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<Startup-Code startupcode="########################################################### INIT #####################################################################\012\012restart:\012\012######################################################## ANIMATIOII ##################################################################\012\012AnimationII := module()                                                                                     \012\012  uses     plots, LinearAlgebra, ImageTools; \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, PreOrd, Ord, LexBoo, LexBoo3, LexOrd, Ordonner_d, Ordonner,\012            rand_i, rand_s, rand_a, ImageDir, ImageRec, Inverse, PrintTable,\012                                                                                                            \012           nw_display, nw_point, nw_text, nw_line, nw_polygon, nw_rectangle, nw_circle, nw_disk, nw_ellipse,\012            nw_arrow, nw_coords, nw_curvcar, nw_curvpar, nw_fieldplot, nw_implicit, nw_inequal,\012            NW_arrow, NWD_arrow, NWE_arrow, NW_point, NW_line, NWD_line, NWE_line, NW_disk, NW_circle, \012            NW_rectangle, NW_polygon, \012            NWE_curvcar, NWE_curvpar, NWD_curvcar, NWD_curvpar, NWC_curvcar, NWC_curvpar, \012            NWC_implicit, NWE_implicit,\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, nw_implicit3d,\012            NW_arrow3d, NWD_arrow3d, NWE_arrow3d, NW_point3d, NW_line3d, NWD_line3d, NWE_line3d, NW_polygon3d,\012            NWC_curvpar3d, NWD_curvpar3d, NWE_curvpar3d, NWC_implicit3d, NWE_implicit3d,\012           nw_surfparXd, \012                                                                                                            \012           FAUNE;\012  local   Paragraphe;\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:\012PreOrd := proc(L_,k_,i_) local j__,L__:\012 L__ := L_:\012 for j__ from i_ to nops(L__) do \012  if evalf(L__[j__][k_])&gt;evalf(L__[i_][k_]) then L__ := Echanger(L__,i_,j__) end if:\012  end do:\012 L__:\012 end proc:\012Ord := proc(L_,k_,sens_) local i__,L__:\012 L__ := L_:\012 for i__ from 1 to nops(L__) do L__ := PreOrd(L__,k_,i__) end do:\012 if sens_=&quot;&gt;&quot; then L__ else ListTools:-Reverse(L__) end if:\012 end proc:\012LexBoo := proc(u_,v_,k_) local u__,v__,boo__,k__:\012 boo__ := true:\012 u__ := evalf(u_): v__ := evalf(v_):\012 for k__ from 1 to k_-1 do\012  boo__ := boo__ and evalb(u__[k__]=v__[k__]):\012  end do:\012 boo__ := boo__ and evalb(u__[k_]&lt;=v__[k_]):\012 not(boo__):\012 end proc:\012LexBoo3 := [(u_,v_) -&gt; LexBoo(u_,v_,1),(u_,v_) -&gt; LexBoo(u_,v_,2),(u_,v_) -&gt; LexBoo(u_,v_,3)]:\012LexOrd := proc(L_,k_,sens_) local kmin__,L__,k__:\012 kmin__ := min(k_,nops(V2L(L_[1]))):\012 L__ := L_:\012 for k__ from 1 to kmin__ do L__ := sort(L__,LexBoo3[k__]) end do:\012 if sens_=&quot;&gt;&quot; then L__ else ListTools:-Reverse(L__) end if:\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:\012rand_i := proc(E_,F_) local F__,x__,y__,f__:\012 F__ := F_: f__ := table([]):\012 if nops(E_)&gt;nops(F_) then return [] end if:\012 for x__ in E_ do\012  y__ := RandomTools[Generate](choose(F__)):\012  f__[x__] := y__:\012  F__ := F__ minus {y__}:\012  end do:\012 f__:\012 end proc:\012rand_s := proc(E_,F_) local E__,x__,y__,f__:\012 E__ := E_: f__ := table([]):\012 if nops(E_)&lt;nops(F_) then return [] end if:\012 for y__ in F_ do\012  x__ := RandomTools[Generate](choose(E__)):\012  f__[x__] := y__:\012  E__ := E__ minus {x__}:\012  end do:\012 for x__ in E__ do\012  y__ := RandomTools[Generate](choose(F_)):\012  f__[x__] := y__:\012  end do:\012 f__:\012 end proc:\012rand_a := proc(E_,F_) local x__,y__,f__:\012 f__ := table([]):\012 for x__ in E_ do\012  y__ := RandomTools[Generate](choose(F_)):\012  f__[x__] := y__:\012  end do:\012 f__:\012 end proc:\012ImageDir := (f_,x_) -&gt; f_[x_]:\012ImageRec := (f_,y_) -&gt; SearchAllInTable(y_,f_):\012Inverse := proc(f_,E_,F_) local invf__,y__:\012 invf__ := table([ ]):\012 for y__ in F_ do invf__[y__] := ImageRec(f_,y__) end do:\012 invf__:\012 end proc:\012PrintTable := f_ -&gt; [seq( [x__,f_[x__]], x__ in Indices(f_) )]:\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;:                                                                       \012nw_display   := G_  -&gt; plots[display](G_):\012nw_point     := proc(M_,AT_)  local G1__,G2__: \012 G1__ := plots[pointplot](M_,symbol=AT_[4],color=AT_[1]):\012 if type(AT_[3],list) then G2__ := plots[textplot]([M_[1],M_[2],'typeset'(op(AT_[2]))],color=AT_[1],align=AT_[3],font=[TIMES,roman,9])\012                      else G2__ := NULL\012                      end if:\012 plots[display]([ G1__,G2__ ]):\012 end proc:\012nw_text     := proc(M_,AT_) \012 if AT_[3]='nul' then plots[textplot]([M_[1],M_[2],'typeset'(op(AT_[2]))],color=AT_[1],font=[TIMES,AT_[4][1],AT_[4][2]])\012                 else plots[textplot]([M_[1],M_[2],'typeset'(op(AT_[2]))],color=AT_[1],font=[TIMES,AT_[4][1],AT_[4][2]],align=AT_[3])\012                 end if:\012 end proc:\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_ellipse   := (Cab_,AT_,boo_) -&gt; \012 plots[display](plottools[ellipse](V2L(Cab_[1]),Cab_[2],Cab_[3],color=AT_[1],transparency=AT_[2],linestyle=AT_[3],thickness=AT_[4],filled=boo_)):\012nw_arrow     := (MV_,AT_) -&gt; \012 plots[display](plots[arrow](MV_[1],[MV_[2]],shape=arrow,color=AT_[1],head_length=AT_[2],head_width=AT_[3],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_,filled_:=false,y_:=NULL) \012 if filled_ then \012  plots[display](plot(\012   F_[1](x__,y_), x__=I2R(F_[2]),\012   linestyle=AT_[3],thickness=AT_[4],labels=[x,y],discont=false,filled=[color=AT_[1],transparency=AT_[2]]))\012 else\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 if:\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[display](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:\012nw_implicit := proc(F_,AT_,filled_:=0,t_:=NULL)\012 if filled_=0 then \012  plots[display](plots[implicitplot](\012   F_[1](x__,y__,t_)=0,x__=I2R(F_[2][1]),y__=F_[2][2][1](x__)..F_[2][2][2](x__),\012   color=AT_[1],gridrefine=AT_[2],linestyle=AT_[3],thickness=AT_[4]))\012 else if filled_=1 then\012  plots[display](plots[implicitplot](\012   F_[1](x__,y__,t_)=0,x__=I2R(F_[2][1]),y__=F_[2][2][1](x__)..F_[2][2][2](x__),\012   coloring=AT_[1],gridrefine=AT_[2],grid=AT_[3],transparency=AT_[4],\012   filledregions))\012 else if filled_=2 then\012  plots[display](plots[implicitplot](\012   F_[1](x__,y__,t_)&lt;=0,x__=I2R(F_[2][1]),y__=F_[2][2][1](x__)..F_[2][2][2](x__),\012   coloring=AT_[1],gridrefine=AT_[2],grid=AT_[3],transparency=AT_[4],\012   filledregions))\012 end if end if end if:\012 end proc:\012nw_inequal := proc(F_,AT_,boo_:=true,t_:=NULL)\012 if boo_ then \012  plots[display](plots[inequal](\012   F_[1](x__,y__,t_),x__=I2R(F_[2][1]),y__=I2R(F_[2][2]),\012   'optionsfeasible'=[seq( [color=AT_[1][1][k__],transparency=AT_[1][2]], k__=1..nops(AT_[1][1]) )],\012   'optionsexcluded'=[color=AT_[2][1],transparency=AT_[2][2]],\012   'optionsclosed'=[color=AT_[3][1],thickness=AT_[3][2]],\012   'optionsimplicit'=[gridrefine=AT_[4]] ))\012 else\012  plots[display](plots[inequal](\012   F_[1](x__,y__,t_),x__=I2R(F_[2][1]),y__=I2R(F_[2][2]),\012   'optionsfeasible'=[seq( [color=AT_[1][1][k__],transparency=AT_[1][2]], k__=1..nops(AT_[1][1]) )],\012   'optionsexcluded'=[color=AT_[2][1],transparency=AT_[2][2]],\012   'optionsclosed'=[color=AT_[3][1],thickness=AT_[3][2]],\012   'optionsimplicit'=[gridrefine=AT_[4]],\012   'nolines' ))\012 end if:\012 end proc:\012\012                                                                                                            \012NWC_curvcar  := proc(FF_,AT_,filled_:=false,y_:=NULL) \012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_curvcar([FF_[1][k__],FF_[2]],AT_[k__],filled_,y_) , k__=1..nops(FF_[1]) ) ])\012  else plots[display]([ seq( nw_curvcar([FF_[1][k__],FF_[2]],AT_,filled_,y_)      , k__=1..nops(FF_[1]) ) ])\012  end if:\012 end proc:\012NWD_curvcar  := proc(FF_,AT_,filled_:=false,y_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_curvcar([FF_[1],FF_[2][k__]],AT_[k__],filled_,y_) , k__=1..nops(FF_[2]) ) ])\012  