[1],[MV_[2]],color=AT_[1],shape=arrow,width=[AT_[4]])):\012nw_coords    := proc(Nr_,AT_) local G__,R__,C__,S__:\012 G__  := [AT_[4],AT_[4]]:\012 R__ := [seq(Nr_[2][k__][1]..Nr_[2][k__][2],k__=1..2)]:\012 C__ := [seq(col(2,k__),k__=0..1)]:\012 S__ := [AT_[3],AT_[3]]:\012 plots[display](coordplot(Nr_[1],R__,colour=C__,linestyle=S__,grid=G__)):\012 end proc:\012nw_curvcar  := proc(F_,AT_,y_:=NULL) \012 plots[display](plot(\012   F_[1](x__,y_), x__=I2R(F_[2]),\012   color=AT_[1],linestyle=AT_[3],thickness=AT_[4],labels=[x,y],discont=false)):\012 end proc:\012nw_curvpar := proc(F_,AT_,v_:=NULL) \012 plots[display](plot(\012   [op(V2L(F_[1](u__,v_))), u__=I2R(F_[2])],\012   color=AT_[1],linestyle=AT_[3],thickness=AT_[4],labels=[x,y],discont=false)):\012 end proc:\012nw_fieldplot := proc(F_,AT_)\012 plots[fieldplot](\012   V2L(F_[1](x__,y__)),x__=I2R(F_[2][1]),y__=I2R(F_[2][2]),\012   color=AT_[1],clipping=AT_[2],grid=AT_[3],fieldstrength=AT_[4]):\012 end proc:\012                                                                                                            \012NWC_curvcar  := proc(FF_,AT_,y_:=NULL) \012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_curvcar([FF_[1][k__],FF_[2]],AT_[k__],y_) , k__=1..nops(FF_[1]) ) ])\012  else plots[display]([ seq( nw_curvcar([FF_[1][k__],FF_[2]],AT_,y_)      , k__=1..nops(FF_[1]) ) ])\012  end if:\012 end proc:\012NWD_curvcar  := proc(FF_,AT_,y_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_curvcar([FF_[1],FF_[2][k__]],AT_[k__],y_) , k__=1..nops(FF_[2]) ) ])\012  else plots[display]([ seq( nw_curvcar([FF_[1],FF_[2][k__]],AT_,y_)      , k__=1..nops(FF_[2]) ) ])\012  end if:\012 end proc:\012NWE_curvcar := proc(FF_,AT_,y_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_curvcar(FF_[k__],AT_[k__],y_) , k__=1..nops(FF_) ) ])\012  else plots[display]([ seq( nw_curvcar(FF_[k__],AT_,y_)      , k__=1..nops(FF_) ) ])\012  end if:\012 end proc:\012NWC_curvpar := proc(FF_,AT_,v_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_curvpar([FF_[1][k__],FF_[2]],AT_[k__],v_) , k__=1..nops(FF_[1]) ) ])\012  else plots[display]([ seq( nw_curvpar([FF_[1][k__],FF_[2]],AT_,v_)      , k__=1..nops(FF_[1]) ) ])\012  end if:\012 end proc:\012NWD_curvpar := proc(FF_,AT_,v_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_curvpar([FF_[1],FF_[2][k__]],AT_[k__],v_) , k__=1..nops(FF_[2]) ) ])\012  else plots[display]([ seq( nw_curvpar([FF_[1],FF_[2][k__]],AT_,v_)      , k__=1..nops(FF_[2]) ) ])\012  end if:\012 end proc:\012NWE_curvpar := proc(FF_,AT_,v_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_curvpar(FF_[k__],AT_[k__],v_) , k__=1..nops(FF_) ) ])\012  else plots[display]([ seq( nw_curvpar(FF_[k__],AT_,v_)      , k__=1..nops(FF_) ) ])\012  end if:\012 end proc:\012NW_arrow := proc(MVV_,AT_)  \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_arrow([MVV_[1],MVV_[2][k__]],AT_[k__]),k__=1..nops(MVV_[2]) ) ])\012  else plots[display]([ seq( nw_arrow([MVV_[1],MVV_[2][k__]],AT_)     ,k__=1..nops(MVV_[2]) ) ])\012  end if:\012 end proc:\012NWD_arrow := NW_arrow:\012NWE_arrow := proc(MVMV_,AT_) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_arrow(MVMV_[k__],AT_[k__]),k__=1..nops(MVMV_) ) ])\012  else plots[display]([ seq( nw_arrow(MVMV_[k__],AT_)     ,k__=1..nops(MVMV_) ) ])\012  end if:\012 end proc:\012NW_point  := proc(MM_,AT_)  \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_point(MM_[k__],AT_[k__]),k__=1..nops(MM_) ) ])\012  else plots[display]([ seq( nw_point(MM_[k__],AT_)     ,k__=1..nops(MM_) ) ])\012  end if:\012 end proc:\012NW_line   := proc(MMNN_,AT_)\012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_line([MMNN_[1][k__],MMNN_[2][k__]],AT_[k__]),k__=1..nops(MMNN_[1]) ) ])\012  else plots[display]([ seq( nw_line([MMNN_[1][k__],MMNN_[2][k__]],AT_)     ,k__=1..nops(MMNN_[1]) ) ])\012  end if:\012 end proc:\012NWD_line  := proc(MNN_,AT_)\012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_line([MNN_[1],MNN_[2][k__]],AT_[k__]),k__=1..nops(MNN_[2]) ) ])\012  else plots[display]([ seq( nw_line([MNN_[1],MNN_[2][k__]],AT_)     ,k__=1..nops(MNN_[2]) ) ])\012  end if:\012 end proc:\012NWE_line  := proc(MNMN_,AT_)\012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_line(MNMN_[k__],AT_[k__]),k__=1..nops(MNMN_) ) ])\012  else plots[display]([ seq( nw_line(MNMN_[k__],AT_)     ,k__=1..nops(MNMN_) ) ])\012  end if:\012 end proc:\012NW_polygon := proc(MMMM_,AT_)  \012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_polygon(MMMM_[k__],AT_[k__]),k__=1..nops(MMMM_) ) ])\012  else plots[display]([ seq( nw_polygon(MMMM_[k__],AT_)     ,k__=1..nops(MMMM_) ) ])\012  end if:\012 end proc:\012Paragraphe := &quot;Outils Graphiques 3D&quot;:                                                                      \012\012nw_point3d := (M_,AT_) -&gt; \012 plots[display]\012  ([ plots[pointplot3d](M_,symbol=AT_[4],color=AT_[1]),\012     plots[textplot3d]([M_[1],M_[2],M_[3],typeset(AT_[2])],align=AT_[3],color=AT_[1]) ]):\012nw_line3d := (MN_,AT_) -&gt; \012 plots[display](plottools[line](V2L(MN_[1]),V2L(MN_[2]),linestyle=AT_[3],color=AT_[1],thickness=AT_[4])):\012nw_polygon3d   := (MM_,AT_) -&gt; \012 plots[display](plottools[polygon]([seq(V2L(MM_[k]),k=1..nops(MM_))],color=AT_[1],transparency=AT_[2])):\012nw_parallelepiped3d   := (MM_,AT_) -&gt; \012 plots[display](plottools[parallelepiped](op(MM_)),color=AT_[1],transparency=AT_[2]):\012nw_surfcar3d  := proc(F_,AT_,w_:=NULL) local x__,y__:\012 plots[display](plot3d(\012  F_[1](x__,y__,w_), \012  x__=I2R(F_[2])[1],y__=I2R(F_[2])[2], \012  color=AT_[1],transparency=AT_[2],style=AT_[3],grid=[AT_[4],AT_[4]]),\012  labels=[x,y,z]\012  ):\012 end proc:\012nw_surfcar3d_domx  := proc(F_,AT_,w_:=NULL) local x__,y__:\012 plots[display](plot3d(\012  F_[1](x__,y__,w_), \012  x__=I2R(F_[2][1]),y__=F_[2][2][1](x__)..F_[2][2][2](x__), \012  color=AT_[1],transparency=AT_[2],style=AT_[3],grid=[AT_[4],AT_[4]]),\012  labels=[x,y,z]\012  ):\012 end proc:\012nw_surfcar3d_domy  := proc(F_,AT_,w_:=NULL) local x__,y__:\012 plots[display](plot3d(\012  F_[1](x__,y__,w_), \012  x__=F_[2][1][1](y__)..F_[2][1][2](y__),y__=I2R(F_[2][2]), \012  color=AT_[1],transparency=AT_[2],style=AT_[3],grid=[AT_[4],AT_[4]]),\012  labels=[x,y,z]\012  ):\012 end proc:\012nw_surfcyl3d  := proc(F_,AT_,w_:=NULL) local r__,t__:\012 addcoords(nw_cylindrical,[z,r,theta],[r*cos(theta),r*sin(theta),z]):\012 plots[display](plot3d(\012  F_[1](r__,t__,w_), \012  r__=I2R(F_[2])[1],t__=I2R(F_[2])[2], \012  coords=nw_cylindrical,\012  color=AT_[1],transparency=AT_[2],style=AT_[3],grid=[AT_[4],AT_[4]]),\012  labels=[x,y,z]\012  ):\012 end proc:\012nw_surfcyl3d_domr  := proc(F_,AT_,w_:=NULL) local r__,t__:\012 addcoords(nw_cylindrical,[z,r,theta],[r*cos(theta),r*sin(theta),z]):\012 plots[display](plot3d(\012  F_[1](r__,t__,w_), \012  r__=I2R(F_[2][1]),t__=F_[2][2][1](r__)..F_[2][2][2](r__), \012  coords=nw_cylindrical,\012  color=AT_[1],transparency=AT_[2],style=AT_[3],grid=[AT_[4],AT_[4]]),\012  labels=[x,y,z]\012  ):\012 end proc:\012nw_surfcyl3d_domt  := proc(F_,AT_,w_:=NULL) local r__,t__:\012 addcoords(nw_cylindrical,[z,r,theta],[r*cos(theta),r*sin(theta),z]):\012 plots[display](plot3d(\012  F_[1](r__,t__,w_), \012  r__=F_[2][1][1](t__)..F_[2][1][2](t__),t__=I2R(F_[2][2]), \012  coords=nw_cylindrical,\012  color=AT_[1],transparency=AT_[2],style=AT_[3],grid=[AT_[4],AT_[4]]),\012  labels=[x,y,z]\012  ):\012 end proc:\012nw_surfpar3d := proc(F_,AT_,w_:=NULL) local u__,v__:\012 plots[display](plot3d(\012  V2L(F_[1](u__,v__,w_)), \012  u__=I2R(F_[2])[1],v__=I2R(F_[2])[2], \012  color=AT_[1],transparency=AT_[2],style=AT_[3],grid=[AT_[4],AT_[4]],coords=rectangular),\012  labels=[x,y,z]\012  ):\012 end proc:\012nw_curvpar3d := proc(F_,AT_,v_:=NULL) local u__:\012 plots[display](plots[spacecurve](\012  V2L(F_[1](u__,v_)),\012  u__= I2R(F_[2]),\012  color=AT_[1],linestyle=AT_[3],thickness=AT_[4])):\012 end proc:\012nw_arrow3d     := (MV_,AT_)   -&gt;\012 plots[display]\012  ([ plottools[line](V2L(MV_[1]),V2L(MV_[1]+MV_[2]),color=AT_[1],linestyle=AT_[3],thickness=AT_[4]),\012     plottools[point](V2L(MV_[1]+MV_[2]),color=AT_[1],symbol=solidsphere) ]):\012nw_coords3d := proc(Nr_,AT_) local G__,R__,V__,C__,S__:\012 G__ := [AT_[4],AT_[4]]:\012 R__ := I2R(Nr_[2]):\012 V__ := stdRG(3,1):\012 C__ := [seq(col(3,k__),k__=0..2)]:\012 S__ := AT_[3]:\012 coordplot3d(Nr_[1],R__,colour=C__,style=S__,grid=G__,view=V__):\012 end proc:\012\012Paragraphe := &quot;Outils Graphiques XD&quot;:                                                                      \012\012nw_surfparXd := proc(F_,AT_,w_:=NULL) local u__,v__:\012 plots[display](plot3d(\012  V2L(F_[1]([u__,v__],w_)), \012  u__=I2R(F_[2])[1],v__=I2R(F_[2])[2], \012  color=AT_[1],transparency=AT_[2],style=AT_[3],grid=[AT_[4],AT_[4]],coords=rectangular),\012  labels=[x,y,z]\012  ):\012 end proc:\012                                                                                                            \012NW_arrow3d     := (MVV_,AT_)  -&gt;  \012 plots[display](seq(nw_arrow3d([MVV_[1],MVV_[2][k__]],AT_[k__]),k__=1..nops(MVV_[2]))):\012NW_point3d     := (MM_,AT_)   -&gt;  \012 plots[display]([seq( nw_point3d(MM_[k__],AT_[k__]),k__=1..nops(MM_))]):\012NW_line3d      := (MMNN_,AT_) -&gt; \012 plots[display]([seq(nw_line3d([MMNN_[1][k__],MMNN_[2][k__]],AT_),k__=1..nops(MMNN_[1]))]):\012NW_polygon3d   := (MMMM_,AT_) -&gt;  \012 plots[display]([seq( nw_polygon3d(MMMM_[k__],AT_),k__=1..nops(MMMM_))]):\012NWC_curvpar3d := proc(FF_,AT_,v_:=NULL) \012 plots[display]([\012  seq( nw_curvpar3d([FF_[1][k__],FF_[2]],AT_,v_) , k__=1..nops(FF_[1]) )\012 ]):\012 end proc:\012\012Paragraphe := &quot;Acc\303\250s Donn\303\251es&quot;:                                                                              \012\012 Paragraphe := &quot;Structure PC&quot;:                                                                              \012\012Code := (PC_) -&gt; [indices(PC_)]:\012nbA  := proc(PC_) local L__,k__,cd__:\012 cd__ := Code(PC_):\012 L__ := {}:\012 for k__ from 1 to nops(cd__) do\012  L__ := L__ union {cd__[k__][1]}:\012  end do:\012 nops(L__)-1:\012 end proc:\012nbS := proc(PC_,a_) local k__,s__,cd__:\012 cd__ := Code(PC_):\012 s__ := 0:\012 for k__ from 1 to nops(cd__) do\012  if cd__[k__][1]=a_ then s__ := s__+1 end if:\012  end do:\012 s__-1:\012 end proc:\012nbV := (PC_,a_,s_) -&gt; nops(PC_[a_,s_]):\012isinPC := proc(PC_,a_,s_) local t1__,t2__:\012 t1__ := (a_&gt;=0 and a_&lt;=nbA(PC_)):\012 if t1__ then t2__ := (s_&gt;=1 and s_&lt;=nbS(PC_,a_)) else t2__ := false end if:\012 (t1__ and t2__):\012 end proc:\012iA    := (PC_,a_) -&gt; PC_[a_,0]:\012iP    := proc(PC_) local Lia0__,Lia__:\012 Lia0__ := [seq( evalf(abs(iA(PC_,a__)[2]-iA(PC_,a__)[1])) , a__=1..nbA(PC_) )]:\012 Lia__ := remove(x-&gt;evalf(x=0),Lia0__):\012 Lia__ := map(x__-&gt;x__/min(Lia__),Lia0__):\012 