else plots[display]([ seq( nw_curvcar([FF_[1],FF_[2][k__]],AT_,filled_,y_)      , k__=1..nops(FF_[2]) ) ])\012  end if:\012 end proc:\012NWE_curvcar := proc(FF_,AT_,filled_:=false,y_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_curvcar(FF_[k__],AT_[k__],filled_,y_) , k__=1..nops(FF_) ) ])\012  else plots[display]([ seq( nw_curvcar(FF_[k__],AT_,filled_,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_disk := proc(CrCr_,AT_)  \012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_disk(CrCr_[k__],AT_[k__]),k__=1..nops(CrCr_) ) ])\012  else plots[display]([ seq( nw_disk(CrCr_[k__],AT_)     ,k__=1..nops(CrCr_) ) ])\012  end if:\012 end proc:\012NW_circle := proc(CrCr_,AT_)  \012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_circle(CrCr_[k__],AT_[k__]),k__=1..nops(CrCr_) ) ])\012  else plots[display]([ seq( nw_circle(CrCr_[k__],AT_)     ,k__=1..nops(CrCr_) ) ])\012  end if:\012 end proc:\012NW_rectangle := proc(MNMN_,AT_)  \012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_rectangle(MNMN_[k__],AT_[k__]),k__=1..nops(MNMN_) ) ])\012  else plots[display]([ seq( nw_rectangle(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:\012NWC_implicit := proc(FF_,AT_,filled_,t_:=NULL)  \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_implicit([FF_[1][k__],FF_[2]],AT_[k__],filled_,t_) , k__=1..nops(FF_[1]) ) ])\012  else plots[display]([ seq( nw_implicit([FF_[1][k__],FF_[2]],AT_,filled_,t_)      , k__=1..nops(FF_[1]) ) ])\012  end if:\012 end proc:\012NWE_implicit := proc(FF_,AT_,filled_,t_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_implicit(FF_[k__],AT_[k__],filled_,t_) , k__=1..nops(FF_) ) ])\012  else plots[display]([ seq( nw_implicit(FF_[k__],AT_,filled_,t_)      , k__=1..nops(FF_) ) ])\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:\012nw_implicit3d := proc(F_,AT_,t_:=NULL)\012 plots[implicitplot3d](\012   F_[1](x__,y__,z__,t_),x__=I2R(F_[2][1]),y__=I2R(F_[2][2]),z__=I2R(F_[2][3]),\012   color=AT_[1],transparency=AT_[2],style=AT_[3],grid=AT_[4],labels=[&quot;&quot;,&quot;&quot;,&quot;&quot;]):\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                                                                                                            \012NWC_curvpar3d := proc(FF_,AT_,v_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_curvpar3d([FF_[1][k__],FF_[2]],AT_[k__],v_) , k__=1..nops(FF_[1]) ) ])\012  else plots[display]([ seq( nw_curvpar3d([FF_[1][k__],FF_[2]],AT_,v_)      , k__=1..nops(FF_[1]) ) ])\012  end if:\012 end proc:\012NWD_curvpar3d := proc(FF_,AT_,v_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_curvpar3d([FF_[1],FF_[2][k__]],AT_[k__],v_) , k__=1..nops(FF_[2]) ) ])\012  else plots[display]([ seq( nw_curvpar3d([FF_[1],FF_[2][k__]],AT_,v_)      , k__=1..nops(FF_[2]) ) ])\012  end if:\012 end proc:\012NWE_curvpar3d := proc(FF_,AT_,v_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_curvpar3d(FF_[k__],AT_[k__],v_) , k__=1..nops(FF_) ) ])\012  else plots[display]([ seq( nw_curvpar3d(FF_[k__],AT_,v_)      , k__=1..nops(FF_) ) ])\012  end if:\012 end proc:\012NW_arrow3d := proc(MVV_,AT_)  \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_arrow3d([MVV_[1],MVV_[2][k__]],AT_[k__]),k__=1..nops(MVV_[2]) ) ])\012  else plots[display]([ seq( nw_arrow3d([MVV_[1],MVV_[2][k__]],AT_)     ,k__=1..nops(MVV_[2]) ) ])\012  end if:\012 end proc:\012NWD_arrow3d := NW_arrow3d:\012NWE_arrow3d := proc(MVMV_,AT_) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_arrow3d(MVMV_[k__],AT_[k__]),k__=1..nops(MVMV_) ) ])\012  else plots[display]([ seq( nw_arrow3d(MVMV_[k__],AT_)     ,k__=1..nops(MVMV_) ) ])\012  end if:\012 end proc:\012NW_point3d  := proc(MM_,AT_)  \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_point3d(MM_[k__],AT_[k__]),k__=1..nops(MM_) ) ])\012  else plots[display]([ seq( nw_point3d(MM_[k__],AT_)     ,k__=1..nops(MM_) ) ])\012  end if:\012 end proc:\012NW_line3d   := proc(MMNN_,AT_)\012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_line3d([MMNN_[1][k__],MMNN_[2][k__]],AT_[k__]),k__=1..nops(MMNN_[1]) ) ])\012  else plots[display]([ seq( nw_line3d([MMNN_[1][k__],MMNN_[2][k__]],AT_)     ,k__=1..nops(MMNN_[1]) ) ])\012  end if:\012 end proc:\012NWD_line3d  := proc(MNN_,AT_)\012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_line3d([MNN_[1],MNN_[2][k__]],AT_[k__]),k__=1..nops(MNN_[2]) ) ])\012  else plots[display]([ seq( nw_line3d([MNN_[1],MNN_[2][k__]],AT_)     ,k__=1..nops(MNN_[2]) ) ])\012  end if:\012 end proc:\012NWE_line3d  := proc(MNMN_,AT_)\012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_line3d(MNMN_[k__],AT_[k__]),k__=1..nops(MNMN_) ) ])\012  else plots[display]([ seq( nw_line3d(MNMN_[k__],AT_)     ,k__=1..nops(MNMN_) ) ])\012  end if:\012 end proc:\012NW_polygon3d   := (MMMM_,AT_) -&gt;  \012 plots[display]([seq( nw_polygon3d(MMMM_[k__],AT_),k__=1..nops(MMMM_))]):\012NWC_implicit3d := proc(FF_,AT_,t_:=NULL)  \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_implicit3d([FF_[1][k__],FF_[2]],AT_[k__],t_) , k__=1..nops(FF_[1]) ) ])\012  else plots[display]([ seq( nw_implicit3d([FF_[1][k__],FF_[2]],AT_,t_)      , k__=1..nops(FF_[1]) ) ])\012  end if:\012 end proc:\012NWE_implicit3d := proc(FF_,AT_,t_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_implicit3d(FF_[k__],AT_[k__],t_) , k__=1..nops(FF_) ) ])\012  else plots[display]([ seq( nw_implicit3d(FF_[k__],AT_,t_)      , k__=1..nops(FF_) ) ])\012  end if:\012 end proc:\012\012                                                                                                            \012\012FAUNE := proc() local img:\012 img := Read(cat(savelibname,&quot;\134\134faune.jpg&quot;)):\012 img := GetSubImage(img,1,1,4300,3672):\012 img := Scale(img,0.1):\012 img := Preview(img):\012 end proc:\012\012end module:                                                                                                                                              \012                                                                                                            \012######################################################### ALGLIN ###################################################################\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######################################################## 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###################################################### GEOMETRIE #################################################################\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#################################################### PROBCOMB###################################################################\012\012ProbComb := module()                                                                                      \012\012  uses     plots, LinearAlgebra, StringTools, ListTools,\012           AnimationII, AlgLin, Analyse, Geometrie; \012  export   OPT0,\012           last, l2l1, l1l2, L2L1, L1L2, ll2t, swq, repeat, RepeatName, nr2v, v2nr, b2p, rot45, invrot45, \012           DisplayP, DisplayW, PrintP, PrintW, PrintF, PrintI,\012           Succ, Pred, nodeT, NodeT, nodeP, NodeP, Node, blade, biss, \012           rule_null, Range, Rule, ModifyBF, Name, \012           Prob, Vertices, Universe, Joker, Event, ProbEvent,\012           DisplayEventProb, DisplayEventSet, PrintEventProb, PrintEventSet,\012           Data1, Data2, Data3, Data, EventData1, EventData2, EventData3, EventData,\012           EmptyTree, Tree, UnivTree, EventTree, HighLight, HighLightSubTree,\012           PathNode, PathData1, PathData2, PathData3, PathData, EventPathData, UnivPath, EventPath,\012           EventWalk;\012  local    paragraphe;\012option package;\012\012                                                                                                          \012                                                                                                          \012OPT0 := table([ &quot;ij&quot; = [1,8], &quot;eps&quot; = 0.1, &quot;hs&quot; = 1.5, &quot;vs&quot; = 2, &quot;br&quot; = 3, &quot;mo&quot; = &quot;T&quot; ]):\012                                                                                                          \012\012last := L_ -&gt; L_[nops(L_)]:\012l1l2 := L_ -&gt; [seq( [L_[1][k__],L_[2][k__]], k__=1..nops(L_[1])) ]:\012l2l1 := L_ -&gt; [ [seq(L_[k__][1], k__=1..nops(L_))] , [seq(L_[k__][2], k__=1..nops(L_))] ]:\012L2L1 := LL_ -&gt; [ [seq([seq(LL_[n__][r__][1],r__=1..nops(LL_[n__]))],n__=1..nops(LL_))], \012                 [seq([seq(LL_[n__][r__][2],r__=1..nops(LL_[n__]))],n__=1..nops(LL_))] ]:\012L1L2 := LL_ -&gt; [seq( [seq([LL_[1][n__][r__],LL_[2][n__][r__]],r__=1..nops(LL_[n__]))], n__=1..nops(LL_) )]:\012ll2t := (LL_,br_) -&gt; ListTools[Flatten]([seq([op(LL_[k__]),br_],k__=1..nops(LL_)-1),last(LL_)]):\012swq := s__ -&gt; parse(convert(s__,string)):\012repeat := (n_,b_) -&gt; [seq(b_,k__=1..n_)]:\012RepeatName := proc(bb_,ww_) local k__,ww__:\012 ww__ := []:\012 for k__ from 1 to nops(ww_) do\012  if bb_[k__]=1 then ww__ := [op(ww__),ww_[k__]]\012                else ww__ := [op(ww__),seq(ww_[k__][l__],l__=1..bb_[k__])]\012                end if:\012  end do:\012 ww__:\012 end proc:\012nr2v := proc(nr_,B_) local q__,v__,n__:\012 q__ := nr_[2]-1: \012 v__ := []:\012 n__ := nr_[1]:\012 while q__&lt;&gt;0 do\012  v__ := [op(v__),irem(q__,B_[n__])]: \012  q__ := iquo(q__,B_[n__]): \012  n__ := n__-1:\012  end do:\012 v__ := map(x__-&gt;x__+1,v__):\012 v__ := ListTools[Reverse](v__):\012 if nr_=[0,0] then [1] else [seq(1,k__=1..nr_[1]-nops(v__)),op(v__)] end if:\012 end proc:\012v2nr := proc(v_,B_,n_:=nops(v_)) local b__,r__,k__:\012 b__ := 1: \012 r__ := 0:\012 for k__ from n_ to 2 by -1 do\012  r__ := r__ + (v_[k__]-1)*b__:\012  b__ := b__*B_[k__]:\012  end do:\012 r__ := r__ + (v_[1]-1)*b__:\012 [n_,r__+1]:\012 end proc:\012b2p := proc(bb_) local i__,s__,p__:\012 s__ := add(bb_[i__], i__=1..nops(bb_)):\012 [seq( [bb_[i__],s__], i__=1..nops(bb_) )]:\012 end proc:\012rot45 := M_ -&gt; [(M_[1]-M_[2])/2,(M_[1]+M_[2])/2]:\012invrot45 := m_ -&gt; [m_[1]+m_[2],-m_[1]+m_[2]]:\012DisplayP := proc(p_,plab_) local p__:\012 if       plab_ = 'cb' then p__ := [p_[1]]:\012  else if plab_ = 'pr' then p__ := [p_[1],&quot;/&quot;,p_[2]]:\012  else if plab_ = 'sq' then p__ := [p_]:\012  else if plab_ = 'op' then p__ := p_:\012  else                      p__ := [p_]:\012  end if end if end if end if:\012 p__:\012 end proc:\012DisplayW := proc(v_,B_,WW_,vlab_) local k__,w__,nr__:\012 if vlab_ = 'cc' \012  then w__ := &quot;&quot;:\012       for k__ from 1 to nops(v_) do \012        nr__ := v2nr(v_,B_,k__):\012        w__ := [op(w__),WW_[nr__[1]][nr__[2]]] end do:\012  else if vlab_ = 'la' \012   then nr__ := v2nr(v_,B_):\012        w__ := [WW_[nr__[1]][nr__[2]]]:\012  else if vlab_ = 'sq' \012   then w__ := []:\012        for k__ from 1 to nops(v_) do \012        nr__ := v2nr(v_,B_,k__):\012        w__ := [op(w__),WW_[nr__[1]][nr__[2]]] end do: \012        w__ := [w__]: \012  else  if vlab_ = 'op'\012   then nr__ := v2nr(v_,B_):\012        w__ := WW_[nr__[1]][nr__[2]]:\012  else  w__ := [v_]:\012  end if end if end if end if:\012 w__:\012 end proc:\012PrintP := proc(p_,plab_) local p__:\012 if       plab_ = 'cb' then p__ := [p_[1]]:\012  else if plab_ = 'pr' then p__ := cat(p_[1],&quot;/&quot;,p_[2]):\012  else if plab_ = 'sq' then p__ := [p_]:\012  else if plab_ = 'op' then p__ := p_:\012  else                      p__ := [p_]:\012  end if end if end if end if:\012 p__:\012 end proc:\012PrintW := proc(v_,B_,WW_,vlab_) local k__,w__,nr__:\012 if vlab_ = 'cc' \012  then w__ := &quot;&quot;:\012       for k__ from 1 to nops(v_) do \012        nr__ := v2nr(v_,B_,k__):\012        w__ := cat(op(w__),WW_[nr__[1]][nr__[2]]) \012        end do:\012  else if vlab_ = 'la' \012   then nr__ := v2nr(v_,B_):\012        w__ := [swq(WW_[nr__[1]][nr__[2]])]:\012  else if vlab_ = 'sq' \012   then w__ := []:\012        for k__ from 1 to nops(v_) do \012         nr__ := v2nr(v_,B_,k__):\012         w__ := [op(w__),swq(WW_[nr__[1]][nr__[2]])] \012         end do: \012        w__ := [w__]: \012  else  if vlab_ = 'op'\012   then nr__ := v2nr(v_,B_):\012        w__ := cat(op(WW_[nr__[1]][nr__[2]])):\012  else  w__ := [v_]:\012  end if end if end if end if:\012 w__:\012 end proc:\012PrintI := x_ -&gt; InertForm[Display](InertForm[Parse](x_),inert=false):\012PrintF := proc(x_,vis_)\012 if vis_ = 'no' then &quot;&quot; else x_ end if:\012 end proc:\012Succ  := proc(nr_,B_) local n__,r__:\012 n__ := nr_[1]: r__ := nr_[2]:\012 [n__+1,[(r__-1)*B_[n__+1]+1,r__*B_[n__+1]]]:\012 end proc:\012Pred  := proc(nr_,B_) local n__,r__:\012 n__ := nr_[1]: r__ := nr_[2]:\012 if n__&gt;1 then [n__-1,floor((r__-1)/B_[n__])+1] else [0,0] end if:\012 end proc:\012nodeT := (o_,ij_,b_,l_) -&gt; [o_[1]+ij_[1],o_[2]+ij_[2]*(l_-(b_+1)/2)]:\012NodeT := proc(B_,o_,OPT_:=OPT0) local n__,k__,r__,ij__,B__,O__,OO__: \012 B__ := 1: \012 ij__ := OPT_[&quot;ij&quot;]:\012\012 OO__ := [[o_]]: \012 for n__ from 1 to nops(B_) do\012  ij__ := [ij__[1],ij__[2]/B_[n__]]:\012  O__ := []: \012  for r__ from 1 to B__ do\012   for k__ from 1 to B_[n__] do\012    O__ := [op(O__),nodeT(OO__[n__][r__],ij__,B_[n__],k__)]\012    end do \012   end do:\012  B__ := B__*B_[n__]: \012  OO__ := [op(OO__),O__]:\012  end do:\012\012 OO__:\012 end proc:\012nodeP := (o_,ij_,b_,l_) -&gt; [o_[1]+ij_[1],o_[2]+ij_[2]*(-1)^l_]:\012NodeP := proc(B_,o_,OPT_:=OPT0) local n__,k__,r__,ij__,B__,O__,OO__:\012 ij__ := OPT_[&quot;ij&quot;]:\012 B__ := 1: \012 \012 OO__ := [[o_]]: \012 for n__ from 1 to nops(B_) do\012  O__ := []: \012  for r__ from 1 to B__ do\012   for k__ from 1 to B_[n__] do\012    O__ := [op(O__),nodeP(OO__[n__][r__],ij__,B_[n__],k__)]\012    end do \012   end do:\012  B__ := B__*B_[n__]: \012  OO__ := [op(OO__),O__]:\012  end do:\012\012 OO__:\012 end proc:\012Node :=  proc(B_,o_,OPT_:=OPT0) local mode__:\012 mode__ := OPT_[&quot;mo&quot;]:\012 if       mode__ = &quot;T&quot; then NodeT(B_,o_,OPT_) \012  else if mode__ = &quot;P&quot; then NodeP(B_,o_,OPT_)\012  end if end if:\012 end proc:\012blade := proc(o1_,o2_,t_,p_,w_,e_,at_,JOK_,OPT_:=OPT0) local w__,t__,o__,p__, col__, sty__,fss__, \012                                                             pt__i, pt__a, pt__g, dk__i, dk__a,dk__g,\012                                                             aw__i,aw__a,aw__g, tx__i,tx__a,tx__g:\012 col__ := at_[1]: sty__ := at_[2]: fss__ := at_[3]:\012 if evalb(w_ in JOK_) then sty__ := ['dot',sty__[2],sty__[3]]:\012                           w__ := &quot;&quot;:\012                      else w__ := w_:\012                      end if:\012 o__   := (1-t_)*o1_+t_*o2_:\012 pt__i := o2_:\012 pt__a := [col__[1],w__,sty__[3],fss__[1]]: \012 pt__g := nw_text(pt__i,pt__a):\012 aw__a := [col__[2],'nul',sty__[1],sty__[2]]:\012 aw__i := [o1_,o2_]:\012 aw__g := nw_line(aw__i,aw__a):\012 tx__i := [o__[1],o__[2]+e_]:\012 tx__a := [col__[3],p_,'nul',fss__[2]]:\012 tx__g := nw_text(tx__i,tx__a):\012\012 display([pt__g,aw__g,tx__g], axes=none, scaling=constrained):\012 end proc:\012biss := proc(n_,o_,at_,OPT_) local ij__,col__,sty__,biss__i,biss__a,biss__g:\012 ij__ := OPT_[&quot;ij&quot;]:\012 col__ := at_[1]: sty__ := at_[2]:\012 biss__i := [o_,[o_[1]+(n_+1)*ij__[1],o_[2]]]:\012 biss__a := [col__[2],'nul',sty__[1],sty__[2]]:\012 biss__g := nw_line(biss__i,biss__a):\012 display(biss__g):\012 end proc:\012                                                                                                          \012rule_null := (BF_,n_,bb_,i_) -&gt; [seq( 0,k__=1..nops(BF_[n_](bb_,i_)) )]:\012Range := proc(XF_) local bb__,n__,B__:\012 bb__ := XF_[1]:\012 B__ := [nops(bb__)]:\012 for n__ from 2 to nops(XF_) do \012  bb__ := XF_[n__](bb__,1):\012  B__ := [op(B__),nops(bb__)]:\012  end do:\012 B__:\012 end proc:\012Rule := proc(BF_,X_:=NULL) local n__,r__,i__,b__,bb__,BB__,Bb__:\012 bb__ := BF_[1]:\012 BB__ := [[bb__]]: \012 for n__ from 1 to nops(BF_)-1 do\012  Bb__ := []: \012  for r__ from 1 to nops(BB__[n__]) do\012   bb__ := BB__[n__][r__]:\012   for i__ from 1 to nops(bb__) do\012    if bb__[i__]=0 then b__ := rule_null(BF_,n__,bb__,i__)\012                   else b__ := BF_[n__+1](bb__,i__,X_)\012                   end if:\012    Bb__ := [op(Bb__),b__]:\012    end do end do:\012  BB__ := [op(BB__),Bb__]:\012  end do:\012\012 BB__:\012 end proc:\012ModifyBF := proc(var_,max_,BF1_,BF2_) local n__,k__,BF__:\012 n__ := nops(var_):\012 BF__ := BF1_:\012 for k__ from 1 to n__ do\012  if var_[k__]&lt;=max_[k__] then BF__[k__] := BF2_[k__] end if:\012  end do:\012 BF__:\012 end proc:\012                                                                                                          \012Name := proc(WF_,X_:=NULL) local n__,r__,i__,w__,ww__,WW__,Ww__:\012 ww__ := WF_[1]:\012 WW__ := [[ww__]]: \012 for n__ from 1 to nops(WF_)-1 do\012  Ww__ := []: \012  for r__ from 1 to nops(WW__[n__]) do\012   ww__ := WW__[n__][r__]:\012   for i__ from 1 to nops(ww__) do\012    w__ := WF_[n__+1](ww__,i__,X_):\012    Ww__ := [op(Ww__),w__]:\012    end do end do:\012  WW__ := [op(WW__),Ww__]:\012  end do:\012\012 [seq( [seq(op(WW__[n__][k__]),k__=1..nops(WW__[n__]))], n__=1..nops(WW__))]:\012 end proc:\012                                                                                                          \012                                                                                                          \012Prob := proc(BB_) local n__,r__,bb__,P__,PP__:\012 PP__ := []: \012 for n__ from 1 to nops(BB_) do\012  P__ := []:\012  for r__ from 1 to nops(BB_[n__]) do\012   bb__ := BB_[n__][r__]:\012   P__ := [op(P__),op(b2p(bb__))]:\012   end do:\012  PP__ := [op(PP__),P__]:\012  end do:\012\012 PP__:\012 end proc:\012Universe := proc(B_,PP_) local n__,r__,p__,v__,k__,l__,m__,nr__,vp__,VP__,VPk__,UU__:\012 n__ := nops(PP_): \012\012 VP__ := [seq([],k__=1..n__)]:\012 for r__ from 1 to nops(PP_[n__]) do\012  nr__ := [n__,r__]: \012  p__ := [1,1]: \012  while (nr__[1]&gt;=1 and PP_[nr__[1]][nr__[2]][1]=0) do \012   nr__ := Pred(nr__,B_):\012   end do:\012  v__ := nr2v(nr__,B_):\012  while nr__[1]&gt;=1 do \012   p__ := [p__[1]*PP_[nr__[1]][nr__[2]][1],p__[2]*PP_[nr__[1]][nr__[2]][2]]:\012   nr__ := Pred(nr__,B_):\012   end do:\012  VP__[nops(v__)] := [op(VP__[nops(v__)]),[v__,p__]]:\012  end do:\012 VP__ := [seq( ListTools[MakeUnique](VP__[k__]), k__=1..nops(VP__) )]:\012\012 UU__ := []:\012 for k__ from 1 to nops(VP__)-1 do\012  for vp__ in VP__[k__] do\012   m__ := 1:\012   VPk__ := VP__[k__+1]:\012   while (m__&lt;=nops(VPk__) and vp__[1]&lt;&gt;VPk__[m__][1][1..k__]) do m__ := m__+1 end do:\012   if m__&gt;nops(VPk__) then UU__ := [op(UU__),vp__] end if:\012   end do:\012  end do:\012 UU__ := [op(UU__),op(last(VP__))]:\012\012 UU__:\012 end proc:\012Joker := proc(B_,UU_,WW_,JOK_,OPT_:=OPT0) local n__,k__,m__,v__,p__,vp__,nr__,UUN__,UUJ__,\012                                                vv__,JJ__,JJN__,JJJ__,JJJ1__,JJJ2__,JJJJ__:\012 UUN__ := []: UUJ__ := []:\012 for k__ from 1 to nops(UU_) do\012  vp__ := UU_[k__]: v__ := vp__[1]: p__ := vp__[2]:\012  m__ := 1: \012  nr__ := v2nr(v__,B_,m__):\012  while evalb(m__&lt;=nops(v__) and not(WW_[nr__[1]][nr__[2]] in JOK_)) do \012   m__ := m__+1:\012   if m__&lt;=nops(v__) then nr__ := v2nr(v__,B_,m__) end if:\012   end do:\012  if m__&lt;=nops(v__) \012   then v__ := [seq(v__[k__],k__=1..m__-1),v__[m__]]:\012        UUJ__ := [op(UUJ__),[v__,p__]]:\012   else UUN__ := [op(UUN__),vp__]\012   end if:\012  end do:\012 JJ__ := [UUN__,UUJ__]:\012\012 JJN__ := JJ__[1]: JJJ__ := l2l1(JJ__[2]):  \012 JJJ1__ := JJJ__[1]: JJJ2__ := JJJ__[2]: JJJJ__ := []:\012 while nops(JJJ1__)&gt;0 do\012  v__ := JJJ1__[1]:\012  vv__ := ListTools[Reverse]([ListTools[SearchAll](v__,JJJ1__)]):\012  p__ := add(JJJ2__[k__],k__ in vv__):\012  JJJJ__ := [op(JJJJ__),[v__,p__]]:\012  for k__ from 1 to nops(vv__) do \012   JJJ1__ := subsop(vv__[k__]=NULL,JJJ1__):\012   JJJ2__ := subsop(vv__[k__]=NULL,JJJ2__):\012   end do:\012  end do:\012\012 [op(JJN__),op(JJJJ__)]:\012 end proc:\012Vertices := proc(JJ_) local n__,v__,k__,V__,VV__:\012 V__ := l2l1(JJ_)[1]: \012 n__ := max(seq(nops(V__[k__]),k__=1..nops(V__))):\012\012 VV__ := [seq([],k__=1..n__)]:\012 for v__ in V__ do \012  VV__[nops(v__)] := [op(VV__[nops(v__)]),v__]:\012  end do:\012 for k__ from 1 to nops(VV__) do\012  VV__[k__] := [op(VV__[k__]),seq( v__[1..k__],v__ in last(VV__) )]:\012  end do:\012\012 [seq( ListTools[MakeUnique](VV__[k__]), k__ = 1..nops(VV__) )]:\012 end proc:\012Event := proc(B_,UU_,EVENTRULE_,eventrule_,BB_,WW_,log_:=&quot;&quot;) local k__,v__,p__,boo__,EP__:\012 EP__ := []:\012 for k__ from 1 to nops(UU_) do\012  v__ := UU_[k__][1]: p__ := UU_[k__][2]:\012  if log_ = &quot;&quot; then boo__ := eventrule_(v__,EVENTRULE_,B_,BB_,WW_)\012               else boo__ := eventrule_(v__,EVENTRULE_,B_,BB_,WW_,log_) \012               end if:\012  if boo__ then EP__ := [op(EP__),[v__,p__]] end if:\012  end do:\012 EP__:\012 end proc:\012DisplayEventProb := proc(EE_,plab_) \012 [seq( DisplayP(e__[2],plab_), e__ in EE_ )]:\012 end proc:\012DisplayEventSet := proc(B_,EE_,WW_,vlab_) \012 [seq( DisplayW(e__[1],B_,WW_,vlab_), e__ in EE_ )]:\012 end proc:\012PrintEventProb := proc(EE_,plab_) \012 [seq( PrintP(e__[2],plab_), e__ in EE_ )]:\012 end proc:\012PrintEventSet := proc(B_,EE_,WW_,vlab_) \012 [seq( PrintW(e__[1],B_,WW_,vlab_), e__ in EE_ )]:\012 end proc:\012ProbEvent := proc(EE_,plab_) local e__,p__,p___:\012 p__ := 0:\012 for e__ in EE_ do\012  p___ := e__[2]:\012  if       plab_ = 'cb' then p__ := p__ + p___[1]\012   else if plab_ = 'pr' then p__ := p__ + p___[1]/p___[2]\012   else                       p__ := p__\012   end if end if:\012  end do:\012 p__:\012 end proc:\012                                                                                                          \012Data1 := proc(B_,JJ_,PP_,OO_,WW_,prt_,OPT_:=OPT0) local b__,o__,v__,n__,r1__,r2__,r20__,o1__,o2__,t__,w__,p__,e__,\012                                                        ij__,eps__,ww__,nr1__,nr2__,OO__,DT__,VV__,PP__:\012 eps__ := OPT_[&quot;eps&quot;]:\012\012 VV__ := Vertices(JJ_): \012 o__  := OO_[1][1]: OO__ := OO_[2..nops(OO_)]: \012\012 DT__ := [seq([],k__=1..nops(VV__))]:\012 if nops(VV__)&gt;0 then\012  b__ := B_[1]:\012  for v__ in VV__[1] do\012   nr2__ := v2nr(v__,B_,1):\012   r2__  := nr2__[2]:\012   o1__  := o__:\012   o2__  := OO__[1][r2__]:\012   t__   := 1/2:\012   w__   := WW_[nr2__[1]][nr2__[2]]: w__ := DisplayW(v__,B_,WW_,prt_[2]):\012   p__   := PP_[1][r2__]: p__ := DisplayP(p__,prt_[1]):\012   e__   := signum(r2__-1-(b__-1)/2)*eps__:\012   DT__[1] := [op(DT__[1]),[o1__,o2__,t__,p__,w__,e__]]:\012   end do:\012  end if:\012\012 for n__ from 2 to nops(VV__) do\012  b__ := b__*B_[n__]:\012  for v__ in VV__[n__] do\012   nr1__ := v2nr(v__,B_,n__-1):\012   nr2__ := v2nr(v__,B_,n__):\012   r1__  := nr1__[2]:\012   r2__  := nr2__[2]:\012   o1__  := OO__[n__-1][r1__]:\012   o2__  := OO__[n__][r2__]:\012   t__   := 1/2:\012   w__   := WW_[nr2__[1]][nr2__[2]]: w__ := DisplayW(v__,B_,WW_,prt_[2]):\012   p__   := PP_[n__][r2__]: p__ := DisplayP(p__,prt_[1]):\012   r20__ := Succ([n__-1,r1__],B_)[2][1]:\012   e__   := signum(r2__-r20__-(B_[n__]-1)/2)*eps__/b__:\012   DT__[n__] := [op(DT__[n__]),[o1__,o2__,t__,p__,w__,e__]]:\012   end do \012  end do:\012\012 [seq( op(DT__[k__]), k__ = 1..nops(DT__) )]:\012 end proc:\012Data2 := proc(B_,JJ_,OO_,WW_,pw_,prt_,OPT_:=OPT0) local k__,n__,nr__,o1__,o2__,t__,w__,p__,e__,vp__,pw__,\012                                                        ij__,hs__,OO__,P__,W__,DT__:\012 ij__ := OPT_[&quot;ij&quot;]: hs__ := OPT_[&quot;hs&quot;]:\012 \012 pw__ := l2l1(JJ_):\012 P__ := pw_[1]:  W__ := pw_[2]:\012 if P__ = [] then P__ := DisplayEventProb(JJ_,prt_[1]) end if:\012 if W__ = [] then W__ := DisplayEventSet(B_,JJ_,WW_,prt_[2]) end if:\012 \012 OO__ := OO_[2..nops(OO_)]: n__ := nops(OO__):\012\012 DT__ := []:\012 for k__ from 1 to nops(JJ_) do\012  vp__ := JJ_[k__]:\012  nr__ := v2nr(vp__[1],B_):\012  o1__ := OO__[nr__[1]][nr__[2]]:\012  o2__ := [o1__[1]+(n__-nr__[1])*ij__[1]+hs__*ij__[1],o1__[2]]:\012  t__  := 1-hs__/(2*(n__-nr__[1]+hs__)):\012  w__  := W__[k__]:\012  p__  := P__[k__]:\012  e__  := 0:\012  DT__ := [op(DT__),[o1__,o2__,t__,p__,w__,e__]]:\012  end do:\012 \012 DT__:\012 end proc:\012Data3 := proc(B_,OO_,pw_,prt_,OPT_:=OPT0) local k__,n__,y__,o__,o1__,o2__,t__,w__,p__,e__,\012                                               ij__,hs__,vs__,B__,P__,W__,OO__,DT__:\012 ij__ := OPT_[&quot;ij&quot;]: hs__ := OPT_[&quot;hs&quot;]: vs__ := OPT_[&quot;vs&quot;]: \012 n__ := nops(B_): B__ := mul(B_[k__],k__=1..n__):\012\012 P__ := pw_[1]: W__ := pw_[2]:\012 if evalb(P__ =  [] and W__ &lt;&gt; []) then P__ := [seq(&quot;&quot;,k__=1..nops(B_)+1)] end if:\012 if evalb(P__ &lt;&gt; [] and W__ =  []) then W__ := [seq(&quot;&quot;,k__=1..nops(B_)+1)] end if:\012 if evalb(P__ =  [] and W__ =  []) then n__ := 0 end if:\012\012 o__ := OO_[1][1]:\012 y__ := o__[2]-(ij__[2]/B__)*((B__+1)/2+vs__):\012 \012 DT__ := []:\012 for k__ from 1 to n__ do\012  o1__ := [o__[1]+(k__-1)*ij__[1],y__]:\012  o2__ := [o__[1]+(k__)*ij__[1],y__]:\012  t__  := 1/2:\012  w__  := W__[k__]:\012  p__  := P__[k__]:\012  e__  := 0:\012  DT__ := [op(DT__),[o1__,o2__,t__,p__,w__,e__]]:\012  end do:\012\012 if n__&gt;0 then\012  o1__ := [o__[1]+n__*ij__[1],y__]:\012  o2__ := [o1__[1]+hs__*ij__[1],y__]:\012  t__  := 1/2:\012  w__  := W__[n__+1]:\012  p__  := P__[n__+1]:\012  e__  := 0:\012  DT__ := [op(DT__),[o1__,o2__,t__,p__,w__,e__]]:\012  end if:\012\012 DT__:\012 end proc:\012Data := proc(B_,JJ_,PP_,OO_,WW_,PW_,PRT_,Chx_,OPT_:=OPT0)\012 if       Chx_[1]=1 then Data1(B_,JJ_,PP_,OO_,WW_,              PRT_[op(Chx_)],OPT_)\012  else if Chx_[1]=2 then Data2(B_,JJ_    ,OO_,WW_,PW_[op(Chx_)],PRT_[op(Chx_)],OPT_)\012  else if Chx_[1]=3 then Data3(B_        ,OO_    ,PW_[op(Chx_)],PRT_[op(Chx_)],OPT_)\012  end if end if end if:\012 end proc:\012EventData := proc(B_,JU_,JE_,PP_,OO_,WW_,PW_,PRT_,chx_,OPT_:=OPT0) local dt__,NOD__,DTU__,DTE__:\012 DTU__ := Data(B_,JU_,PP_,OO_,WW_,PW_,PRT_,[chx_,1],OPT_):\012 NOD__ := [seq(dt__[1..2],dt__ in DTU__)]:\012 DTE__ := Data(B_,JE_,PP_,OO_,WW_,PW_,PRT_,[chx_,2],OPT_):\012 for dt__ in DTE__ do\012  if member(dt__[1..2],NOD__,'k__') then \012   DTU__ := subsop(k__=NULL,DTU__):\012   NOD__ := subsop(k__=NULL,NOD__): \012   end if:\012  end do:\012 [DTU__,DTE__]:\012 end proc:\012                                                                                                          \012EmptyTree := proc() \012 display(nw_point([0,0],[&quot;White&quot;,nul,nul,point]),axes=none):\012 end proc:\012Tree := proc(DT_,prt_,at_,JOK_,OPT_:=OPT0) local s__,dt__,A__:\012 A__ := []:\012 for s__ from 1 to nops(DT_) do\012  dt__ := DT_[s__]:\012  A__ := [op(A__),blade(dt__[1],dt__[2],dt__[3],PrintF(dt__[4],prt_[1]),PrintF(dt__[5],prt_[2]),dt__[6],at_,JOK_,OPT_)]:\012  end do:\012 if DT_ = [] then EmptyTree() else display(A__) end if:\012 end proc:\012UnivTree := proc(B_,JU_,PP_,OO_,WW_,PW_,PRT_,CHX_,AT_,JOK_,OPT_:=OPT0) local k__,chx__,T__,DT__:\012 T__ := []:\012 for k__ from 1 to nops(CHX_) do\012  chx__ := CHX_[k__]:\012  DT__  := Data(B_,JU_,PP_,OO_,WW_,PW_,PRT_,[chx__,1],OPT_):\012  T__  := [op(T__),Tree(DT__,PRT_[chx__,1],AT_[chx__,1],JOK_,OPT_)]:\012  end do:\012 display(T__):\012 end proc:\012EventTree := proc(B_,JU_,JE_,PP_,OO_,WW_,PW_,PRT_,CHX_,AT_,JOK_,OPT_:=OPT0) local k__,chx__,DT__,T__:\012 T__ := []:\012 for k__ from 1 to nops(CHX_) do\012  chx__ := CHX_[k__]:\012  DT__  := EventData(B_,JU_,JE_,PP_,OO_,WW_,PW_,PRT_,chx__,OPT_):\012  T__  := [op(T__),seq(Tree(DT__[l__],PRT_[chx__,l__],AT_[chx__,l__],JOK_,OPT_),l__=1..2)]:\012  end do:\012 display(T__):\012 end proc:\012HighLight := proc(G_,V_,B_,o_,hl_,OPT_:=OPT0) local ij__,hs__,eps__,col__,sty__,tck__,n__,nr__,r__,\012                                                    v__,o__,k__,leaf__,leaf__i,leaf__a,leaf__g,OO__: \012 ij__ := OPT_[&quot;ij&quot;]: hs__ := OPT_[&quot;hs&quot;]: eps__ := OPT_[&quot;eps&quot;]:\012 col__ := hl_[1]: sty__ := hl_[2]: tck__ := hl_[3]:\012\012 OO__ := Node(B_,o_,OPT_):\012 OO__ := OO__[2..nops(OO__)]:\012\012 leaf__i := []:\012 for v__ in V_ do\012  leaf__ := [o_,o_]:\012  for n__ from 1 to nops(v__) do\012   nr__ := v2nr(v__,B_,n__):\012   r__  := nr__[2]:\012   o__  := OO__[n__][r__]:\012   leaf__ := [op(leaf__),o__]:\012   end do:\012  leaf__i := [op(leaf__i),leaf__]:\012  end do:\012 leaf__a := [col__,'nul',sty__,tck__]:\012 leaf__g := [seq([ seq( nw_line([leaf__i[k__][l__],leaf__i[k__][l__+1]],leaf__a),l__=1..nops(leaf__i[k__])-1) ],k__=1..nops(leaf__i))];\012 leaf__g := [seq(seq( display([G_,display(leaf__g[k__][1..l__])]),l__=1..nops(leaf__g[k__])),k__=1..nops(leaf__g))];\012\012 display(leaf__g,insequence=true):\012 end proc:\012HighLightSubTree := proc(G_,V_,B_,o_,hl_,OPT_:=OPT0) local ij__,hs__,eps__,col__,sty__,tck__,n__,nr__,r__,vpq__,\012                                                           v__,p__,q__,o__,k__,leaf__,leaf__i,leaf__a,leaf__g,OO__: \012 ij__ := OPT_[&quot;ij&quot;]: hs__ := OPT_[&quot;hs&quot;]: eps__ := OPT_[&quot;eps&quot;]:\012 col__ := hl_[1]: sty__ := hl_[2]: tck__ := hl_[3]:\012\012 OO__ := Node(B_,o_,OPT_):\012 OO__ := OO__[2..nops(OO__)]:\012\012 leaf__i := []:\012 for vpq__ in V_ do\012  v__ := vpq__[1]: p__ := vpq__[2]: q__ := vpq__[3]:\012  if p__ = 0 then o__ := o_\012             else  nr__ := v2nr(v__,B_,p__):\012                   r__  := nr__[2]:\012                   o__ := OO__[p__][r__]:\012             end if:\012  leaf__ := [o__,o__]:\012  for n__ from p__+1 to q__ do\012   nr__ := v2nr(v__,B_,n__):\012   r__  := nr__[2]:\012   o__  := OO__[n__][r__]:\012   leaf__ := [op(leaf__),o__]:\012   end do:\012  leaf__i := [op(leaf__i),leaf__]:\012  end do:\012 leaf__a := [col__,'nul',sty__,tck__]:\012 leaf__g := [seq(display([ seq( nw_line([leaf__i[k__][l__],leaf__i[k__][l__+1]],leaf__a),l__=1..nops(leaf__i[k__])-1) ]),k__=1..nops(leaf__i))];\012 leaf__g := [seq(display([G_,leaf__g[k__]]),k__=1..nops(leaf__g))];\012\012 display(leaf__g,insequence=true):\012 end proc:\012                                                                                                          \012PathNode := proc(OO_) local n__,k__,o__,oo__,ooo__,O__,OO__:\012 OO__ := []:\012 for n__ from 1 to nops(OO_) do\012  O__ := OO_[n__]:\012  oo__ := ListTools[MakeUnique](O__):\012  OO__ := [op(OO__),oo__]:\012  end do:\012 OO__:\012 end proc:\012PathData1 := proc(B_,JJ_,PP_,OO_,WW_,prt_,OPT_:=OPT0) local C,k__,p__,q__,n__,pq__,DT__,OO__,WW__:\012 C := 'C':\012 DT__ := Data1(B_,JJ_,PP_,OO_,WW_,prt_,OPT_):\012 DT__ := ListTools[MakeUnique](DT__):\012 for k__ from 1 to nops(DT__) do\012  pq__ := rot45(DT__[k__][2]):\012  p__ := pq__[1]: q__ := pq__[2]: n__ := p__+q__:\012  DT__[k__][5] := [C[n__]^p__]:\012  end do:\012 DT__:\012 end proc:\012PathData2 := proc(B_,JJ_,OO_,WW_,pw_,prt_,OPT_:=OPT0) local DT__:\012 DT__ := Data2(B_,JJ_,OO_,WW_,pw_,prt_,OPT_):\012 ListTools[MakeUnique](DT__):\012 end proc:\012PathData3 := proc(B_,OO_,pw_,prt_,Chx_,OPT_:=OPT0) local k__,n__,y__,o__,o1__,o2__,t__,w__,p__,e__,\012                                                         ij__,eps__,hs__,vs__,B__,P__,W__,OO__,DT__:\012 ij__ := OPT_[&quot;ij&quot;]: eps__ := OPT_[&quot;eps&quot;]: hs__ := OPT_[&quot;hs&quot;]: vs__ := OPT_[&quot;vs&quot;]: \012 n__ := nops(B_):\012 \012 P__ := pw_[1]: W__ := pw_[2]:\012 if evalb(P__ =  [] and W__ &lt;&gt; []) then P__ := [seq(&quot;&quot;,k__=1..n__+1)] end if:\012 if evalb(P__ &lt;&gt; [] and W__ =  []) then W__ := [seq(&quot;&quot;,k__=1..n__+1)] end if:\012 if evalb(P__ =  [] and W__ =  []) then n__ := 0 end if:\012\012 OO__ := PathNode(OO_): OO__ := OO_[2..nops(OO_)]:\012 o__ := last(OO__)[1]: o__ := [o__[1]-n__*ij__[1],o__[2]-vs__]:\012 y__ := o__[2]:\012 \012 DT__ := []:\012 for k__ from 1 to n__ do\012  o1__ := [o__[1]+(k__-1)*ij__[1],y__]:\012  o2__ := [o__[1]+(k__)*ij__[1],y__]:\012  t__  := 1/2:\012  w__  := W__[k__]:\012  p__  := P__[k__]:\012  e__  := 0:\012  DT__ := [op(DT__),[o1__,o2__,t__,p__,w__,e__]]:\012  end do:\012\012 if n__&gt;0 then\012  o1__ := [o__[1]+n__*ij__[1],y__]:\012  o2__ := [o1__[1]+hs__*ij__[1],y__]:\012  t__  := 1/2:\012  w__  := W__[n__+1]:\012  p__  := P__[n__+1]:\012  e__  := 0:\012  DT__ := [op(DT__),[o1__,o2__,t__,p__,w__,e__]]:\012  end if:\012\012 if Chx_[2]=1 then \012  for k__ from 1 to n__ do\012   o1__ := OO__[k__][1]:\012   o2__ := [o1__[1],y__-eps__]:\012   t__  := 1:\012   w__  := cat(&quot;p+q=&quot;,k__):\012   p__  := &quot;&quot;:\012   e__  := -eps__:\012   DT__ := [op(DT__),[o1__,o2__,t__,p__,w__,e__]]:\012   end do:\012  end if:\012\012 DT__:\012 end proc:\012PathData := proc(B_,JJ_,PP_,OO_,WW_,PW_,PRT_,Chx_,OPT_:=OPT0)\012 if       Chx_[1]=1 then