end proc:\012\012                                                                                                            \012\012DOS   := (PC_,a_,s_,v_) -&gt; PC_[a_,s_][v_,1]:\012GRS   := (PC_,a_,s_,v_) -&gt; PC_[a_,s_][v_,2]:\012ATS   := (PC_,a_,s_,v_) -&gt; PC_[a_,s_][v_,3]:\012NIS   := (PC_,a_,s_,v_) -&gt; PC_[a_,s_][v_,4]:\012\012nbIS   := (PC_,a_)  -&gt; SPEED*add(NIS(PC_,a_,s__,1),s__=1..nbS(PC_,a_)):\012nbIE   := PC_       -&gt; add( ceil(iP(PC_)[a__]*nbIS(PC_,a__)) , a__=1..nbA(PC_) ):\012nbIF   := PC_       -&gt; max([ seq( nbIS(PC_,a__) , a__=1..nbA(PC_) ) ])*max(iP(PC_)):\012\012DOSt  := (PC_,a_,s_,v_)    -&gt; unapply(DOS(PC_,a_,s_,v_),t_):\012ATSt  := (PC_,a_,s_,v_)    -&gt; unapply(ATS(PC_,a_,s_,v_),t_):\012doSt  := (PC_,a_,s_,v_,l_) -&gt; unapply(DOS(PC_,a_,s_,v_)[l_],t_):\012\012 Paragraphe := &quot;Structure PIECE&quot;:                                                                           \012\012P_pc   := PIECE_ -&gt; PIECE_[1]:\012P_bkg  := PIECE_ -&gt; PIECE_[2][&quot;b&quot;]:\012P_view := PIECE_ -&gt; PIECE_[2][&quot;v&quot;]:\012P_mode := PIECE_ -&gt; PIECE_[2][&quot;m&quot;]:\012P_dim  := PIECE_ -&gt; PIECE_[2][&quot;d&quot;]:\012P_jeu  := PIECE_ -&gt; PIECE_[2][&quot;j&quot;]:\012P_lit  := PIECE_ -&gt; PIECE_[2][&quot;l&quot;]:\012P_tpc  := PIECE_ -&gt; PIECE_[2][&quot;t&quot;]:\012P_opt  := PIECE_ -&gt; \012 table([ &quot;b&quot;=PIECE_[2][&quot;b&quot;],&quot;v&quot;=PIECE_[2][&quot;v&quot;],&quot;m&quot;=PIECE_[2][&quot;m&quot;],\012         &quot;d&quot;=PIECE_[2][&quot;d&quot;],&quot;j&quot;=PIECE_[2][&quot;j&quot;],&quot;l&quot;=PIECE_[2][&quot;l&quot;],&quot;t&quot;=PIECE_[2][&quot;t&quot;] ]):\012P_nbi  := proc(PIECE_,vrs_) local PC__:\012 PC__ := P_pc(PIECE_):\012  if       vrs_[&quot;j&quot;]=&quot;E&quot; then nbIE(PC__) \012   else if vrs_[&quot;j&quot;]=&quot;F&quot; then nbIF(PC__) \012   else                       nbIS(PC__,vrs_[&quot;j&quot;])\012  end if end if:\012 end proc:\012\012 Paragraphe := &quot;Structure FILM&quot;:                                                                            \012\012F_film  := (FILM_,T_) -&gt; FILM_[1](FILM_[2],T_): \012F_set   := proc(FILM_,T_) local ind__,boo__:\012 ind__ := Indices(F_film(FILM_,T_)):\012 ind__ := DeleteAllInList(0,ind__):\012 boo__ := x__ -&gt; type(x__,string):\012 remove(boo__,ind__):\012 end proc:\012F_jeu   := (FILM_,T_) -&gt; F_film(FILM_,T_)[0]:\012F_out   := proc(FILM_,T_) local film__,ind__,boo__,k__:\012 film__ := F_film(FILM_,T_):\012 ind__ := Indices(film__):\012 boo__ := x__ -&gt; type(x__,string):\012 ind__ := sort(select(boo__,ind__),lexorder):\012 [seq(film__[k__],k__ in ind__)]:\012 end proc:\012\012Paragraphe := &quot;Proc\303\251dures G\303\251om\303\251triques Ad-Hoc&quot;:                                                             \012\012null2d       := (PC_,a_,s_,v_,t_) -&gt; EP2D:\012nwpoint      := (PC_,a_,s_,v_,t_) -&gt; nw_point     (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwpolygon    := (PC_,a_,s_,v_,t_) -&gt; nw_polygon   (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwrectangle  := (PC_,a_,s_,v_,t_) -&gt; nw_rectangle (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwcircle     := (PC_,a_,s_,v_,t_) -&gt; nw_circle    (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwdisk       := (PC_,a_,s_,v_,t_) -&gt; nw_disk      (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwarrow      := (PC_,a_,s_,v_,t_) -&gt; nw_arrow     (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwline       := (PC_,a_,s_,v_,t_) -&gt; nw_line      (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwcoords     := (PC_,a_,s_,v_,t_) -&gt; nw_coords    (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwcurvcar    := (PC_,a_,s_,v_,t_) -&gt; nw_curvcar   (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwcurvpar    := (PC_,a_,s_,v_,t_) -&gt; nw_curvpar   (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwfieldplot  := (PC_,a_,s_,v_,t_) -&gt; nw_fieldplot (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwcurvcar_t  := (PC_,a_,s_,v_,t_) -&gt; nw_curvcar   (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_),t_):\012nwcurvpar_t  := (PC_,a_,s_,v_,t_) -&gt; nw_curvpar   (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_),t_):\012NWarrow      := (PC_,a_,s_,v_,t_) -&gt; NW_arrow     (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012NWDarrow     := (PC_,a_,s_,v_,t_) -&gt; NWD_arrow    (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012NWEarrow     := (PC_,a_,s_,v_,t_) -&gt; NWE_arrow    (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012NWCcurvcar   := (PC_,a_,s_,v_,t_) -&gt; NWC_curvcar  (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012NWCcurvpar   := (PC_,a_,s_,v_,t_) -&gt; NWC_curvpar  (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012NWDcurvcar   := (PC_,a_,s_,v_,t_) -&gt; NWD_curvcar  (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012NWDcurvpar   := (PC_,a_,s_,v_,t_) -&gt; NWD_curvpar  (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012NWEcurvcar   := (PC_,a_,s_,v_,t_) -&gt; NWE_curvcar  (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012NWEcurvpar   := (PC_,a_,s_,v_,t_) -&gt; NWE_curvpar  (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012NWpoint      := (PC_,a_,s_,v_,t_) -&gt; NW_point     (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012NWline       := (PC_,a_,s_,v_,t_) -&gt; NW_line      (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012NWDline      := (PC_,a_,s_,v_,t_) -&gt; NWD_line     (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012NWEline      := (PC_,a_,s_,v_,t_) -&gt; NWE_line     (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012NWpolygon    := (PC_,a_,s_,v_,t_) -&gt; NW_polygon   (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012NWDcurvcar_t := (PC_,a_,s_,v_,t_) -&gt; NWD_curvpar  (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_),t_):\012NWDcurvpar_t := (PC_,a_,s_,v_,t_) -&gt; NWD_curvpar  (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_),t_):\012NWCcurvcar_t := (PC_,a_,s_,v_,t_) -&gt; NWC_curvcar  (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_),t_):\012NWCcurvpar_t := (PC_,a_,s_,v_,t_) -&gt; NWC_curvpar  (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_),t_):\012                                                                                                            \012null3d             := (PC_,a_,s_,v_,t_) -&gt; EP3D:\012nwpoint3d          := (PC_,a_,s_,v_,t_) -&gt; nw_point3d        (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwline3d           := (PC_,a_,s_,v_,t_) -&gt; nw_line3d         (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwpolygon3d        := (PC_,a_,s_,v_,t_) -&gt; nw_polygon3d      (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwparallelepiped3d := (PC_,a_,s_,v_,t_) -&gt; nw_parallelepiped3d(DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwarrow3d          := (PC_,a_,s_,v_,t_) -&gt; nw_arrow3d        (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwcoords3d         := (PC_,a_,s_,v_,t_) -&gt; nw_coords3d       (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwsurfcar3d        := (PC_,a_,s_,v_,t_) -&gt; nw_surfcar3d      (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwsurfcar3d_domx   := (PC_,a_,s_,v_,t_) -&gt; nw_surfcar3d_domx (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwsurfcar3d_domy   := (PC_,a_,s_,v_,t_) -&gt; nw_surfcar3d_domy (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwsurfcyl3d        := (PC_,a_,s_,v_,t_) -&gt; nw_surfcyl3d      (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwsurfcyl3d_domr   := (PC_,a_,s_,v_,t_) -&gt; nw_surfcyl3d_domr (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwsurfcyl3d_domt   := (PC_,a_,s_,v_,t_) -&gt; nw_surfcyl3d_domt (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwsurfpar3d        := (PC_,a_,s_,v_,t_) -&gt; nw_surfpar3d      (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwcurvpar3d        := (PC_,a_,s_,v_,t_) -&gt; nw_curvpar3d      (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012NWarrow3d          := (PC_,a_,s_,v_,t_) -&gt; NW_arrow3d        (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012NWpoint3d          := (PC_,a_,s_,v_,t_) -&gt; NW_point3d        (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012NWline3d           := (PC_,a_,s_,v_,t_) -&gt; NW_line3d         (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012NWpolygon3d        := (PC_,a_,s_,v_,t_) -&gt; NW_polygon3d      (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012NWCcurvpar3d       := (PC_,a_,s_,v_,t_) -&gt; NWC_curvpar3d     (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwcurvpar3d_t      := (PC_,a_,s_,v_,t_) -&gt; nw_curvpar3d      (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_),t_):\012NWCcurvpar3d_t     := (PC_,a_,s_,v_,t_) -&gt; NWC_curvpar3d     (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_),t_):\012nwsurfcar3d_t      := (PC_,a_,s_,v_,t_) -&gt; nw_surfcar3d      (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_),t_):\012nwsurfcar3d_domx_t := (PC_,a_,s_,v_,t_) -&gt; nw_surfcar3d_domx (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_),t_):\012nwsurfcar3d_domy_t := (PC_,a_,s_,v_,t_) -&gt; nw_surfcar3d_domy (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_),t_):\012nwsurfcyl3d_t      := (PC_,a_,s_,v_,t_) -&gt; nw_surfcyl3d      (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_),t_):\012nwsurfcyl3d_domr_t := (PC_,a_,s_,v_,t_) -&gt; nw_surfcyl3d_domr (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_),t_):\012nwsurfcyl3d_domt_t := (PC_,a_,s_,v_,t_) -&gt; nw_surfcyl3d_domt (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_),t_):\012nwsurfpar3d_t      := (PC_,a_,s_,v_,t_) -&gt; nw_surfpar3d      (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_),t_):\012                                                                                                            \012nwsurfparXd        := (PC_,a_,s_,v_,t_) -&gt; nw_surfparXd      (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_)):\012nwsurfparXd_t      := (PC_,a_,s_,v_,t_) -&gt; nw_surfparXd      (DOSt(PC_,a_,s_,v_)(t_) ,ATSt(PC_,a_,s_,v_)(t_),t_):\012\012Paragraphe := &quot;S\303\251quencement&quot;:                                                                               \012\012selection := proc(L_,t_) local L__, k__:\012 L__ := ListTools[PartialSums](L_):\012 L__ := [seq(L__[kk__]/DER(L__),kk__=1..nops(L__))]:\012 k__ := 1:\012 while (is(t_&gt;=L__[k__]) and k__&lt;nops(L__)) do k__ := k__+1 end do:\012 if is(t_&lt;=DER(L__)) then k__ := k__-1 end if:\012 if k__=nops(L__) then k__:=0 end if:\012 k__:\012 end proc:\012selectionA := proc(PC_,a_,t_) local L__, ss__:\012 L__ := [0,seq(NIS(PC_,a_,s__,1) , s__=1..nbS(PC_,a_))]:\012 ss__ := selection(L__,i2t(iA(PC_,a_),t_)):\012 if ss__=0 then [[-1,-1]] else [[a_,ss__]] end if:\012 end proc:\012selectionE := proc(PC_,t_) local L__, a__, aa__,ss__:\012 aa__ := 0:\012 for a__ from 1 to nbA(PC_) do\012  if ( is(evalf(t_-iA(PC_,a__)[1])&gt;=0) and is(evalf(t_-iA(PC_,a__)[2])&lt;=0) ) then aa__ := a__ end if: \012  end do:\012 if aa__=0 then [[-1,-1]] else selectionA(PC_,aa__,t_) end if:\012 end proc:\012selectionF := (PC_,t_) -&gt; [seq( op(selectionA(PC_,a__,t_)) , a__=1..nbA(PC_) )]:\012                                                                                                            \012tempo := proc(II_,N_) local L__:\012 L__ := [seq(abs(II_[k__][2]-II_[k__][1]),k__=1..nops(II_))]:\012 L__ := ListTools[PartialSums](L__):\012 L__ := [seq(L__[k__]/DER(L__),k__=1..nops(L__)-1),1]:\012 L__ := map(x__-&gt;floor(evalf(N_*x__)),L__):\012 L__ := [L__[1] , seq(L__[k__]-L__[k__-1],k__=2..nops(L__))]:\012 end proc:\012tempoA := proc(PC_,a_,N_) local II__:\012 II__ := [seq([0,NIS(PC_,a_,s__,1)],s__=1..nbS(PC_,a_))]:\012 [tempo(II__,N_)]:\012 end proc: \012tempoE := proc(PC_,N_) local II__, tempo__:\012 II__ := [seq(iA(PC_,a__),a__=1..nbA(PC_))]:\012 tempo__ := tempo(II__,N_):\012 [seq( op(tempoA(PC_,a__,tempo__[a__])) , a__=1..nbA(PC_) )]:\012 end proc:\012tempoF := proc(PC_,N_)\012 [seq( op(tempoA(PC_,a__,N_)) , a__=1..nbA(PC_) )]:\012 end proc:\012                                                                                                            \012filtre := proc(L_,k_) local LC__, ss__, tt__:\012 LC__ := ListTools[PartialSums](L_):\012 ss__ := 1:\012 while is(k_&gt;LC__[ss__]) do ss__ := ss__+1 end do:\012 LC__ := [-1,op(LC__)]:\012 if L_[ss__]&lt;=1 then tt__ := 0 else tt__ := (k_-LC__[ss__]-1)/(LC__[ss__+1]-LC__[ss__]-1): end if:\012 [ss__,tt__]:\012 end proc:\012filtreA := proc(PC_,a_,k_,N_) local fil__:\012 fil__ := filtre(op(tempoA(PC_,a_,N_)),k_):\012 [[a_,fil__[1],t2i(iA(PC_,a_),fil__[2])]]:\012 end proc:\012filtreE := proc(PC_,k_,N_) local nbi__, nbia__, nbis__,  aa__, ss__, tt__, fil__:\012 nbi__ := tempoE(PC_,N_):\012 nbia__ := [seq( add(nbi__[a__][s__],s__=1..nops(nbi__[a__])) , a__=1..nops(nbi__) )]:\012 nbia__ := ListTools[PartialSums](nbia__):\012 aa__ := 1:\012 while is(k_&gt;nbia__[aa__]) do aa__ := aa__+1 end do:\012 nbia__ := [0,op(nbia__)]:\012 fil__ := filtre(nbi__[aa__],k_-nbia__[aa__]):\012 [[aa__,fil__[1],t2i(iA(PC_,aa__),fil__[2])]]:\012 end proc:\012filtreF := proc(PC_,k_,N_) local nbi__, fil__:\012 nbi__ := tempoF(PC_,N_):\012 fil__ := [seq( filtre(nbi__[a__],k_) , a__=1..nops(nbi__) )]:\012 [seq( [a__,fil__[a__][1],t2i(iA(PC_,a__),fil__[a__][2])] , a__=1..nops(nbi__) )]:\012 end proc:\012\012Paragraphe := &quot;Montage&quot;:                                                                                   \012\012 Paragraphe := &quot;Routines&quot;:                                                                                 \012\012image  := V_ -&gt; plots[display](V_):\012voir   := proc(img_,fds_,view_,mode_,dim_,lit_:=none,tpc_:=0)       \012 if dim_[1]=2 then plots[display](image([img_,fds_]),view=view_,scaling=mode_[1],axes=mode_[2])\012              else plots[display](image([img_,fds_]),view=view_,scaling=mode_[1],axes=mode_[2],\012                                  orientation=dim_[2],lightmodel=lit_,transparency=tpc_)\012              end if:\012 end proc:\012animerS := proc(F_,fds_,view_,mode_,dim_,N_,lit_:=none,tpc_:=0)      \012 if dim_[1]=2 then plots[display]([seq( image([F_(n__),fds_]),n__=0..N_ )],\012                                   view=view_,scaling=mode_[1],axes=mode_[2],insequence=true)\012              else plots[display]([seq( image([F_(n__),fds_]),n__=0..N_ )],\012                                   view=view_,scaling=mode_[1],axes=mode_[2],insequence=true,\012                                   orientation=dim_[2],lightmodel=lit_,transparency=tpc_)\012              end if:\012 end proc:\012animerEF := proc(F_,fds_,view_,mode_,dim_,N1_,N2_,lit_:=none,tpc_:=0)      \012 if dim_[1]=2 then plots[display]([seq( seq( image([F_(n1__,n2__),fds_]),n1__=0..N1_[n2__]),n2__ in N2_)],\012                                   view=view_,scaling=mode_[1],axes=mode_[2],insequence=true)\012              else plots[display]([seq( seq( image([F_(n1__,n2__),fds_]),n1__=0..N1_[n2__]),n2__ in N2_)],\012                                   view=view_,scaling=mode_[1],axes=mode_[2],insequence=true,\012                                   orientation=dim_[2],lightmodel=lit_,transparency=tpc_)\012              end if:\012 end proc:\012\012 Paragraphe := &quot;Structure PC&quot;:                                                                             \012\012vue    := (PC_,a_,s_,v_,t_) -&gt; image(GRS(PC_,a_,s_,v_)(PC_,a_,s_,v_,t_)):\012plan   := (PC_,a_,s_,t_)    -&gt; image([seq( vue(PC_,a_,s_,v__,t_) , v__=nbV(PC_,a_,s_)..1 , -1 )]):\012\012FondP  := PC_               -&gt; image(plan(PC_,0,1,0)):\012FondS  := (PC_,a_,s_)       -&gt; image([ seq( plan(PC_,a_,s__,iA(PC_,a_)[2]) , s__=s_-1..1 , -1 ) ,\012                                       plan(PC_,a_,1,iA(PC_,a_)[1]) , FondP(PC_) ]):\012FondSA := (PC_,a_,s_)       -&gt; image([ FondS(PC_,a_,s_) ,   \012                                       seq( FondS(PC_,a__,nbS(PC_,a__)+1) , a__=a_-1..1 , -1 ) ]):\012FondA  := (PC_,a_)          -&gt; image([ seq( seq ( plan(PC_,a__,nbS(PC_,a__),iA(PC_,a__)[k__]) , \012                                            a__=a_-1..1 , -1 ) , k__=2..2 , -1 ) , FondP(PC_) ]):\012\012                                                                                                            \012\012Fond := proc(PC_,a_,s_,bkg_)\012 if       (bkg_[1] and bkg_[2])      then FondSA(PC_,a_,s_)\012  else if (bkg_[1] and not(bkg_[2])) then FondA(PC_,a_)\012  else if (not(bkg_[1]) and bkg_[2]) then FondS(PC_,a_,s_)\012  else                                    NULL\012  end if end if end if:\012 end proc:\012Scene  := proc(PC_,a_,s_,t_,bkg_) local scene__:\012 if isinPC(PC_,a_,s_) then scene__ := plan(PC_,a_,s_,t_) \012                      else scene__ := FondP(PC_)\012                      end if:\012 image([scene__,Fond(PC_,a_,s_,bkg_)]):\012 end proc:\012\012 Paragraphe := &quot;Structure PIECE&quot;:                                                                           \012\012PieceMS := proc(PIECE_,a_,t_,bkg_) local PC__, as__:\012 PC__ := P_pc(PIECE_):\012 as__ := selectionA(PC__,a_,t_)[1]:\012 Scene(PC__,a_,as__[2],t_,bkg_):\012 end proc:\012PieceME := proc(PIECE_,t_,bkg_) local PC__, as__:\012 PC__ := P_pc(PIECE_):\012 as__ := selectionE(PC__,t_)[1]:\012 Scene(PC__,as__[1],as__[2],t_,bkg_):\012 end proc:\012PieceMF := proc(PIECE_,t_,bkg_) local PC__, as__:\012 PC__ := P_pc(PIECE_):\012 as__ := selectionF(PC__,t_):\012 image([seq( Scene(PC__,as__[a__][1],as__[a__][2],t_,bkg_) , a__=nops(as__)..1 , -1 )]):\012 end proc:\012PieceM  := proc(PIECE_,t_,bkg_,jeu_)\012 if       jeu_=&quot;E&quot; then  PieceME(PIECE_,t_,bkg_) \012  else if jeu_=&quot;F&quot; then  PieceMF(PIECE_,t_,bkg_) \012   else                  PieceMS(PIECE_,jeu_,t_,bkg_)\012   end if end if:\012 end proc:\012                                                                                                            \012PieceAS := proc(PIECE_,a_,r_,bkg_) local PC__, filtre__:\012 PC__ := P_pc(PIECE_):\012 filtre__ := filtreA(PC__,a_,r_[1],r_[2])[1]:\012 Scene(PC__,a_,filtre__[2],filtre__[3],bkg_):\012 end proc:\012PieceAE := proc(PIECE_,r_,bkg_) local PC__, filtre__:\012 PC__ := P_pc(PIECE_):\012 filtre__ := filtreE(PC__,r_[1],r_[2])[1]:\012 Scene(PC__,filtre__[1],filtre__[2],filtre__[3],bkg_):\012 end proc:\012PieceAF := proc(PIECE_,r_,bkg_) local PC__, filtre__:\012 PC__ := P_pc(PIECE_):\012 filtre__ := filtreF(PC__,r_[1],r_[2]):\012 image([seq( Scene(PC__,filtre__[a__][1],filtre__[a__][2],filtre__[a__][3],bkg_) ,\012             a__=nops(filtre__)..1 , -1 )]):\012 end proc:\012PieceA  := proc(PIECE_,r_,bkg_,jeu_)\012 if       jeu_=&quot;E&quot; then  PieceAE(PIECE_,r_,bkg_) \012  else if jeu_=&quot;F&quot; then  PieceAF(PIECE_,r_,bkg_) \012   else                  PieceAS(PIECE_,jeu_,r_,bkg_)\012   end if end if:\012 end proc:\012                                                                                                            \012Piece := proc(PIECE_,r_,vis_,vrs_)\012 if vis_=&quot;V&quot; then PieceM(PIECE_,r_,vrs_[&quot;b&quot;],vrs_[&quot;j&quot;]) else PieceA(PIECE_,r_,vrs_[&quot;b&quot;],vrs_[&quot;j&quot;])\012  end if: end proc:\012\012 Paragraphe := &quot;Structure FILM&quot;:                                                                            \012\012SelTimeInFilm := proc(film_,P_,t_) local ref__,p__,sel__:\012 ref__ := []: \012 for p__ in P_ do \012  sel__ := selectionE(P_pc(film_[p__]),t_):\012  if sel__&lt;&gt;[[-1,-1]] then ref__ := [op(ref__),p__] end if:\012  end do:\012 ref__:\012 end proc:\012SelRangInFilm := proc(film_,P_,k_) local nbp__,p__:\012 nbp__ := nops(P_):\012 p__ := floor(nbp__*k_/SLIDER)+1: if p__&gt;nbp__ then p__ := nbp__ end if:\012 [p__,nbp__*k_-(p__-1)*SLIDER]:\012 end proc:\012VoirS    := proc(FILM_,p_,t_,T_,vrs_:=VO,pub_:=NULL) local piece__,fond__,vrs__,FSt__:\012 piece__ := F_film(FILM_,T_)[p_]: \012 fond__ := image([pub_,FondP(P_pc(piece__))]): vrs__ := MergeTable(P_opt(piece__),vrs_):\012\012 FSt__ := PieceM(piece__,t_,vrs__[&quot;b&quot;],vrs__[&quot;j&quot;]):\012 voir(FSt__,fond__,vrs__[&quot;v&quot;],vrs__[&quot;m&quot;],vrs__[&quot;d&quot;],vrs__[&quot;l&quot;],vrs__[&quot;t&quot;]):\012 end proc:\012VoirEF  := proc(FILM_,P_,t_,T_,jeu_:=&quot;VO&quot;,vrs_:=VO,pub_:=NULL) \012           local film__,fond__,fondEF__,vrs__,vrsEF__,bkg__,jeu__,nop__,FSt__:\012 film__ := F_film(FILM_,T_):\012 fond__ := p__ -&gt; FondP(P_pc(film__[p__])):\012 fondEF__ := image([ pub_ , seq( fond__(p__) , p__ in P_ ) ]):\012 vrs__  := p__ -&gt; MergeTable(P_opt(film__[p__]),vrs_): \012 vrsEF__ := vrs__(P_[1]):\012 bkg__  := p__ -&gt; vrs__(p__)[&quot;b&quot;]: jeu__  := p__ -&gt; vrs__(p__)[&quot;j&quot;]: \012\012 if jeu_=&quot;E&quot; then nop__ := SelTimeInFilm(film__,P_,t_) end if:\012 if jeu_=&quot;F&quot; then                        FSt__ := image([ seq( PieceM(film__[l__],t_,bkg__(l__),jeu__(l__)) , l__ in P_ ) ])\012  else if (nop__&lt;&gt;[] and jeu_&lt;&gt;&quot;R&quot;) then FSt__ := PieceM(film__[nop__[1]],t_,bkg__(nop__[1]),jeu__(nop__[1]))\012  else                                   FSt__ := fondEF__\012  end if end if:\012\012 if (jeu_=&quot;E&quot; or jeu_=&quot;F&quot;) then\012  voir(FSt__,fondEF__,vrsEF__[&quot;v&quot;],vrsEF__[&quot;m&quot;],vrsEF__[&quot;d&quot;],vrsEF__[&quot;l&quot;],vrsEF__[&quot;t&quot;])\012 end if: end proc:\012DefilerS   := proc(FILM_,p_,k_,T_,vrs_:=VO,pub_:=NULL) local piece__,fond__,vrs__,FSk__:\012 piece__ := F_film(FILM_,T_)[p_]: \012 fond__ := image([pub_ , FondP(P_pc(piece__))]): vrs__ := MergeTable(P_opt(piece__),vrs_):\012\012 FSk__ := PieceA(piece__,[k_,SLIDER],vrs__[&quot;b&quot;],vrs__[&quot;j&quot;]):\012 voir(FSk__,fond__,vrs__[&quot;v&quot;],vrs__[&quot;m&quot;],vrs__[&quot;d&quot;],vrs__[&quot;l&quot;],vrs__[&quot;t&quot;]):\012 end proc:\012DefilerEF := proc(FILM_,P_,k_,T_,jeu_:=&quot;VO&quot;,vrs_:=VO,pub_:=NULL) \012             local film__,fond__,fondEF__,vrs__,vrsEF__,bkg__,jeu__,nop__,FSk__:\012 film__ := F_film(FILM_,T_):\012 fond__ := p__ -&gt; FondP(P_pc(film__[p__])):\012 fondEF__ := image([ pub_ , seq( fond__(p__) , p__ in P_ ) ]):\012 vrs__  := p__ -&gt; MergeTable(P_opt(film__[p__]),vrs_): \012 vrsEF__ := vrs__(P_[1]):\012 bkg__  := p__ -&gt; vrs__(p__)[&quot;b&quot;]: jeu__  := p__ -&gt; vrs__(p__)[&quot;j&quot;]: \012\012 if jeu_=&quot;E&quot; then nop__ := SelRangInFilm(film__,P_,k_) end if:\012 if jeu_=&quot;F&quot; then \012  FSk__ := image([ seq( PieceA(film__[l__],[k_,SLIDER],bkg__(l__),jeu__(l__)), l__ in P_ ) ])\012 else if jeu_=&quot;E&quot; then\012  FSk__ := PieceA(film__[nop__[1]],[nop__[2],SLIDER],bkg__(nop__[1]),jeu__(nop__[1]))\012  end if end if:\012\012 if (jeu_=&quot;E&quot; or jeu_=&quot;F&quot;) then \012  voir(FSk__,fondEF__,vrsEF__[&quot;v&quot;],vrsEF__[&quot;m&quot;],vrsEF__[&quot;d&quot;],vrsEF__[&quot;l&quot;],vrsEF__[&quot;t&quot;])\012 end if: end proc:\012AnimerS   := proc(FILM_,p_,T_,vrs_:=VO,pub_:=NULL) local piece__,fond__,vrs__,nbi__,FS__:\012 piece__ := F_film(FILM_,T_)[p_]: \012 fond__ := image([ pub_ , FondP(P_pc(piece__)) ]): vrs__ := MergeTable(P_opt(piece__),vrs_):\012 nbi__   := P_nbi(piece__,vrs__):\012\012 FS__ := k__ -&gt; PieceA(piece__,[k__,nbi__],vrs__[&quot;b&quot;],vrs__[&quot;j&quot;]):\012 animerS(FS__,fond__,vrs__[&quot;v&quot;],vrs__[&quot;m&quot;],vrs__[&quot;d&quot;],nbi__,vrs__[&quot;l&quot;],vrs__[&quot;t&quot;]):\012 end proc:\012AnimerEF := proc(FILM_,P_,T_,jeu_:=&quot;VO&quot;,vrs_:=VO,pub_:=NULL) \012            local film__,fond__,fondEF__,vrs__,vrsEF__,bkg__,jeu__,nbi__,FS__:\012 film__ := F_film(FILM_,T_):\012 fond__ := p__ -&gt; FondP(P_pc(film__[p__])):\012 fondEF__ := image([ pub_ , seq( fond__(p__) , p__ in P_ ) ]):\012 vrs__  := p__ -&gt; MergeTable(P_opt(film__[p__]),vrs_): \012 vrsEF__ := vrs__(P_[1]):\012 bkg__  := p__ -&gt; vrs__(p__)[&quot;b&quot;]: jeu__  := p__ -&gt; vrs__(p__)[&quot;j&quot;]: \012 nbi__  := table([ seq( p__ = P_nbi(film__[p__],vrs__(p__)), p__ in P_ ) ]):\012\012 if jeu_=&quot;F&quot; then \012  FS__ := k__ -&gt; image([ seq( PieceA(film__[l__],[k__,nbi__[l__]],bkg__(l__),jeu__(l__)), l__ in P_ ) ])\012 else if jeu_=&quot;E&quot; then\012  FS__ := (k__,p__) -&gt; PieceA(film__[p__],[k__,nbi__[p__]],bkg__(p__),jeu__(p__))\012 end if end if:\012\012 if jeu_=&quot;F&quot; then\012  animerS (FS__,fondEF__,vrsEF__[&quot;v&quot;],vrsEF__[&quot;m&quot;],vrsEF__[&quot;d&quot;],nbi__[P_[1]],vrsEF__[&quot;l&quot;],vrsEF__[&quot;t&quot;])\012 else if jeu_=&quot;E&quot; then\012  animerEF(FS__,fondEF__,vrsEF__[&quot;v&quot;],vrsEF__[&quot;m&quot;],vrsEF__[&quot;d&quot;],nbi__,P_    ,vrsEF__[&quot;l&quot;],vrsEF__[&quot;t&quot;])\012 end if end if: end proc:\012                                                                                                            \012Seance := proc(FILM_,P_,t_,T_,vis_,jeu_:=&quot;VO&quot;,vrs_:=VOp(nops(P_)),pub_:=NULL) local jeu__, vrs__, P__, p__, record__:\012 if jeu_=&quot;VO&quot; then jeu__ := F_jeu(FILM_,T_) else jeu__ := jeu_ end if:\012 if P_=[] then P__ :=  F_set(FILM_,T_) else P__ := P_ end if:\012 if vrs_=[] then vrs__ := VOp(nops(P__)) else vrs__ := vrs_ end if:\012\012 if vis_=&quot;V&quot; then\012  if nops(P__)=1 then     record__[1]   := VoirS (FILM_,P__[1],t_,T_      ,vrs__[P__[1]],pub_)\012   else if jeu__=&quot;R&quot; then \012   for p__ in P__ do      record__[p__] := VoirS (FILM_,p__   ,t_,T_      ,vrs__[p__]   ,pub_) end do\012   else                   record__[1]   := VoirEF(FILM_,P__   ,t_,T_,jeu__,vrs__[1]     ,pub_)\012  end if end if end if:\012 if vis_=&quot;D&quot; then\012  if nops(P__)=1 then     record__[1]   := DefilerS (FILM_,P__[1],t_,T_      ,vrs__[P__[1]],pub_)\012   else if jeu__=&quot;R&quot; then \012   for p__ in P__ do      record__[p__] := DefilerS (FILM_,p__   ,t_,T_      ,vrs__[p__]   ,pub_) end do\012   else                   record__[1]   := DefilerEF(FILM_,P__   ,t_,T_,jeu__,vrs__[1]     ,pub_)\012  end if end if end if:\012 if vis_=&quot;A&quot; then\012  if nops(P__)=1 then     record__[1]   := AnimerS (FILM_,P__[1],T_      ,vrs__[P__[1]],pub_)\012   else if jeu__=&quot;R&quot; then \012   for p__ in P__ do      record__[p__] := AnimerS (FILM_,p__   ,T_      ,vrs__[p__]   ,pub_) end do\012   else                   record__[1]   := AnimerEF(FILM_,P__   ,T_,jeu__,vrs__[1]     ,pub_)\012  end if end if end if:\012 record__:\012 end proc:\012Calculs := (FILM_,T_) -&gt; F_out(FILM_,T_):\012Paragraphe := &quot;Divers&quot;:                                                                                     \012\012slider2d := proc(T_) local forme__, T__, img__:\012 forme__ := Matrix([[0, 0],[0, 1],[1, 1],[1,0]]):\012 T__ := T_:\012 if T__[1]&lt;0 then T__[1] := 0 \012  else if T__[1]&gt;1 then T__[1] := 1 \012  end if \012 end if:\012 if T__[2]&lt;0 then T__[2] := 0 \012  else if T__[2]&gt;1 then T__[2] := 1 \012  end if \012 end if:\012 img__ := [plots[pointplot](T__,color=white),plots[polygonplot](forme__,color = RGB(0.5,0,0),transparency=0.5)]:\012 [T__,image(img__,view=[0..1,0..1],axis=[gridlines=[5,color=RGB(0.5,0,0)]],tickmarks=[0,0])]:\012 end proc:\012Curseur := proc()\012 SLIDER:\012 end proc:\012                                                                                                            \012VIDE2D := table([]): \012VIDE2D[0,0] := I_01: VIDE2D[0,1] := [ [nul,null2d,[nul,nul,nul,nul],1] ]: \012VIDE2D[1,0] := I_01: VIDE2D[1,1] := [ [nul,null2d,[nul,nul,nul,nul],1] ]:\012VIDE3D := table([]): \012VIDE3D[0,0] := I_01: VIDE3D[0,1] := [ [nul,null3d,[nul,nul,nul,nul],1] ]: \012VIDE3D[1,0] := I_01: VIDE3D[1,1] := [ [nul,null3d,[nul,nul,nul,nul],1] ]:\012FILMVIDE2D := proc(p,PAR,T_) local k,PC,VS:\012 PC := [ seq( table(), k=1..p ) ]: VS := VOE2D:                                                    \012 for k from 1 to p do\012  PC[k][0,0] := I_01:\012  PC[k][0,1] := [ [nul,null2d,[nul,nul,nul,nul],1] ]: \012  PC[k][1,0] := I_01:\012  PC[k][1,1] := [ [nul,null2d,[nul,nul,nul,nul],1] ]: \012  end do:\012 table([ 0=&quot;R&quot;, seq( k = [PC[k],VS], k=1..p ) ]): \012 end proc:\012FILMVIDE3D := proc(p,PAR,T_) local k,PC,VS:\012 PC := [ seq( table(), k=1..p ) ]: VS := VOE3D:                                                    \012 for k from 1 to p do\012  PC[k][0,0] := I_01:\012  PC[k][0,1] := [ [nul,null3d,[nul,nul,nul,nul],1] ]: \012  PC[k][1,0] := I_01:\012  PC[k][1,1] := [ [nul,null3d,[nul,nul,nul,nul],1] ]: \012  end do:\012 table([ 0=&quot;R&quot;, seq( k = [PC[k],VS], k=1..p ) ]): \012 end proc:\012\012end module:                                                                                                                                                                                                         \012                                                                                                            \012######################################################### ALGLIN ###################################################################\012                                                                                                            \012############################################################################################################\012AlgLin := module()                                                                                          \012\012  uses     plots, LinearAlgebra, AnimationII; \012  export   O_2, O_3, EMAT, EVEC,\012           ID2, ROT2,REF2,PROJ2_VD, DIL2_VD, REF2_VD, id, hom, trans, rot2, ref2, proj2_vd, dil2_vd, \012             ref2_vd, Id, Hom, Trans, Rot2, Ref2, Proj2_vd, Dil2_vd, Ref2_vd, \012             MinusVect, AugmentMatrix, AugmentVector, Famille, BaseCan, \012             FindOrtho2d, FindOrtho3d, Orthogonal2d, Orthogonal3d, OrthoDec, Ker, Img, Vs_Param, DetVect, \012             EigenSpaceReal, EigenAngles2d,\012           ID3, ROT3,PROJ3_VD, PROJ3_VN, DIL3_VN, REF3_VN, ANTISYM3, rot3, proj3_vd, proj3_vn, dil3_vn,  \012             ref3_vn, Rot3, Proj3_vn, Dil3_vn, Ref3_vn, Cercle3d, Angles3d, Pol, Spheric;\012  local    Paragraphe;\012  option package;\012\012Paragraphe := &quot;Constantes &amp; Variables globales&quot;:                                                            \012\012O_2  := &lt;0,0&gt;: O_3 := &lt;0,0,0&gt;:\012EMAT   := (n,p) -&gt; Matrix(n,p,(i,j)-&gt;NULL):\012EVEC   := n -&gt; Vector(n,i-&gt;NULL):\012\012 Paragraphe := &quot;Alg\303\250bre Lin\303\251aire&quot;:                                                                          \012\012ID2      :=         IdentityMatrix(2):\012ROT2     := t_      -&gt; &lt;&lt;cos(t_),sin(t_)&gt;|&lt;-sin(t_),cos(t_)&gt;&gt;:\012REF2     := t_      -&gt; &lt;&lt;cos(t_),sin(t_)&gt;|&lt;sin(t_),-cos(t_)&gt;&gt;:\012PROJ2_VD := a_      -&gt; (1/(a_^%T.a_))*(a_.a_^%T):\012DIL2_VD  := (a_,k_) -&gt; k_*ID2+(1-k_)*PROJ2_VD(a_):\012REF2_VD  := a_      -&gt; -ID2+2*PROJ2_VD(a_):\012                                                                                                            \012id       := M_            -&gt; M_:\012hom      := (I_,a_,k_,M_) -&gt; evalf(I_+k_            *(M_-I_)):\012trans    := (I_,a_,k_,M_) -&gt; evalf(M_+a_):\012rot2     := (I_,a_,k_,M_) -&gt; evalf(I_+ROT2(k_)      .(M_-I_)):\012ref2     := (I_,a_,k_,M_) -&gt; evalf(I_+REF2(k_)      .(M_-I_)):\012proj2_vd := (I_,a_,k_,M_) -&gt; evalf(I_+PROJ2_VD(a_)  .(M_-I_)):\012dil2_vd  := (I_,a_,k_,M_) -&gt; evalf(I_+DIL2_VD(a_,k_).(M_-I_)):\012ref2_vd  := (I_,a_,k_,M_) -&gt; evalf(I_+REF2_VD(a_)   .(M_-I_)):\012                                                                                                            \012Id       := MM_            -&gt; MM_:\012Hom      := (I_,a_,k_,MM_) -&gt; map[4](hom     ,I_,a_,k_,MM_):\012Trans    := (I_,a_,k_,MM_) -&gt; map[4](trans   ,I_,a_,k_,MM_):\012Rot2     := (I_,a_,k_,MM_) -&gt; map[4](rot2    ,I_,a_,k_,MM_):\012Ref2     := (I_,a_,k_,MM_) -&gt; map[4](ref2    ,I_,a_,k_,MM_):\012Proj2_vd := (I_,a_,k_,MM_) -&gt; map[4](proj2_vd,I_,a_,k_,MM_):\012Dil2_vd  := (I_,a_,k_,MM_) -&gt; map[4](dil2_vd ,I_,a_,k_,MM_):\012Ref2_vd  := (I_,a_,k_,MM_) -&gt; map[4](ref2_vd ,I_,a_,k_,MM_):\012                                                                                                            \012ID3      :=         IdentityMatrix(3):\012PROJ3_VD := a_      -&gt; (1/(a_^%T.a_))*(a_.a_^%T):\012PROJ3_VN := a_      -&gt; ID3-PROJ3_VD(a_):\012DIL3_VN  := (a_,k_) -&gt; ID3-(1-k_)*PROJ3_VD(a_):\012REF3_VN  := a_      -&gt; ID3-2*PROJ3_VD(a_):\012ANTISYM3 := a_      -&gt; &lt;&lt;0,a_[3],-a_[2]&gt;|&lt;-a_[3],0,a_[1]&gt;|&lt;a_[2],-a_[1],0&gt;&gt;:\012ROT3     := (a_,t_) -&gt; cos(t_)*PROJ3_VN(a_)+(ID3-PROJ3_VN(a_))+sin(t_)*ANTISYM3(Normalize(a_,2)):\012                                                                                                            \012rot3     := (I_,a_,k_,M_)  -&gt; evalf(I_+ROT3(a_,k_)   .