PathData1(B_,JJ_,PP_,OO_,WW_              ,PRT_[op(Chx_)]     ,OPT_)\012  else if Chx_[1]=2 then PathData2(B_,JJ_    ,OO_,WW_,PW_[op(Chx_)],PRT_[op(Chx_)]     ,OPT_)\012  else if Chx_[1]=3 then PathData3(B_        ,OO_    ,PW_[op(Chx_)],PRT_[op(Chx_)],Chx_,OPT_)\012  end if end if end if:\012 end proc:\012EventPathData := proc(B_,JU_,JE_,PP_,OO_,WW_,PW_,PRT_,chx_,OPT_:=OPT0) local pdt__,PNOD__,PDTU__,PDTE__:\012 PDTU__ := PathData(B_,JU_,PP_,OO_,WW_,PW_,PRT_,[chx_,1],OPT_):\012 PNOD__ := [seq(pdt__[1..2],pdt__ in PDTU__)]:\012 PDTE__ := PathData(B_,JE_,PP_,OO_,WW_,PW_,PRT_,[chx_,2],OPT_):\012 for pdt__ in PDTE__ do\012  if member(pdt__[1..2],PNOD__,'k__') then \012   PDTU__ := subsop(k__=NULL,PDTU__):\012   PNOD__ := subsop(k__=NULL,PNOD__): \012   end if:\012  end do:\012 [PDTU__,PDTE__]:\012 end proc:\012UnivPath := proc(B_,JU_,PP_,OO_,WW_,PW_,PRT_,CHX_,AT_,JOK_,OPT_:=OPT0) local k__,chx__,T__,PDT__:\012 T__ := [biss(nops(OO_)-1,OO_[1][1],AT_[1,1],OPT_)]:\012 for k__ from 1 to nops(CHX_) do\012  chx__ := CHX_[k__]:\012  PDT__  := PathData(B_,JU_,PP_,OO_,WW_,PW_,PRT_,[chx__,1],OPT_):\012  T__  := [op(T__),Tree(PDT__,PRT_[chx__,1],AT_[chx__,1],JOK_,OPT_)]:\012  end do:\012\012 display(T__):\012 end proc:\012EventPath := proc(B_,JU_,JE_,PP_,OO_,WW_,PW_,PRT_,CHX_,AT_,JOK_,OPT_:=OPT0) local k__,chx__,PDT__,T__:\012 T__ := [biss(nops(OO_)-1,OO_[1][1],AT_[1,1],OPT_)]:\012 for k__ from 1 to nops(CHX_) do\012  chx__ := CHX_[k__]:\012  PDT__  := EventPathData(B_,JU_,JE_,PP_,OO_,WW_,PW_,PRT_,chx__,OPT_):\012  T__  := [op(T__),seq(Tree(PDT__[l__],PRT_[chx__,l__],AT_[chx__,l__],JOK_,OPT_),l__=1..2)]:\012  end do:\012 display(T__):\012 end proc:\012EventWalk := proc(G_,v_,B_,o_,hl_,OPT_:=OPT0) local ij__,hs__,eps__,col__,sty__,tck__,\012                                                    OO__,n__,nr__,r__,o__,x__,y__,k__,\012                                                    leaf__i,leaf__a,leaf__g,walk__i,walk__a,walk__g,\012                                                    walk__leaf: \012 ij__ := OPT_[&quot;ij&quot;]: hs__ := OPT_[&quot;hs&quot;]: eps__ := OPT_[&quot;eps&quot;]:\012 col__ := hl_[1]: sty__ := hl_[2]: tck__ := hl_[3]:\012\012 OO__ := Node(B_,o_,OPT_):\012 OO__ := OO__[2..nops(OO__)]:\012 leaf__i := [o_,o_]:\012 x__ := o_[1]+(nops(B_)+hs__)*ij__[1]:\012 y__ := o_[2]: \012 walk__i := [[x__,y__],[x__,y__]]:\012 \012 n__ := 1:\012 nr__ := v2nr(v_,B_,n__):\012 r__  := nr__[2]:\012 o__  := OO__[n__][r__]:\012 leaf__i := [op(leaf__i),o__]:\012 if v_[n__] = 1 then y__ := y__ - ij__[2] else y__ := y__ + ij__[2] end if:\012 walk__i := [op(walk__i),[x__,y__]]:\012 \012 for n__ from 2 to nops(v_) do\012  nr__ := v2nr(v_,B_,n__):\012  r__  := nr__[2]:\012  o__  := OO__[n__][r__]:\012  if v_[n__-1] &lt;&gt; v_[n__] then x__ := x__+ eps__: \012                               walk__i := [op(walk__i),[x__,y__]]: \012                               leaf__i := [op(leaf__i),last(leaf__i)]:\012   end if:\012  if v_[n__] = 1 then y__ := y__ - ij__[2] else y__ := y__ + ij__[2] end if:\012  leaf__i := [op(leaf__i),o__]:\012  walk__i := [op(walk__i),[x__,y__]]:\012  end do:\012\012 leaf__a := [col__,'nul',sty__,tck__]:\012 leaf__g := [seq(nw_line([leaf__i[k__],leaf__i[k__+1]],leaf__a),k__=1..nops(leaf__i)-1)]:\012 leaf__g := [seq(display([G_,op(leaf__g[1..k])]),k=1..nops(leaf__g))]:\012 walk__a := [col__,'nul',sty__,tck__]:\012 walk__g := [seq(nw_line([walk__i[k__],walk__i[k__+1]],walk__a),k__=1..nops(walk__i)-1)]:\012 walk__g := [seq(display([G_,op(walk__g[1..k])]),k=1..nops(walk__g))]:\012\012 walk__leaf := [seq(display([walk__g[k__],leaf__g[k__]]),k__=1..nops(walk__g))]:\012 \012 display(walk__leaf,scaling=constrained,insequence=true):\012 end proc:\012end module:                                                                                                                                                                     \012\012#################################################### PROBMISC###################################################################\012\012ProbMisc := module()                                                                                      \012\012  uses     plots, LinearAlgebra, StringTools, ListTools,\012           AnimationII, AlgLin, Analyse, Geometrie, ProbComb; \012  export   PW0, PW1,\012           PRTnn, PRTnc, PRTnl, PRTns, PRTni, PRTno, PRTcn, PRTcc, PRTcl, PRTcs, PRTci, PRTco, \012           PRTpn, PRTpc, PRTpl, PRTps, PRTpi, PRTpo, PRTsn, PRTsc, PRTsl, PRTss, PRTsi, PRTso,\012           PRTin, PRTic, PRTil, PRTis, PRTii, PRTio, PRTon, PRToc, PRTol, PRTos, PRToi, PRToo,\012           PseudoString2List, PseudoList2List, RealList2List, RealList2String, FixedPoint, DeleteByRank, \012           TypeList, DecodeV, DecodeM,\012           rule_nssr, rule_nsar, rule_tasr, rule_taar, rule_dec,\012           name_comb_l, name_perm_l, name_multiperm_l, name_dec,\012           event_empty, event_full, event_all, event_sample, \012           event_isin_nset_wset, event_isin_nseq_wseq, event_iseq_wone_nany, \012           event_isin_wone_nany, event_isin_wset_alone, event_isin_ww_anywhere,\012           event_less_wone_numb, event_equal_wone_numb, event_more_wone_numb, \012           event_path_through_each, event_path_side_which, event_path_side_end,\012           event_fix_equal_set, event_fix_include_set, event_fix_equal_nb, event_fix_more_nb,\012           event_strict_increase, event_isin_wset,\012           event_ta_lessorequal, event_ta_greater, event_ta_equal;\012  local    paragraphe;\012option package;\012\012                                                                                                          \012                                                                                                          \012                                                                                                          \012PRTnn := ['no','no']: PRTnc := ['no','cc']: PRTnl := ['no','la']: PRTns := ['no','sq']: PRTni := ['no','id']: PRTno := ['no','op']:\012PRTcn := ['cb','no']: PRTcc := ['cb','cc']: PRTcl := ['cb','la']: PRTcs := ['cb','sq']: PRTci := ['cb','id']: PRTco := ['cb','op']:\012PRTpn := ['pr','no']: PRTpc := ['pr','cc']: PRTpl := ['pr','la']: PRTps := ['pr','sq']: PRTpi := ['pr','id']: PRTpo := ['pr','op']:\012PRTsn := ['sq','no']: PRTsc := ['sq','cc']: PRTsl := ['sq','la']: PRTss := ['sq','sq']: PRTsi := ['sq','id']: PRTso := ['sq','op']:\012PRTin := ['id','no']: PRTic := ['id','cc']: PRTil := ['id','la']: PRTis := ['id','sq']: PRTii := ['id','id']: PRTio := ['id','op']:\012PRTon := ['op','no']: PRToc := ['op','cc']: PRTol := ['op','la']: PRTos := ['op','sq']: PRToi := ['op','id']: PRToo := ['op','op']:\012PW0 := [[],[]]: PW1 := m -&gt; [[seq(1,k=1..m)],[seq(&quot;&quot;,k=1..m)]]:\012                                                                                                          \012PseudoString2List := proc(s_) local n__,k__,s__,l__,m__:\012 n__ := StringTools[Length](s_):\012 k__ := 1:\012 s__ := [convert(s_[1],name)]:\012 while k__ &lt; n__ do\012  l__ := k__+1: \012  if StringTools[IsDigit](s_[l__]) \012   then while evalb( l__ &lt; n__ and StringTools[IsDigit](s_[l__])) do l__ := l__+1: end do:\012         if `not`(StringTools[IsDigit](s_[l__])) then l__ := l__-1 end if:\012         m__ := parse(s_[k__+1..l__]):\012         s__ := [op(s__[1..nops(s__)-1]),s__[nops(s__)][m__]]:\012   else s__ := [op(s__),convert(s_[l__],name)]:\012   end if: \012  k__ := l__:\012  end do:\012 if k__ &lt; n__ then s__ := [op(s__),s_[n__]] end if:\012 s__ :\012 end proc:\012PseudoList2List := proc(L_) local s__:\012 s__ := map(convert,L_,string):\012 map(op,map(PseudoString2List,s__)):\012 end proc:\012RealList2List := proc(L_) local k__,s__,L__:\012 L__ := []:\012 for k__ from 1 to nops(L_) do\012  s__ := convert(L_[k__],string):\012  if type(L_[k__],indexed) then s__ := cat(s__[1],s__[3..StringTools[Length](s__)-1]) end if:\012  L__ := [op(L__),s__]:\012  end do:\012 map(convert,L__,name):\012 end proc:\012RealList2String := proc(L_) local L__:\012 L__ := RealList2List(L_):\012 cat(op(L__)):\012 end proc:\012FixedPoint := proc(v_) local k__,fix__:\012 fix__ := []:\012 for k__ from 1 to nops(v_) do\012  if v_[k__] = k__ then