(M_-I_)):\012proj3_vd := (I_,a_,k_,M_)  -&gt; evalf(I_+PROJ3_VD(a_)  .(M_-I_)):\012proj3_vn := (I_,a_,k_,M_)  -&gt; evalf(I_+PROJ3_VN(a_)  .(M_-I_)):\012dil3_vn  := (I_,a_,k_,M_)  -&gt; evalf(I_+DIL3_VN(a_,k_).(M_-I_)):\012ref3_vn  := (I_,a_,k_,M_)  -&gt; evalf(I_+REF3_VN(a_)   .(M_-I_)):\012\012Rot3     := (I_,a_,k_,MM_) -&gt; map[4](rot3    ,I_,a_,k_,MM_):\012Proj3_vn := (I_,a_,k_,MM_) -&gt; map[4](proj3_vn,I_,a_,k_,MM_):\012Dil3_vn  := (I_,a_,k_,MM_) -&gt; map[4](dil3_vn ,I_,a_,k_,MM_):\012Ref3_vn  := (I_,a_,k_,MM_) -&gt; map[4](ref3_vn ,I_,a_,k_,MM_):\012                                                                                                            \012MinusVect := proc(LV1,LV2) local L,v1,v2,b:\012 L := []: \012 for v1 in LV1 do\012  b := 0:\012  for v2 in LV2 do if Equal(v2,v1) then b := 1 end if: end do:\012  if b=0 then L := [op(L),v1] end if:\012  end do:\012 L:\012 end proc:\012AugmentMatrix := proc(A_,n_,p_) local A__:\012 A__ := Matrix(n_,p_):\012 A__[1..RowDimension(A_),1..ColumnDimension(A_)] := A_:\012 A__:\012 end proc:\012AugmentVector := proc(VV_,n_,p_) local A__:\012 A__ := Matrix(n_,p_):\012 A__[1..Dimension(VV_[1]),1..nops(VV_)] := convert(VV_,Matrix):\012 [seq(Column(A__,k__),k__=1..ColumnDimension(A__))]:\012 end proc:\012Famille  := proc(VV_) local libre__,liee__:\012 libre__ := Basis(VV_):\012 liee__ := convert(`minus`(convert(VV_,set),convert(libre__,set)),list):\012 [libre__,liee__]:\012 end proc:\012BaseCan  := n_ -&gt; [seq(UnitVector(k__,n_),k__=1..n_)]:\012FindOrtho2d := V_ -&gt; &lt;-V_[2],V_[1]&gt;:\012FindOrtho3d := proc(V_) local U__:\012 U__ := &lt;-V_[3],0,V_[1]&gt;:\012 if Equal(U__,&lt;0,0,0&gt;) then U__ := &lt;0,-V_[3],V_[2]&gt; end if:\012 U__:\012 end proc:\012Orthogonal2d := proc(VS_) local VO__:\012 if (nops(VS_)=1 and VS_=[&lt;0,0&gt;]) then VO__ := BaseCan(2):\012  else if nops(VS_)=1             then VO__ := [FindOrtho2d(VS_[1])]:\012  else if nops(VS_)=2             then VO__ := [&lt;0,0&gt;]:\012  end if end if end if: \012 VO__:\012 end proc:\012Orthogonal3d := proc(VS_) local U1__,VO__:\012 if (nops(VS_)=1 and Equal(VS_[1],&lt;0,0,0&gt;)) then VO__ := BaseCan(3):\012  else if nops(VS_)=1                       then U1__ := FindOrtho3d(VS_[1]): \012                                                 VO__ := [U1__,CrossProduct(VS_[1],U1__)]: \012  else if nops(VS_)=2                       then VO__ := [CrossProduct(VS_[1],VS_[2])]:\012  else if nops(VS_)=3                       then VO__ := [&lt;0,0,0&gt;]\012  end if end if end if end if:\012 VO__:\012 end proc:\012OrthoDec := proc(VS_,X_) local X1__:\012 if nops(VS_)=1       then X1__ := DotProduct(VS_[1],X_)*VS_[1]: \012  else if nops(VS_)=2 then X1__ := DotProduct(VS_[1],X_)*VS_[1]+DotProduct(VS_[2],X_)*VS_[2]:\012  else if nops(VS_)=3 then X1__ := X_:\012  end if end if end if:\012 [X1__,X_-X1__]:\012 end proc:\012Ker := A_ -&gt; LexOrd(convert(NullSpace(A_)  ,list),3,&quot;&lt;&quot;): \012Img := A_ -&gt; LexOrd(convert(ColumnSpace(A_),list),3,&quot;&lt;&quot;): \012DetVect  := VV_ -&gt; Determinant(convert(VV_,Matrix)):\012EigenSpaceReal := proc(A_) local eigenvectors__,eigenspaces__,k__:\012 eigenvectors__ := Eigenvectors(A_,output='list'):\012 eigenspaces__  := []:\012 for k__ from 1 to nops(eigenvectors__) do\012  if Im(eigenvectors__[k__][1])=0 then \012   eigenspaces__ := [op(eigenspaces__),eigenvectors__[k__]]\012   end if:\012  end do:\012 for k__ from 1 to nops(eigenspaces__) do eigenspaces__[k__][3] := LexOrd(convert(eigenspaces__[k__][3],list),3,&quot;&lt;&quot;) end do:\012 Ord(eigenspaces__,1,&quot;&lt;&quot;):\012 end proc:\012EigenAngles2d := proc(eigenspaces_) local angles__,k__,l__,esk__:\012 angles__ := []:\012 for k__ from 1 to nops(eigenspaces_) do \012  esk__ := eigenspaces_[k__]:\012  angles__ := [ op(angles__),\012                   seq( [esk__[1],evalf(argument( esk__[3][l__][1]+I*esk__[3][l__][2]))], l__=1..nops(esk__[3]) ),\012                   seq( [esk__[1],evalf(argument(-esk__[3][l__][1]-I*esk__[3][l__][2]))], l__=1..nops(esk__[3]) ) ]:\012 \012  end do:\012 Ord(angles__,2,&quot;&lt;&quot;):\012 end proc:\012                                                                                                            \012Vs_Param  := proc(VS_,t_) local res__:\012 if nops(VS_)=1       then res__ := t_*VS_[1]\012  else if nops(VS_)=2 then res__ := t_[1]*VS_[1]+t_[2]*VS_[2]\012  else if nops(VS_)=3 then res__ := t_[1]*VS_[1]+t_[2]*VS_[2]+t_[3]*VS_[3]\012  end if end if end if:\012 res__:\012 end proc:\012Cercle3d := proc(I_,a_,t_) local P__,ImP__:\012 P__ := PROJ3_VN(a_):\012 ImP__ := GramSchmidt(ColumnSpace(P__),normalized,conjugate=false):\012 I_+ImP__[1]*cos(t_)+ImP__[2]*sin(t_):\012 end proc:\012Cercle3d := proc(I_,a_,t_) local a__,b__,c__:\012 a__ := Normalize(a_,Euclidean):\012 b__ := Normalize(FindOrtho3d(a__),Euclidean):\012 c__ := CrossProduct(a__,b__):\012 I_+b__*cos(t_)+c__*sin(t_):\012 end proc:\012Angles3d := proc(u) local spheric:\012 spheric := u -&gt; map(evalf,Student[VectorCalculus][MapToBasis](u,spherical)):\012 map(evalf,[spheric(u)[3]*180/Pi,spheric(u)[2]*180/Pi,0]):\012 end proc:\012Pol     := (r_,theta_) -&gt; &lt;r_*cos(theta_),r_*sin(theta_)&gt;:\012Spheric := (r_,theta_,phi_) -&gt; &lt;r_*cos(theta_)*sin(phi_),r_*sin(theta_)*sin(phi_),r_*cos(phi_)&gt;:\012\012end module:                                                                                                 \012############################################################################################################\012                                                                                                            \012######################################################## ANALYSE ##################################################################\012############################################################################################################\012Analyse := module()                                                                                         \012\012  uses     plots, LinearAlgebra, AnimationII; \012  export   Comp1, DD, dd, dd2, dd3, Om, Om3, Img1, Img2, View_p, ImDom, Recup, IIRecup, lim, Approx,\012           Comp2, DDP, ddp, ddp2,ddp3;\012  local    Paragraphe;\012  option package;\012\012Paragraphe := &quot;Constantes &amp; Variables globales&quot;:                                                            \012\012 Paragraphe := &quot;Analyse&quot;:                                                                                   \012Comp1  := (f_,n_)       -&gt; [seq( unapply(f_(t_)[k__],t_),k__=1..n_)]:\012DD     := (f_,n_,p_)    -&gt; map(D@@p_,Comp1(f_,n_)):\012dd     := (f_,n_,p_)    -&gt; unapply(convert(map(apply,DD(f_,n_,p_),t_),Vector),t_):\012dd2    := (f_,p_)       -&gt; dd(f_,2,p_):\012dd3    := (f_,p_)       -&gt; dd(f_,3,p_):\012Comp2  := (f_,n_)       -&gt; [seq( unapply(f_(u_,v_)[k__],u_,v_),k__=1..n_)]:\012DDP    := (f_,n_,i_,j_) -&gt; map(D[seq(1,ii__=1..i_),seq(2,jj__=1..j_)],Comp2(f_,n_)):\012ddp    := (f_,n_,i_,j_) -&gt; unapply(convert(map(apply,DDP(f_,n_,i_,j_),u_,v_),Vector),u_,v_):\012ddp2   := (f_,i_,j_) -&gt; ddp(f_,2,i_,j_):\012ddp3   := (f_,i_,j_) -&gt; ddp(f_,3,i_,j_):\012Om     := t_      -&gt; &lt;cos(t_),sin(t_)&gt;:\012Om3    := t_      -&gt; &lt;cos(t_),sin(t_),0&gt;:\012Img1   := proc(f_,II_,N_) local min__, max__: \012 min__ := evalf(min( seq( seq(f_(t2i(II_[k__],j__/N_)),j__=0..N_) , k__=1..nops(II_) ) )):\012 max__ := evalf(max( seq( seq(f_(t2i(II_[k__],j__/N_)),j__=0..N_) , k__=1..nops(II_) ) )):\012 [min__,max__]:\012 end proc:\012Img2   := proc(f_,II_,N_) local img1__, img2__:\012 img1__ := Img1(Comp1(f_,2)[1],II_,N_):\012 img2__ := Img1(Comp1(f_,2)[2],II_,N_):\012 [[img1__[1],img1__[2]],[img2__[1],img2__[2]]]:\012 end proc:\012View_p := proc(f_,II_,N_,Mrg_) local img__:\012 img__ := Img2(f_,II_,N_):\012 if nops(Mrg_)=1 then [img__[1,1]-Mrg_[1]..img__[1,2]+Mrg_[1],img__[2,1]-Mrg_[1]..img__[2,2]+Mrg_[1]]\012  else [img__[1,1]-Mrg_[1]..img__[1,2]+Mrg_[2],img__[2,1]-Mrg_[3]..img__[2,2]+Mrg_[4]]\012  end if:\012 end proc:\012ImDom := proc(II_,phi_) local k__:\012 [seq( [min(phi_(II_[k__][1]),phi_(II_[k__][2])),max(phi_(II_[k__][1]),phi_(II_[k__][2]))] , k__=1..nops(II_) )]:\012 end proc:\012Recup := proc(str_,eps_,inf_) local str__,sgn__,x__:\012 sgn__ := StringTools[Take](StringTools[Reverse](str_),1):\012 if (sgn__=&quot;+&quot; or sgn__=&quot;-&quot;) then str__ := StringTools[Take](str_,StringTools[Length](str_)-1)\012                             else str__ := str_\012                             end if: \012 x__ := parse(str__):\012 if str__=&quot;+inf&quot;       then [+infinity,inf_]\012  else if str__=&quot;-inf&quot; then [-infinity,-inf_]\012  else if sgn__=&quot;+&quot;    then [x__,x__+eps_]\012  else if sgn__=&quot;-&quot;    then [x__,x__-eps_]\012  else                      [x__,x__]\012  end if end if end if\012 end if:\012 end proc:\012IIRecup := proc(II_,Eps_,Inf_) local k__,L1__,L2__:\012 L1__ := [ seq( Recup(II_[k__][1],Eps_[k__][1],Inf_[k__][1]) , k__=1..nops(II_) ) ]:\012 L2__ := [ seq( Recup(II_[k__][2],Eps_[k__][2],Inf_[k__][2]) , k__=1..nops(II_) ) ]:\012 [ [ seq( [L1__[k__][1],L2__[k__][1]] , k__=1..nops(II_) ) ] , [ seq( [L1__[k__][2],L2__[k__][2]] , k__=1..nops(II_) ) ] ]:\012 end proc:\012lim := proc(f_,x0_) local sgn__,x__,x0__:\012 sgn__ := StringTools[Take](StringTools[Reverse](x0_),1):\012 if (sgn__=&quot;+&quot; or sgn__=&quot;-&quot;) then x0__ := parse(StringTools[Take](x0_,StringTools[Length](x0_)-1))\012                             else x0__ := parse(x0_)\012  end if:\012 if x0_=&quot;+inf&quot;        then limit(f_(x__),x__=infinity)\012  else if x0_=&quot;-inf&quot;  then limit(f_(x__),x__=-infinity)\012   else if sgn__=&quot;+&quot;  then limit(f_(x__),x__=x0__,right)\012    else if sgn__=&quot;-&quot; then limit(f_(x__),x__=x0__,left)\012     else                   limit(f_(x__),x__=x0__)\012     end if\012    end if\012   end if\012  end if:\012 end proc:\012Approx := (n_,val_) -&gt; [seq( [val_,val_] , k__=1..n_ )]:\012\012end module:                                                                                                 \012############################################################################################################\012                                                                                                            \012###################################################### GEOMETRIE #################################################################\012                                                                                                            \012############################################################################################################\012Geometrie := module()                                                                                       \012\012  uses     plots, LinearAlgebra, AnimationII; \012  export   POL, SPH, M_dat, A_dat, P_dat, L_dat, E_dat, MAPLE_dat,\012           bar2, bar3, Bar2, Bar3, polyreg, BAR2_1, BAR2_2, curvecoords, polarcoords, lincartcoords, \012             linpolcoords, detplot, CharPlot, WordPlot,\012           CharParam, WordParam, curvecoords3d, sphericalcoords3d, lincartcoords3d, \012             linsphcoords3d, detplot3d;\012  local    Paragraphe;\012  option package;\012\012Paragraphe := &quot;Constantes &amp; Variables globales&quot;:                                                            \012POL := [0,2*Pi]: SPH := [[0,2*Pi],[0,Pi]]:\012M_dat := [&lt;0,0&gt;,&lt;0,1&gt;,&lt;0.5,0.5&gt;,&lt;1,1&gt;,&lt;1,0&gt;]:\012A_dat := [&lt;0,0&gt;,&lt;0.5,1&gt;,&lt;1,0&gt;,&lt;0.75,0.5&gt;,&lt;0.25,0.5&gt;]:\012P_dat := [&lt;0,0&gt;,&lt;0,1&gt;,&lt;1,1&gt;,&lt;1,0.5&gt;,&lt;0,0.5&gt;]:\012L_dat := [&lt;0,1&gt;,&lt;0,0&gt;,&lt;1,0&gt;]:\012E_dat := [&lt;1,0&gt;,&lt;0,0&gt;,&lt;0,0.5&gt;,&lt;0.5,0.5&gt;,&lt;0,0.5&gt;,&lt;0,1&gt;,&lt;1,1&gt;]:\012MAPLE_dat := [M_dat,A_dat,P_dat,L_dat,E_dat]:\012 Paragraphe := &quot;G\303\251om\303\251trie&quot;:                                                                                \012bar2     := (M_,N_,t_)          -&gt; map(expand,evalf((1-t_)*M_+t_*N_)):\012bar3     := (M_,N_,P_,s_,t_)    -&gt; map(expand,evalf((1-s_-t_)*M_+s_*N_+t_*P_)):\012Bar2     := (MM_,NN_,t_)        -&gt; [seq(bar2(MM_[k__],NN_[k__],t_),k__=1..nops(MM_))]:\012Bar3     := (MM_,NN_,PP_,s_,t_) -&gt; [seq(bar3(MM_[k__],NN_[k__],PP_[k__],s_,t_),k__=1..nops(MM_))]:\012polyreg  := (n_,N_)             -&gt;  [seq(evalf(&lt;cos(k__*2*Pi/n_),sin(k__*2*Pi/n_)&gt;),k__=0..N_-1)]:\012BAR2_1   := proc(MM_,t_) local MMMM__:\012 MMMM__ := RElist1(MM_): Bar2(MMMM__[1],MMMM__[2],t_):\012 end proc:\012BAR2_2   := proc(MM_,t_) local MMMM__:\012 MMMM__ := RElist2(MM_): Bar2(MMMM__[1],MMMM__[2],t_):\012 end proc:\012                                                                                                            \012CharParam := proc(M_,A_,a_,b_) local dil__,par__,M__:\012 dil__ := (U__,t__) -&gt; &lt;a_(t__)*U__[1],b_(t__)*U__[2]&gt;:\012 M__   := (k__,t__) -&gt; dil__(M_[k__],t__):\012 [seq( unapply(A_(t__)+(1-s__)*M__(k__,t__)+s__*M__(k__+1,t__),s__,t__), k__=1..nops(M_)-1 )]:\012 end proc:\012WordParam := proc(MM_,A_,a_,b_,space_) local dil__,MM__,a__,A__:\012 dil__ := (U__,t__) -&gt; &lt;a_(t__)*U__[1],b_(t__)*U__[2]&gt;:\012 MM__  := (l__,k__,t__) -&gt; dil__(MM_[l__][k__],t__):\012 a__   := (l__,t__) -&gt; (l__-1)*a_(t__)*(1+space_):\012 A__   := (l__,t__) -&gt; &lt;A_(t__)[1]+a__(l__,t__),A_(t__)[2]&gt;:\012 [seq( seq( unapply(A__(l__,t__)+(1-s__)*MM__(l__,k__,t__)+s__*MM__(l__,k__+1,t__),s__,t__), \012  k__=1..nops(MM_[l__])-1 ), l__=1..nops(MM_) )]:\012 end proc:\012curvecoords    := proc(F_) local G__,R__,V__,default__,coords__,t__:\012 G__  := 20,20:\012 R__ := -1..1,-1..1:\012 V__ := R__:\012 default__ := [R__,G__,V__]:\012 addcoords(coords__,[seq(t__[j__],j__=1..2)],V2L(F_(t__)),default__):\012 coords__:\012 end proc:\012polarcoords   := proc() local F__:\012 F__ := t__ -&gt; &lt;t__[1]*cos(t__[2]),t__[1]*sin(t__[2])&gt;:\012 curvecoords(F__):\012 end proc:\012lincartcoords := proc(B_) local F__:\012 F__  := t__ -&gt; [seq(CombLinS(B_,t__)[j__],j__=1..2)]:\012 curvecoords(F__):\012 end proc:\012linpolcoords  := proc(A_) local pol__,F__:\012 pol__ := t__ -&gt; &lt;t__[1]*cos(t__[2]),t__[1]*sin(t__[2])&gt;:\012 F__  := t__ -&gt; [seq(CombLinS(M2L(A_),pol__(t__))[j__],j__=1..2)]:\012 curvecoords(F__):\012 end proc:\012detplot := proc(A_,n_) local F__,g__,max__:\012 F__   := (t__,x__,y__) -&gt; (1/t__)*(A_^(-1)).&lt;x__,y__&gt;:\012 max__ := 2*Norm(A_,1)+Norm(A_.&lt;1/2,1/2&gt;,infinity):\012 g__   := t__ -&gt; implicitplot( Norm(F__(t__,x__,y__)-&lt;1/2,1/2&gt;,infinity)=1/2,\012                               x__=0..max__,y__=0..max__,gridrefine=4       ):\012 plots[display]( [seq( g__(k__/n_) , k__=1..n_ ) ] , axes=normal ):\012 end proc:\012CharPlot := proc(M_,AT_,A_,a_,b_,t_) local ff__: \012 ff__ :=  CharParam(M_,A_,a_,b_):\012 NW_CurveParam([ff__,I_01],AT_,t_):\012 end proc:\012WordPlot := proc(MM_,AT_,A_,a_,b_,space_,t_) local FF__:\012 FF__ :=  WordParam(MM_,A_,a_,b_,space_):\012 NW_CurveParam([FF__,I_01],AT_,t_):\012 end proc:\012                                                                                                            \012curvecoords3d := proc(F_) local G__,R__,V__,default__,coords__,t__:\012 G__  := [seq(k__/10,k__=0..10)]:\012 R__ := [-1..1,-1..1,-1..1]:\012 V__ := R__:\012 default__ := [G__,G__,G__,R__,V__]:\012 addcoords(coords__,[seq(t__[j__],j__=1..3)],convert(F_(t__),list),default__):\012 coords__:\012 end proc:\012sphericalcoords3d := proc() local F__:\012 F__ := t__ -&gt; \012  &lt;t__[1]*cos(t__[2])*sin(t__[3]),t__[1]*sin(t__[2])*sin(t__[3]),t__[1]*cos(t__[3])&gt;:\012 curvecoords3d(F__):\012 end proc:\012lincartcoords3d := proc(B_) local F__:\012 F__  := t__ -&gt; [seq(CombLinS(B_,t__)[j__],j__=1..3)]:\012 curvecoords3d(F__):\012 end proc:\012linsphcoords3d := proc(A_) local sph__,F__:\012 sph__ := t__ -&gt; \012  &lt;t__[1]*cos(t__[2])*sin(t__[3]),t__[1]*sin(t__[2])*sin(t__[3]),t__[1]*cos(t__[3])&gt;:\012 F__  := t__ -&gt; [seq(CombLinS(M2L(A_),sph__(t__))[j__],j__=1..3)]:\012 curvecoords3d(F__):\012 end proc:\012detplot3d := proc(A_,n_) local F__,g__,max__:\012 F__   := (t__,x__,y__,z__) -&gt; (1/t__)*(A_^(-1)).&lt;x__,y__,z__&gt;:\012 max__ := 2*Norm(A_,1)+Norm(A_.&lt;1/2,1/2,1/2&gt;,infinity):\012 g__   := t__ -&gt; implicitplot3d( Norm(F__(t__,x__,y__,z__)-&lt;1/2,1/2,1/2&gt;,infinity)=1/2,\012                                 x__=0..max__,y__=0..max__,z__=0..max__,grid=[10,10,10] ):\012 plots[display]( [seq( g__(k__/n_) , k__=1..n_ ) ] , axes=normal, style=patchnogrid ):\012 end proc:\012\012end module:                                                                                                 \012############################################################################################################\012                                                                                                            \012######################################################## FILM ##################################################################\012                                                                                                            \012ODE_CO := module()                                                                                      \012\012  uses    plots, LinearAlgebra, AnimationII, AlgLin, Analyse;\012  export  ODE_11_E1, ODE_11_P1, \012          ODE_12_E1, ODE_12_P1,\012          ODE_13_E1, ODE_13_P1,\012          ODE_21_E1, ODE_21_P1,\012          ODE_22_E1, ODE_22_P1;\012  option package;\012\012##########################################################################################################\012ODE_11_E1 := [1/x,4*sin(x),[[&quot;0+&quot;,&quot;+inf&quot;]],[Pi/4,0],3,[0.2,10]]:                                          \012ODE_11_P1 := proc(PAR,T)                                                                                  \012\012px := PAR[1]: qx := PAR[2]: Dom := PAR[3]: M0 := PAR[4]: n := PAR[5]: epsinf := PAR[6]:\012\012p := unapply(px,x): q := unapply(qx,x):\012eps := epsinf[1]: inf := epsinf[2]:\012nba  := nops(Dom): DomDom := IIRecup(Dom,Approx(nba,eps),Approx(nba,inf)):\012DomF := DomDom[1]: DomR := DomDom[2]: \012t0   := DomR[1,1]:\012x0 := M0[1]: y0 := M0[2]:\012\012ode := diff(y(x),x)+p(x)*y(x)=q(x):\012f   := unapply([op(dsolve(ode))][2],x,_C1):\012F   := (xx,c1) -&gt; simplify(f(xx,c1)-f(xx,0)):\012C   := (xx,yy) -&gt; simplify((yy-f(xx,0))/F(xx,1)):\012ci  := C(x0,y0):\012fci := xx -&gt; f(xx,ci):\012\012yk  := [seq(y0+k,k=-n..-1),seq(y0+k,k=1..n)]:\012fck := [seq(unapply(f(x,C(x0,yk[k])),x),k=1..nops(yk))]:\012\012if       Dom[1,1]&lt;&gt;&quot;-inf&quot; then o := &lt;DomF[1,1],0&gt;\012 else if Dom[1,2]&lt;&gt;&quot;+inf&quot; then o := &lt;DomF[1,2],0&gt;\012 else o := O_2\012 end if end if:\012dom := t -&gt; [t0,t]:\012cou := [&quot;HotPink&quot;,&quot;RoyalBlue&quot;]:\012VS2D := table([ &quot;b&quot;=F_F,&quot;v&quot;=default,&quot;m&quot;=U_NR,&quot;d&quot;=[2,[]],&quot;j&quot;=&quot;E&quot; ]):\012\012PC := [seq( table(), k=1..1 )]: VS := [seq(VS2D,k=1..1)]:                                                 \012PC[1][0,0] := I_01: \012PC[1][0,1] := \012  [ [ [fck,DomR[1]] , NWCcurvcar , [cou[1],nul,solid,0]    , 1 ],\012    [ [fci,DomR[1]] , nwcurvcar  , [cou[2],nul,dot,0]      , 1 ],\012    [ M0            , nwpoint    , [cou[2],&quot;M0&quot;,B_R,point] , 1 ],\012    [ o             , nwpoint    , [black,&quot;&quot;,B_R,point]    , 1 ] ]:\012 \012PC[1][1,0] := DomR[1]:\012PC[1][1,1] := \012  [ [ [fci,dom(t_)] , nwcurvcar  , [cou[2],nul,solid,3] , 1 ] ]:\012table([ 0=&quot;R&quot;, seq( k=[PC[k],VS[k]], k=1..1 ),                                                            \012        &quot;r1&quot; = [F(x,K),f(x,0),ci]                                        ]):                              \012\012end proc:\012##########################################################################################################\012\012##########################################################################################################\012ODE_12_E1 := [1/x,4*sin(x),[[&quot;0+&quot;,&quot;+inf&quot;]],[-10,40],3,[1,10]]:                                            \012ODE_12_P1 := proc(PAR,T)                                                                                  \012\012px := PAR[1]: qx := PAR[2]: Domx := PAR[3]: Domy := PAR[4]: n := PAR[5]: epsinf := PAR[6]:\012\012p := unapply(px,x): q := unapply(qx,x):\012eps := epsinf[1]: inf := epsinf[2]:\012nba  := nops(Domx): DomDom := IIRecup(Domx,Approx(nba,eps),Approx(nba,inf)):\012DomF := DomDom[1]: DomR := DomDom[2]: \012t0 := DomR[1,1]:\012x0 := (DomR[1,1]+DomR[1,2])/2:\012\012V := (xx,yy) -&gt; &lt;1,q(xx)-p(xx)*yy&gt;:\012ode := diff(y(x),x)+p(x)*y(x)=q(x):\012f := unapply([op(dsolve(ode))][2],x,_C1):\012F := (xx,c1) -&gt; simplify(f(xx,c1)-f(xx,0)):\012C  := (xx,yy) -&gt; simplify((yy-f(xx,0))/F(xx,1)):\012\012yk := [seq(k,k=-n..n)]:\012fck := [seq(unapply(f(x,C(x0,yk[k])),x),k=1..nops(yk))]:\012\012if       Domx[1,1]&lt;&gt;&quot;-inf&quot; then o := &lt;DomF[1,1],0&gt;\012 else if Domx[1,2]&lt;&gt;&quot;+inf&quot; then o := &lt;DomF[1,2],0&gt;\012 else o := O_2\012 end if end if:\012dom := t -&gt; [t0,t]:\012DOM := [DomR[1],Domy]:\012cou := [&quot;Pink&quot;,&quot;HotPink&quot;]:\012VS2D := table([ &quot;b&quot;=F_F,&quot;v&quot;=default,&quot;m&quot;=U_NR,&quot;d&quot;=[2,[]],&quot;j&quot;=&quot;E&quot; ]):\012\012PC := [seq( table(), k=1..1 )]: VS := [seq(VS2D,k=1..1)]:                                                 \012PC[1][0,0] := I_01: \012PC[1][0,1] := \012  [ [ [V,DOM] , nwfieldplot , [cou[1],true,[20,20],fixed] , 1 ],\012    [ o       , nwpoint     , [black,&quot;&quot;,B_R,point]        , 1 ] ]:\012 \012PC[1][1,0] := DomR[1]:\012PC[1][1,1] := \012  [ [ [fck,dom(t_)] , NWCcurvcar  , [cou[2],nul,solid,0] , 1 ] ]:\012table([ 0=&quot;R&quot;, seq( k=[PC[k],VS[k]], k=1..1 ),                                                            \012        &quot;r1&quot; = [V(x,y)]                                        ]):       \012\012end proc:\012##########################################################################################################\012\012##########################################################################################################\012ODE_13_E1 := [1/x,4*sin(x),[[&quot;0+&quot;, &quot;+inf&quot;]],3,[0.2,10]]:                                                     \012ODE_13_P1 := proc(PAR,T)                                                                                  \012\012px := PAR[1]: qx := PAR[2]: Dom := PAR[3]: n := PAR[4]: epsinf := PAR[5]:\012\012p := unapply(px,x): q := unapply(qx,x):\012eps := epsinf[1]: inf := epsinf[2]:\012nba  := nops(Dom): DomDom := IIRecup(Dom,Approx(nba,eps),Approx(nba,inf)):\012DomF := DomDom[1]: DomR := DomDom[2]: \012t0 := DomR[1,1]:\012\012V := (xx,yy) -&gt; &lt;1,q(xx)-p(xx)*yy&gt;:\012ode := diff(y(x),x)+p(x)*y(x)=q(x):\012f := unapply([op(dsolve(ode))][2],x,_C1):\012F := (xx,c1) -&gt; simplify(f(xx,c1)-f(xx,0)):\012f0 := xx -&gt; f(xx,0):\012\012ck := [seq(k,k=-n..n)]:\012Fck := [seq(unapply(F(x,ck[k]),x),k=1..nops(ck))]:\012fck := [seq(unapply(f(x,ck[k]),x),k=1..nops(ck))]:\012\012if       Dom[1,1]&lt;&gt;&quot;-inf&quot; then o := &lt;DomF[1,1],0&gt;\012 else if Dom[1,2]&lt;&gt;&quot;+inf&quot; then o := &lt;DomF[1,2],0&gt;\012 else o := O_2\012 end if end if:\012dom := t -&gt; [t0,t]:\012cou := [&quot;DarkRed&quot;,&quot;Violet&quot;,&quot;RoyalBlue&quot;]:\012VS2D := table([ &quot;b&quot;=F_F,&quot;v&quot;=default,&quot;m&quot;=U_NR,&quot;d&quot;=[2,[]],&quot;j&quot;=&quot;E&quot; ]):\012\012PC := [seq( table(), k=1..1 )]: VS := [seq(VS2D,k=1..1)]:                                                 \012PC[1][0,0] := I_01: \012PC[1][0,1] := \012  [ [ [f0,DomR[1]]  , nwcurvcar  , [cou[1],nul,solid,3] , 1 ],\012    [ [Fck,DomR[1]] , NWCcurvcar , [cou[2],nul,dash,0]  , 1 ],\012    [ o             , nwpoint    , [black,&quot;&quot;,B_R,point] , 1 ] ]:\012 \012PC[1][1,0] := DomR[1]:\012PC[1][1,1] := \012  [ [ [fck,dom(t_)] , NWCcurvcar  , [cou[3],nul,solid,0] , 1 ] ]:\012table([ 0=&quot;R&quot;, seq( k=[PC[k],VS[k]], k=1..1 ),                                                            \012        &quot;r1&quot; = [F(x,K),f(x,0)]                                        ]):                                 \012\012end proc:\012##########################################################################################################\012\012##########################################################################################################\012ODE_21_E1 := [[1,2,3],4*sin(x),[-1,2],[0,1,1],3]:                                                         \012ODE_21_P1 := proc(PAR,T)                                                                                  \012\012Ode := PAR[1]: hx := PAR[2]: Dom := PAR[3]: Ini := PAR[4]: n := PAR[5]:\012\012a := Ode[1]: b := Ode[2]: c := Ode[3]:\012h := unapply(hx,x):\012t0 := Dom[1]:\012x0 := Ini[1]: y0 := Ini[2]: dy0 := Ini[3]:\012\012M0 := &lt;x0,y0&gt;: vt0 := &lt;1,dy0&gt;:\012ode := a*diff(y(x),x,x)+b*diff(y(x),x)+c*y(x)=h(x);\012f := unapply([op(dsolve(ode))][2],x,_C1,_C2);\012F := (xx,c1,c2) -&gt; simplify(f(xx,c1,c2)-f(xx,0,0)):\012df := D[1](f);\012C  := proc(xx,yy,dyy) local sol:\012 sol := solve({f(xx,c1,c2)=yy,df(xx,c1,c2)=dyy},[c1,c2]):\012 [[op(sol[1,1])][2],[op(sol[1,2])][2]]:\012 end proc:\012ff := (xx,cc) -&gt; f(xx,cc[1],cc[2]):\012ci := C(x0,y0,dy0);\012fci := xx -&gt; ff(xx,ci);\012\012yk  := [seq(y0+k,k=-n..-1) ,seq(y0+k,k=1..n) ]:\012dyk := [seq(dy0+k,k=-n..-1),seq(dy0+k,k=1..n)]:\012fck[1] := [seq(unapply(ff(x,C(x0,yk[k],dy0)),x),k=1..nops(yk)) ]:\012fck[2] := [seq(unapply(ff(x,C(x0,y0,dyk[k])),x),k=1..nops(dyk))]:\012\012dom := t -&gt; [t0,t]:\012cou := [&quot;HotPink&quot;,&quot;RoyalBlue&quot;]:\012VS2D := table([ &quot;b&quot;=F_F,&quot;v&quot;=default,&quot;m&quot;=U_NR,&quot;d&quot;=[2,[]],&quot;j&quot;=&quot;E&quot; ]):\012\012PC := [seq( table(), k=1..2 )]: VS := [seq(VS2D,k=1..2)]:                                                 \012PC[1][0,0] := I_01: \012PC[1][0,1] := \012  [ [ [fck[1],Dom]  , NWCcurvcar , [cou[1],nul,solid,0]    , 1 ],\012    [ [fci,Dom]     , nwcurvcar  , [cou[2],nul,dot,0]      , 1 ],\012    [ M0            , nwpoint    , [cou[2],&quot;M0&quot;,B_R,point] , 1 ],\012    [ [M0,vt0]      , nwarrow    , [cou[2],nul,solid,0.05] , 1 ] ]:\012 \012PC[1][1,0] := Dom:\012PC[1][1,1] := \012  [ [ [fci,dom(t_)] , nwcurvcar  , [cou[2],nul,solid,3] , 1 ] ]:\012\012PC[2][0,0] := I_01: \012PC[2][0,1] := \012  [ [ [fck[2],Dom]  , NWCcurvcar , [cou[1],nul,solid,0]    , 1 ],\012    [ [fci,Dom]     , nwcurvcar  , [cou[2],nul,dot,0]      , 1 ],\012    [ M0            , nwpoint    , [cou[2],&quot;M0&quot;,B_R,point] , 1 ],\012    [ [M0,vt0]      , nwarrow    , [cou[2],nul,solid,0.05] , 1 ] ]:\012 \012PC[2][1,0] := Dom:\012PC[2][1,1] := \012  [ [ [fci,dom(t_)] , nwcurvcar  , [cou[2],nul,solid,3] , 1 ] ]:\012table([ 0=&quot;R&quot;, seq( k=[PC[k],VS[k]], k=1..2 ),                                                            \012        &quot;r1&quot; = [F(x,K[1],K[2]),f(x,0,0),ci]                                        ]):                    \012\012end proc:\012##########################################################################################################\012\012##########################################################################################################\012ODE_22_E1 := [[1,2,3],4*sin(x),[-1,2],3,3]:                                                               \012ODE_22_P1 := proc(PAR,T)                                                                                  \012\012Ode := PAR[1]: hx := PAR[2]: Dom := PAR[3]: n := PAR[4]: p := PAR[5]:\012\012a := Ode[1]: b := Ode[2]: c := Ode[3]:\012h := unapply(hx,x):\012t0 := Dom[1]:\012\012ode := a*diff(y(x),x,x)+b*diff(y(x),x)+c*y(x)=h(x);\012f := unapply([op(dsolve(ode))][2],x,_C1,_C2);\012F := (xx,c1,c2) -&gt; simplify(f(xx,c1,c2)-f(xx,0,0)):\012f0 := xx -&gt; f(xx,0,0);\012\012ck1 := [seq(k,k=-n..n)]:\012ck2 := ck1:\012if       p=1 then ck2 := [seq(0,k=-n..n)]: K[2] := 0:\012 else if p=2 then ck1 := [seq(0,k=-n..n)]: K[1] := 0:\012 end if end if:\012Fck := [seq(unapply(F(x,ck1[k],ck2[k]) ,x),k=1..nops(ck1)) ]:\012fck := [seq(unapply(f(x,ck1[k],ck2[k]) ,x),k=1..nops(ck1)) ]:\012\012dom := t -&gt; [t0,t]:\012cou := [&quot;DarkRed&quot;,&quot;Violet&quot;,&quot;RoyalBlue&quot;]:\012VS2D := table([ &quot;b&quot;=F_F,&quot;v&quot;=default,&quot;m&quot;=U_NR,&quot;d&quot;=[2,[]],&quot;j&quot;=&quot;E&quot; ]):\012\012PC := [seq( table(), k=1..1 )]: VS := [seq(VS2D,k=1..1)]:                                                 \012PC[1][0,0] := I_01: \012PC[1][0,1] := \012  [ [ [f0,Dom]  , nwcurvcar  , [cou[1],nul,solid,3] , 1 ],\012    [ [Fck,Dom] , NWCcurvcar , [cou[2],nul,dash,0]  , 1 ] ]:\012 \012PC[1][1,0] := Dom:\012PC[1][1,1] := \012  [ [ [fck,dom(t_)] , NWCcurvcar  , [cou[3],nul,solid,0] , 1 ] ]:\012table([ 0=&quot;R&quot;, seq( k=[PC[k],VS[k]], k=1..1 ),                                                            \012        &quot;r1&quot; = [F(x,K[1],K[2]),f0(x)]                                        ]):                          \012\012end proc:\012##########################################################################################################\012\012end module: \012                                                                                            \012############################################################################################################\012                                                                                                            \012####################################################### GESTION  ###################################################################\012                                                                                                                           \012###########################################################################################################################\012\012with(DocumentTools): with(StringTools): with(ListTools): with(plots): with(LinearAlgebra): \012with(AnimationII): with(AlgLin): with(Analyse): with(Geometrie): \012with(ODE_CO):                                            \012\012SLIDER := 100: SPEED := 10:     \012\012PAR := ODE_21_E1: abc := PAR[1]: hx := PAR[2]: Dom := PAR[3]: ci := PAR[4]: n := PAR[5]:\012SetProperty(ode21CBB1,'value',&quot;Condition y(x0) variable&quot;):\012SetProperty(ode21TAR1,'value',abc):\012SetProperty(ode21TAR2,'value',hx):\012SetProperty(ode21TAR3,'value',Dom):\012SetProperty(ode21TAR4,'value',ci):\012SetProperty(ode21TAR5,'value',n):\012SetProperty(ode21TAR6,'value',NULL):\012SetProperty(ode21TAR7,'value',NULL):\012SetProperty(ode21TAR8,'value',NULL):\012SetProperty(ode21TAR9,'value',NULL):\012SetProperty(ode21PLS1,'value',EP2D): \012\012PAR := ODE_22_E1: abc := PAR[1]: hx := PAR[2]: Dom := PAR[3]: n := PAR[4]: p := PAR[5]:\012SetProperty(ode22CBB1,'value',&quot;K1 et K2 variables&quot;):\012SetProperty(ode22TAR1,'value',abc):\012SetProperty(ode22TAR2,'value',hx):\012SetProperty(ode22TAR3,'value',Dom):\012SetProperty(ode22TAR4,'value',n):\012SetProperty(ode22TAR5,'value',NULL):\012SetProperty(ode22TAR6,'value',NULL):\012SetProperty(ode22PLS1,'value',EP2D): \012###########################################################################################################################\012                                                                                                                           \012\012"/>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Chamamos o problema de Cauchy de busca de uma solu\303\247\303\243o de (E) que satisfa\303\247a as condi\303\247\303\265es</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">A curva representativa de uma solu\303\247\303\243o \303\251 chamada curva integral.
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">O problema de Cauchy admite uma solu\303\247\303\243o \303\272nica em </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn</Equation> .</Text-field>
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encoding="UTF-8"> as ra\303\255zes reais distintas se </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEnJiM5MTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSI+RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSy1JI21uR0YkNiVRIjBGJ0YyRjRGMkY0">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEnJiM5MTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSI+RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSy1JI21uR0YkNiVRIjBGJ0YyRjRGMkY0</Equation>, <Equation 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ra\303\255zes complexas se </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEnJiM5MTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSI8RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSy1JI21uR0YkNiVRIjBGJ0YyRjRGMkY0">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEnJiM5MTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSI8RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSy1JI21uR0YkNiVRIjBGJ0YyRjRGMkY0</Equation>.</Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">Damos as condi\303\247\303\265es de Cauchy </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]"> . 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size="10" foreground="[0,51,0]" encoding="UTF-8"> n\303\263s flutuamos </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> ent\303\243o resolvemos o sistema obtido: </Font><Equation executable="false" style="2D Math" input-equation="" 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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal" bulletsuffix="."><Font size="10" foreground="[0,51,0]">Determinamos as constantes </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> correspondente \303\240s condi\303\247\303\265es de Cauchy </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> quanto a uma equa\303\247\303\243o homog\303\252nea.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]">1. Se </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiaEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiaEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> \303\251 uma fun\303\247\303\243o constante, ent\303\243o (E) admite uma solu\303\247\303\243o constante</Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW9HRiQ2L1EifkYnLyUlc2l6ZUdRIzEwRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSS1JJW1zdWJHRiQ2JS1JI21pR0YkNidRInlGJ0YvLyUnaXRhbGljR1EldHJ1ZUYnRjIvRjZRJ2l0YWxpY0YnLUYjNigtRlA2KFEiUEYnRi9GU0YyLyUrZXhlY3V0YWJsZUdGOkZWRi9GU0YyRmduRlYvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0YvRjJGZ25GNQ==">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> certo \342\204\235.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]">2. Se </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiaEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiaEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> \303\251 uma fun\303\247\303\243o polinomial de grau </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> ent\303\243o (E) admite uma solu\303\247\303\243o polinomial </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEieUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYoLUYvNihRIlBGJ0YyRjVGOEY7Rj5GMkY1RjhGO0Y+LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGMkY4RjsvRj9RJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEieUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYoLUYvNihRIlBGJ0YyRjVGOEY7Rj5GMkY1RjhGO0Y+LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGMkY4RjsvRj9RJ25vcm1hbEYn</Equation><Font size="10" foreground="[0,51,0]"> de grau </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> certo \342\204\235.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]">3. Se </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiaEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiaEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> \303\251 uma fun\303\247\303\243o exponencial </Font><Equation executable="false" style="Text" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> ent\303\243o dois casos surgem:
</Font><Font size="10" foreground="[0,51,0]">- se </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEickYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEickYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> n\303\243o \303\251 raiz da equa\303\247\303\243o caracter\303\255stica, ent\303\243o (E) admite uma solu\303\247\303\243o da forma </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> certo \342\204\235.
</Font><Font size="10" foreground="[0,51,0]">- se </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEickYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEickYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> \303\251 a raiz da equa\303\247\303\243o caracter\303\255stica:
</Font><Font size="10" foreground="[0,51,0]">  - se </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2KFEnJiM5MTY7RicvJSVzaXplR1EjMTBGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHRjQvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2MFElJm5lO0YnRi9GNUY4RjovJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2J1EiMEYnRi9GNUY4RjpGL0Y1RjhGOg==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2KFEnJiM5MTY7RicvJSVzaXplR1EjMTBGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHRjQvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2MFElJm5lO0YnRi9GNUY4RjovJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2J1EiMEYnRi9GNUY4RjpGL0Y1RjhGOg==</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> ent\303\243o (E) admite uma solu\303\247\303\243o da forma </Font><Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEieUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUYvNihRIlBGJ0YyRjVGOEY7Rj5GMkY4RjsvRj9RJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSShtZmVuY2VkR0YkNictRiM2Jy1GLzYoUSJ4RidGMkY1RjhGO0Y+RjJGOEY7RkZGMkY4RjtGRi1JI21vR0YkNjBRIj1GJ0YyRjhGO0ZGLyUmZmVuY2VHRj0vJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGYW8tRi82KFEnJiM5NTU7RidGMi9GNkY9RjhGO0ZGLUZUNjBRJyZzZG90O0YnRjJGOEY7RkZGV0ZZRmVuRmduRmluRltvRl1vL0Zgb1EmMC4wZW1GJy9GY29GXHBGUC1GVDYwUSJ+RidGMkY4RjtGRkZXRllGZW5GZ25GaW5GW29GXW9GW3BGXXAtSSVtc3VwR0YkNiUtRlQ2MFEvJkV4cG9uZW50aWFsRTtGJ0YyRjhGO0ZGL0ZYUSZ1bnNldEYnL0ZaRmhwL0ZmbkZocC9GaG5GaHAvRmpuRmhwL0Zcb0ZocC9GXm9GaHBGW3AvRmNvUSwwLjExMTExMTFlbUYnLUYjNihGXnAtRi82KFEjcnhGJ0YyRjVGOEY7Rj5GMkY4RjtGRi8lMXN1cGVyc2NyaXB0c2hpZnRHRkpGMkY4RjtGRg==</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> certo \342\204\235.
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]">4. Se </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiaEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiaEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> \303\251 uma fun\303\247\303\243o trigonom\303\251trica </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> ent\303\243o dois casos surgem:
- se i\317\211 n\303\243o \303\251 raiz da equa\303\247\303\243o caracter\303\255stica, ent\303\243o (E) admite uma solu\303\247\303\243o em \342\204\235 da forma </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]">.
<Font encoding="UTF-8">- se i\317\211 Como raiz da equa\303\247\303\243o caracter\303\255stica, (E) admite uma solu\303\247\303\243o em \342\204\235 da forma </Font></Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]">.
Observe que em </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEieUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUYvNihRIlBGJ0YyRjVGOEY7Rj5GMkY4RjsvRj9RJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSShtZmVuY2VkR0YkNictRiM2Jy1GLzYoUSJ4RidGMkY1RjhGO0Y+RjJGOEY7RkZGMkY4RjtGRkYyRjhGO0ZG">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEieUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUYvNihRIlBGJ0YyRjVGOEY7Rj5GMkY4RjsvRj9RJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSShtZmVuY2VkR0YkNictRiM2Jy1GLzYoUSJ4RidGMkY1RjhGO0Y+RjJGOEY7RkZGMkY4RjtGRkYyRjhGO0ZG</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> uma combina\303\247\303\243o </Font><Equation executable="false" style="2D Math" input-equation="" 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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">A equa\303\247\303\243o  </Font><Equation executable="false" style="2D Math" input-equation="" 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<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">A lista abaixo permite escolher entre uma fam\303\255lia de curvas integrais com condi\303\247\303\243o vari\303\241vel </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2KFEieUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EuWzEwMiwxMDIsMTUzXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYnLUYjNictSSVtc3ViR0YkNiUtRiw2KFEieEYnRi9GMkY1RjhGOy1GIzYoLUkjbW5HRiQ2J1EiMEYnRi9GNUY4L0Y8USdub3JtYWxGJ0YvRjJGNUY4RjsvJS9zdWJzY3JpcHRzaGlmdEdGTkYvRjVGOEZPRi9GNUY4Rk9GL0Y1RjhGTw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2KFEieUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EuWzEwMiwxMDIsMTUzXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYnLUYjNictSSVtc3ViR0YkNiUtRiw2KFEieEYnRi9GMkY1RjhGOy1GIzYoLUkjbW5HRiQ2J1EiMEYnRi9GNUY4L0Y8USdub3JtYWxGJ0YvRjJGNUY4RjsvJS9zdWJzY3JpcHRzaGlmdEdGTkYvRjVGOEZPRi9GNUY4Rk9GL0Y1RjhGTw==</Equation><Font size="10" foreground="[102,102,153]" encoding="UTF-8"> e uma fam\303\255lia de curvas integrais com condi\303\247\303\243o vari\303\241vel </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[102,102,153]"> .</Font></Text-field>
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<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" bold="true" foreground="[102,102,153]" encoding="UTF-8" italic="true">Modifique os seguintes dados se considerar \303\272teis: valores de</Font><Font size="10" foreground="[102,102,153]"> </Font><Equation executable="false" style="2D Math" input-equation="" 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Em seguida, clique no bot\303\243o 'Solu\303\247\303\265es'.
Por fim, clique no gr\303\241fico e use as ferramentas que aparecem na parte superior da p\303\241gina para animar o gr\303\241fico.</Font></Text-field>
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end use; 
</MapleCode></EC-TextArea></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L95501" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><EC-TextArea id="ode21TAR8" enabled="true" visible="true" visiblecharacterwidth="50" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="" editable="true" wrapping="true" show-border="true" password="false"><MapleCode action="content-event-handler">use DocumentTools in 
end use; 
</MapleCode></EC-TextArea></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L95519" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><EC-TextArea id="ode21TAR9" enabled="true" visible="true" visiblecharacterwidth="50" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="" editable="true" wrapping="true" show-border="true" password="false"><MapleCode action="content-event-handler">use DocumentTools in 
end use; 
</MapleCode></EC-TextArea></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L95507" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell padding="5" visible="true" fillcolor="[255,255,255]" rowspan="1" backgroundstyle="0" columnspan="1"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L95512" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRicvJSVzaXplR1EjMTBGJy8lK2ZvcmVncm91bmRHUS5bMTAyLDEwMiwxNTNdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation><EC-Button id="ode21BUT1" caption="Solutions" pixel-width="300" pixel-height="200" enabled="true" visible="true" show-border="true" user-size="false" fontcolor="[0,0,0]"><MapleCode action="click-event-handler">use DocumentTools in 

choix := GetProperty(ode21CBB1,'value'):
if choix=&quot;Condition y(x0) variable&quot; then p := 1 
 else p := 2 end if:

abc   := parse(GetProperty(ode21TAR1,'value')):
hx    := parse(GetProperty(ode21TAR2,'value')):
Dom   := parse(GetProperty(ode21TAR3,'value')):
ci    := parse(GetProperty(ode21TAR4,'value')):
n     := parse(GetProperty(ode21TAR5,'value')):
PAR := [abc,hx,Dom,ci,n]:

TITRE := ODE_21_P1:
FILM  := table([1=TITRE,2=PAR]):
SPEED := 10:
res := Calculs(FILM,T):

Y := res[1,1]: yP := res[1,2]: ci := res[1,3]:
Do(%ode21PLS1=Seance(FILM,[],t,T,&quot;A&quot;)[p]):
SetProperty(ode21TAR6,'value',Y):
SetProperty(ode21TAR7,'value',yP):
SetProperty(ode21TAR8,'value',ci[1]):
SetProperty(ode21TAR9,'value',ci[2]):

end use; </MapleCode></EC-Button></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row></Table>
</Section>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 3" underline="true" foreground="[102,102,153]" italic="false" size="10" layout="Heading 3"><Font size="10" underline="true" foreground="[102,102,153]" encoding="UTF-8" italic="false">Gr\303\241fico interativo: visualize as solu\303\247\303\265es em um intervalo I de uma equa\303\247\303\243o diferencial a y '' + b y '+ c y = h (x), obtida como uma deforma\303\247\303\243o das solu\303\247\303\265es da equa\303\247\303\243o homog\303\252nea associada a uma solu\303\247\303\243o espec\303\255fica yP.
Retorna as solu\303\247\303\265es Y da equa\303\247\303\243o homog\303\252nea associada e yP.</Font></Text-field></Title><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L125160" drawlabel="true">
<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
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<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">A lista abaixo permite escolher entre uma fam\303\255lia de curvas integrais com constante </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[102,102,153]"> , <Font encoding="UTF-8">uma fam\303\255lia de curvas integrais com constante </Font></Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[102,102,153]" encoding="UTF-8"> , ou uma fam\303\255lia de curvas integrais com as duas constantes </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[102,102,153]"> variaveis.</Font></Text-field>
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Em seguida, clique no bot\303\243o 'Adi\303\247\303\243o'.
Por fim, clique no gr\303\241fico e use as ferramentas que aparecem na parte superior da p\303\241gina para animar o gr\303\241fico.</Font></Text-field>
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choix := GetProperty(ode22CBB1,'value'):
if       choix=&quot;K2=0&quot; then p := 1 
 else if choix=&quot;K1=0&quot; then p := 2 
 else p := 3 end if end if:

abc   := parse(GetProperty(ode22TAR1,'value')):
hx    := parse(GetProperty(ode22TAR2,'value')):
Dom   := parse(GetProperty(ode22TAR3,'value')):
n     := parse(GetProperty(ode22TAR4,'value')):
PAR := [abc,hx,Dom,n,p]:

TITRE := ODE_22_P1:
FILM  := table([1=TITRE,2=PAR]):
SPEED := 10:
res := Calculs(FILM,T):

Y := res[1,1]: yP := res[1,2]:
Do(%ode22PLS1=Seance(FILM,[],t,T,&quot;A&quot;)[1]):
SetProperty(ode22TAR5,'value',Y):
SetProperty(ode22TAR6,'value',yP):

end use; </MapleCode></EC-Button></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">1. Escreva a equa\303\247\303\243o (E ') verificada por </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]">.</Font></Text-field>
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