fix__ := [op(fix__),k__] end if:\012  end do:\012 convert(fix__,set): \012 end proc:\012DeleteByRank := proc(SS_,joklist_,joksign_) local j__,k__,J__:\012 J__ := []: k__ := 1:\012 while k__ &lt;= nops(SS_) do\012  j__ := k__:\012  while evalb(j__ in joklist_) do\012   j__ := j__+1:\012   end do:\012  if j__=k__ then J__ := [op(J__),SS_[j__]]: k__ := j__+1:\012             else J__ := [op(J__),joksign_]: k__ := j__:\012             end if:\012  end do:\012 J__:\012 end proc:\012TypeList := proc(L_,type_) local k__,L__:\012 L__ := []:\012 for k__ from 1 to nops(L_) do \012  if is(L_[k__],type_) then L__ := [op(L__),L_[k__]] end if:\012  end do:\012 L__:\012 end proc:\012DecodeV := proc(ind_) local L__,vpq__:\012 L__ := StringTools[Explode](ind_):\012 vpq__ := []:\012 if nops(L__) = 2 \012  then if      L__[2] = &quot;#&quot;  then vpq__ := [[parse(L__[1])],0,1]\012       else if L__[1] &lt;&gt; &quot;#&quot; then vpq__ := [map(parse,L__),0,2]\012       end if end if\012  else if L__[1] = &quot;#&quot; then vpq__ := [map(parse,[L__[3],L__[2]]),1,2]\012       end if\012  end if:\012 vpq__:\012 end proc:\012DecodeM := proc(ind_) local L__,ij__:\012 L__ := StringTools[Explode](ind_):\012 ij__ := []:\012 if nops(L__) = 2 \012  then  if      L__[1] = &quot;#&quot; then ij__ := [3,parse(L__[2])]\012        else if L__[2] = &quot;#&quot; then ij__ := [parse(L__[1]),3]\012        else ij__ := map(parse,L__)\012        end if end if:\012  end if:\012 ij__:\012 end proc:\012                                                                                                          \012rule_nssr := (bb_,i_) -&gt;  [seq(bb_[k__],k__=1..i_-1) , bb_[i_]-1 , seq(bb_[k__],k__=i_+1..nops(bb_)) ]:\012rule_nsar := (bb_,i_) -&gt; bb_:\012rule_tasr := proc(bb_,i_) \012 if i_&gt;1 then [seq(bb_[k__],k__=1..i_-1) , bb_[i_]-1 , seq(bb_[k__],k__=i_+1..nops(bb_))]\012         else [seq(0,k__=1..nops(bb_))]\012         end if:\012 end proc:\012rule_taar := (bb_,i_) -&gt; if i_&gt;1 then bb_ else [seq(0,k__=1..nops(bb_))] end if:\012rule_dec := proc(nr_,B_,N_) local n__,v__,s__,b__,k__:\012 n__ := nr_[1]: \012 v__ := nr2v(nr_,B_):\012 s__ := add(v__[k__]-1,k__=1..nops(v__)):\012 b__ := []:\012 if n__ &lt;= nops(B_)-2 \012  then for k__ from 1 to B_[n__+1] do\012        if s__+k__-1 &gt; N_ then b__ := [op(b__),0] else b__ := [op(b__),1] end if:\012        end do:\012  else for k__ from 1 to B_[n__+1] do\012        if s__+k__-1 &lt;&gt; N_ then b__ := [op(b__),0] else b__ := [op(b__),1] end if:\012        end do:\012  end if:\012\012 b__\012 end proc:\012                                                                                                          \012name_comb_l := proc(ww_,i_,X_) local ww__,p__,joklist__,joksign__: \012 p__ := X_[1]: joklist__ := X_[2]: joksign__ := X_[3]:\012 ww__ := combinat[choose](ww_,p__):\012 ww__ := DeleteByRank(ww__,joklist__,joksign__):\012 [seq(map(swq,ww__[k__]),k__=1..nops(ww__))]:\012 end proc:\012name_perm_l := proc(ww_,i_,X_) local ww__,p__,joklist__,joksign__:\012 p__ := X_[1]: joklist__ := X_[2]: joksign__ := X_[3]:\012 ww__ := combinat[permute](ww_[i_],p__):\012 ww__ := DeleteByRank(ww__,joklist__,joksign__):\012 [seq(map(swq,ww__[k__]),k__=1..nops(ww__))]:\012 end proc:\012name_multiperm_l := proc(n_,ww_,i_,univ_) local mot__,part__,pp__,place__,perm__,k__,ww__,u__,WW__:\012 mot__ := univ_[1]: part__ := univ_[2]:\012 WW__ := []:\012 pp__ := nops(part__[n_]):\012 place__ := [seq(ListTools[Search](c__,mot__),c__ in part__[n_])]:\012 perm__  := name_perm_l([part__[n_]],1,[pp__,{},&quot;&quot;]):\012 ww__ := ww_[i_]:\012 for u__ in perm__ do \012  for k__ from 1 to pp__ do\012   ww__[place__[k__]] := u__[k__]:\012   end do:\012  WW__ := [op(WW__),ww__]:\012  end do:\012\012 WW__:\012 end proc:\012name_dec := proc(M_) local code__,m__,k__:\012 code__ := &quot;&quot;:\012 for k__ from 1 to StringTools[Length](M_) do\012  m__ := parse(M_[k__]):\012  if m__=0 then code__ := cat(code__,&quot; &quot;)\012           else code__ := cat(code__,seq(&quot;X &quot;,k__=1..m__))\012           end if:\012  code__ := cat(code__,&quot;| &quot;):\012 end do:\012 code__[1..StringTools[Length](code__)-1]:\012 end proc:\012                                                                                                          \012event_empty := proc(v_,EVENT_,B_,BB_,WW_,log_:=&quot;&quot;)\012 false:\012 end proc:\012event_full := proc(v_,EVENT_,B_,BB_,WW_,log_:=&quot;&quot;)\012 true:\012 end proc:\012event_all := proc(v_,EVENT_,B_,BB_,WW_,log_:=`and`) local k__,boo__:\012 boo__ := []:\012 for k__ from 1 to nops(v_) do\012  boo__ := [op(boo__),evalb(WW_[k__][v2nr(v_,B_,k__)[2]]=EVENT_[k__])]:\012  end do:\012 convert(boo__,log_):\012 end proc:\012event_sample := proc(v_,EVENT_,B_,BB_,WW_,log_:=`and`) local k__,boo__:\012 boo__ := []:\012 for k__ from 1 to nops(v_) do\012  boo__ := [op(boo__),evalb(EVENT_[k__] = WW_[k__][v2nr(v_,B_,k__)[2]])]:\012  end do:\012 convert(boo__,log_):\012 end proc:\012event_isin_nset_wset := proc(v_,EVENT_,B_,BB_,WW_,log_:=`or`) local k__,isin__,boo__,EVENT1__:\012 EVENT1__ := EVENT_[1] intersect {seq(k__,k__=1..nops(v_))}:\012 boo__ := []:\012 for k__ from 1 to nops(EVENT1__) do\012  isin__ := EVENT1__[k__]:\012  boo__ := [op(boo__),evalb(WW_[isin__][v2nr(v_,B_,isin__)[2]] in EVENT_[2])]:\012  end do:\012 convert(boo__,log_):\012 end proc:\012event_isin_nseq_wseq := proc(v_,EVENT_,B_,BB_,WW_,log_:=`and`) local k__,isin__,boo__,EVENT1__:\012 EVENT1__ := convert(convert(EVENT_[1],set) intersect {seq(k__,k__=1..nops(v_))},list):\012 boo__ := []:\012 for k__ from 1 to nops(EVENT1__) do \012  isin__ := EVENT1__[k__]:\012  boo__ := [op(boo__),evalb(WW_[isin__][v2nr(v_,B_,isin__)[2]] in EVENT_[2][k__])]:\012  end do:\012 convert(boo__,log_):\012 end proc:\012event_iseq_wone_nany := proc(v_,EVENT_,B_,BB_,WW_,log_:=`or`) local k__,boo__:\012 boo__ := []:\012 for k__ from 1 to nops(v_) do\012  boo__ := [op(boo__),evalb(EVENT_ = WW_[k__][v2nr(v_,B_,k__)[2]])]:\012  end do:\012 convert(boo__,log_):\012 end proc:\012event_isin_wone_nany := proc(v_,EVENT_,B_,BB_,WW_,log_:=`or`) local k__,boo__:\012 boo__ := []:\012 for k__ from 1 to nops(v_) do\012  boo__ := [op(boo__),evalb(EVENT_ in WW_[k__][v2nr(v_,B_,k__)[2]])]:\012  end do:\012 convert(boo__,log_):\012 end proc:\012event_isin_wset_alone := proc(v_,EVENT_,B_,BB_,WW_,log_:=`or`) local b__,k__,l__,set__,boo__:\012 set__ := i__ -&gt; {seq(k__,k__=1..nops(v_))} minus {i__}:\012 boo__  := [seq(true,k__=1..nops(v_))]:\012 for l__ from 1 to nops(v_) do\012  for k__ in set__(l__) do\012    b__ := evalb(not(WW_[k__][v2nr(v_,B_,k__)[2]] in EVENT_)):\012    boo__[l__] := evalb(boo__[l__] and b__):\012    end do:\012   b__ := evalb(WW_[l__][v2nr(v_,B_,l__)[2]] in EVENT_):\012   boo__[l__] := evalb(boo__[l__] and b__):  \012   end do:\012 convert([seq(boo__[l__],l__=1..nops(v_))],log_):\012 end proc:\012event_isin_ww_anywhere := proc(v_,EVENT_,B_,BB_,WW_,log_:=`or`) local k__,boo__:\012 boo__ := []:\012 for k__ from 1 to nops(v_)-1 do\012  boo__ := [op(boo__),evalb(cat(WW_[k__][v2nr(v_,B_,k__)[2]],WW_[k__+1][v2nr(v_,B_,k__+1)[2]]) in EVENT_)]:\012  end do: \012 convert(boo__,log_):\012 end proc:\012event_less_wone_numb := proc(v_,EVENT_,B_,BB_,WW_,log_:=`true`) local w__,n__,vw__,boo__:\012 w__ := EVENT_[1]: n__ := EVENT_[2]:\012 vw__ := PrintW(v_,B_,WW_,'sq'): \012 boo__ := evalb(ListTools[Occurrences](w__,vw__) &lt;= n__):\012 boo__:\012 end proc:\012event_equal_wone_numb := proc(v_,EVENT_,B_,BB_,WW_,log_:=`true`) local w__,n__,vw__,boo__:\012 w__ := EVENT_[1]: n__ := EVENT_[2]:\012 vw__ := PrintW(v_,B_,WW_,'sq'): \012 boo__ := evalb(ListTools[Occurrences](w__,vw__) = n__):\012 boo__:\012 end proc:\012event_more_wone_numb := proc(v_,EVENT_,B_,BB_,WW_,log_:=`true`) local w__,n__,vw__,boo__:\012 w__ := EVENT_[1]: n__ := EVENT_[2]:\012 vw__ := PrintW(v_,B_,WW_,'sq'):\012 boo__ := evalb(ListTools[Occurrences](w__,vw__) &gt;= n__):\012 boo__:\012 end proc:\012event_path_through_each := proc(v_,EVENT_,B_,BB_,WW_,log_:=`and`) local pq__,n__,v__,boo__:\012 pq__ := EVENT_:\012 n__ := [seq(pq__[k__][1]+pq__[k__][2],k__=1..nops(pq__))]:\012 v__ := [seq(v_[1..n__[k__]],k__=1..nops(n__))]: \012 boo__ := [seq(evalb(ListTools[Occurrences](1,v__[k__]) = pq__[k__][1]),k__=1..nops(n__))]:\012 convert(boo__,log_):\012 end proc:\012event_path_side_which := proc(v_,EVENT_,B_,BB_,WW_,log_:=`and`) local test__,boo__:\012 if       EVENT_ = &quot;&gt;&quot;  then test__ := k___ -&gt; evalb(ListTools[Occurrences](2,v_[1..k___]) &gt;  k___/2)\012  else if EVENT_ = &quot;&lt;&quot;  then test__ := k___ -&gt; evalb(ListTools[Occurrences](2,v_[1..k___]) &lt;  k___/2)\012  else if EVENT_ = &quot;&lt;&gt;&quot; then test__ := k___ -&gt; evalb(ListTools[Occurrences](2,v_[1..k___]) &lt;&gt; k___/2)\012  else if EVENT_ = &quot;&gt;=&quot; then test__ := k___ -&gt; evalb(ListTools[Occurrences](2,v_[1..k___]) &gt;= k___/2)\012  else if EVENT_ = &quot;&lt;=&quot; then test__ := k___ -&gt; evalb(ListTools[Occurrences](2,v_[1..k___]) &lt;= k___/2)\012  end if end if end if end if end if:\012 boo__ := [seq(test__(k__),k__=1..nops(v_))]:\012 convert(boo__,log_):\012 end proc:\012event_path_side_end := proc(v_,EVENT_,B_,BB_,WW_,log_:=`and`) local n__,q__,r__,boo1__,boo2__,boo__:\012 n__ := nops(v_):\012 q__ := iquo(n__,2,'r__'): \012 boo1__ := event_path_through_each(v_,[[q__,q__]],B_,BB_,WW_):\012 boo2__ := event_path_side_which(v_[1..n__-1],EVENT_,B_,BB_,WW_):\012 if r__ = 0 then boo__ := boo1__ and boo2__ else boo__ := false end if:\012 boo__:\012 end proc:\012event_fix_equal_set := proc(v_,EVENT_,B_,BB_,WW_,log_:=`true`) local fix__,wfix__,boo__:\012 fix__ := FixedPoint(v_):\012 wfix__ := {seq(WW_[1][k__],k__ in fix__)}:\012 if wfix__ = EVENT_ then boo__ := `true` else boo__ := `false` end if:\012 boo__:\012 end proc:\012event_fix_include_set := proc(v_,EVENT_,B_,BB_,WW_,log_:=`true`) local fix__,wfix__,boo__:\012 fix__ := FixedPoint(v_):\012 wfix__ := {seq(WW_[1][k__],k__ in fix__)}:\012 if EVENT_ subset wfix__ then boo__ := `true` else boo__ := `false` end if:\012 boo__:\012 end proc:\012event_fix_equal_nb := proc(v_,EVENT_,B_,BB_,WW_,log_:=`true`) local fix__,boo__:\012 fix__ := FixedPoint(v_):\012 if nops(fix__) = EVENT_ then boo__ := `true` else boo__ := `false` end if:\012 boo__:\012 end proc:\012event_fix_more_nb := proc(v_,EVENT_,B_,BB_,WW_,log_:=`true`) local fix__,boo__:\012 fix__ := FixedPoint(v_):\012 if nops(fix__) &gt;= EVENT_ then boo__ := `true` else boo__ := `false` end if:\012 boo__:\012 end proc:\012event_strict_increase := proc(v_,EVENT_,B_,BB_,WW_,log_:=`and`) local k__,boo__:\012 boo__ := []:\012 for k__ from 1 to nops(v_)-1 do\012  boo__ := [op(boo__),evalb(WW_[k__][v2nr(v_,B_,k__)[2]] &lt; WW_[k__+1][v2nr(v_,B_,k__+1)[2]])]:\012  end do: \012 convert(boo__,log_):\012 end proc:\012event_isin_wset := proc(v_,EVENT_,B_,BB_,WW_,log_:=`xor`) local k__,nr__,boo__:\012 boo__ := []:\012 nr__ := v2nr(v_,B_):\012 for k__ from 1 to nops(EVENT_) do\012   boo__ := [op(boo__),evalb(EVENT_[k__] in WW_[nr__[1]][nr__[2]])]:\012   end do:\012 convert(boo__,log_):\012 end proc:\012event_ta_lessorequal := proc(v_,EVENT_,B_,BB_,WW_,log_:=&quot;&quot;) local k__,boo__:\012 boo__ := []:\012 for k__ from 1 to min(nops(v_),EVENT_[1]) do\012  boo__ := [op(boo__),evalb(WW_[k__][v2nr(v_,B_,k__)[2]] in EVENT_[2])]:\012  end do:\012 convert(boo__,`or`):\012 end proc:\012event_ta_greater := proc(v_,EVENT_,B_,BB_,WW_,log_:=&quot;&quot;)\012 evalb(`not`(event_ta_lessorequal(v_,EVENT_,B_,BB_,WW_))):\012 end proc:\012event_ta_equal := proc(v_,EVENT_,B_,BB_,WW_,log_:=&quot;&quot;) local k__,boo__,n__:\012 boo__ := []: n__ := EVENT_[1]: \012 if n__ &gt; nops(v_) \012  then boo__ := `false`\012  else for k__ from 1 to n__-1 do\012        boo__ := [op(boo__),evalb(WW_[k__][v2nr(v_,B_,k__)[2]] in EVENT_[2])]:\012        end do:\012       boo__ := convert(boo__,`or`):\012       boo__ := evalb(not(boo__) and evalb(WW_[n__][v2nr(v_,B_,n__)[2]] in EVENT_[2])):\012  end if:\012 boo__:\012 end proc:\012end module:\012\012#################################################### PROBSTAT###################################################################\012\012ProbStat := module()                                                                                      \012\012  uses     plots, LinearAlgebra, StringTools, ListTools,\012           AnimationII, AlgLin, Analyse, Geometrie, ProbComb, ProbMisc; \012  export   SMean, SVar, SEct, SDiag, SRep, SCov, SCor, SMarg;\012  local    paragraphe;\012option package;\012\012SMean := X_ -&gt; add(X_[1][k__]*X_[2][k__],k__=1..ColumnDimension(X_)):\012SVar  := X_ -&gt; add((X_[1][k__]^2)*X_[2][k__],k__=1..ColumnDimension(X_))-(SMean(X_))^2:\012SEct := X_ -&gt; sqrt(SVar(X_)):\012SDiag := proc(X_,AT_) local Xv__,Xp__,dig__,k__:                                                          \012 Xv__ := convert(Row(X_,1),list): Xp__ := convert(Row(X_,2),list):\012\012 dig__ := []:\012 for k__ from 1 to nops(Xv__) do\012  dig__ := [op(dig__),nw_line([&lt;Xv__[k__],0&gt;,&lt;Xv__[k__],Xp__[k__]&gt;],AT_)]:\012  end do:\012\012 display( dig__, view=default, scaling = unconstrained, axes = boxed ):\012 end proc:\012SRep := proc(X_) local Xp__,Xpc__,k__:\012 Xp__ := convert(Row(X_,2),list):\012 Xpc__ := [Xp__[1]]:\012 for k__ from 2 to nops(Xp__) do\012  Xpc__ := [op(Xpc__),Xp__[k__]+Xpc__[k__-1]]:\012  end do:\012 Xpc__:\012 end proc:\012SCov := proc(X_,Y_,XY_) local dx__,dy__,muX__,muY__,cov__,i__,j__:\012 dx__ := ColumnDimension(X_): dy__ := ColumnDimension(Y_):\012 muX__ := SMean(X_): muY__ := SMean(Y_):\012 cov__ := 0:\012 for i__ from 1 to dx__ do\012  for j__ from 1 to dy__ do\012   cov__ := cov__+X_[1,i__]*Y_[1,j__]*XY_[i__,j__]:\012   end do end do:\012 cov__ - muX__*muY__:\012 end proc:\012SCor := (X_,Y_,XY_) -&gt; SCov(X_,Y_,XY_)/(SEct(X_)*SEct(Y_)):\012SMarg := proc(M_) local n__,p__,i__,j__,M__:\012 n__ := RowDimension(M_):\012 p__ := ColumnDimension(M_):\012 M__ := Matrix(n__+1,p__+1):\012 for i__ from 1 to n__ do\012  for j__ from 1 to p__ do\012   M__[i__,j__] := M_[i__,j__]:\012   end do end do:\012 for i__  from 1 to n__ do\012  M__[i__,p__+1] := add(M_[i__,j__],j__=1..p__):\012  end do:\012 for j__  from 1 to p__ do\012  M__[n__+1,j__] := add(M_[i__,j__],i__=1..n__):\012  end do:\012 M__[n__+1,p__+1] := 1:\012 M__:\012 end proc:\012end module:                                                          \012\012######################################################## FILM ##################################################################            \012\012VAII_CO := module()                                                                                      \012\012  uses     DocumentTools, StringTools, ListTools, plots, LinearAlgebra, \012           AnimationII, AlgLin, Analyse, Geometrie, ProbComb, ProbMisc; \012  export   nada;\012  local    Paragraphe;\012  option package;\012\012########################################################\012\012end module:                                                                                                                                                                                                                                                                                                                          \012\012####################################################### GESTION  ###############################################################\012with(DocumentTools): with(StringTools): with(ListTools): with(plots): with(LinearAlgebra):                                 \012with(AnimationII): with(AlgLin): with(Analyse): with(Geometrie): with(ProbComb): with(ProbMisc): with(ProbStat):\012################################################################################################################################\012with(VAII_CO):\012\012col1 := [[&quot;IndianRed&quot;,&quot;LightPink&quot;,&quot;DarkRed&quot;],[&quot;SteelBlue&quot;,&quot;LightSteelBlue&quot;,&quot;DarkBlue&quot;]]:\012col2 := col1:\012col3 := col1:\012COL := Matrix(3,2,[col1,col2,col3]):\012\012sty1 := [['solid',0,'nul'],['solid',1,'nul']]:\012sty2 := [['dot',0,'right'],['dot',1,'right']]:\012sty3 := [['dash',0,'nul'],['dash',1,'nul']]:\012STY := Matrix(3,2,[sty1,sty2,sty3]):\012\012fss1 := [[[ROMAN,9],[ROMAN,9]],[[ROMAN,9],[ROMAN,9]]]:\012fss2 := fss1:\012fss3 := [[[ROMAN,9],[ROMAN,9]],[[ROMAN,9],[ROMAN,9]]]:\012FSS := Matrix(3,2,[fss1,fss2,fss3]):\012\012AT  := Matrix(3,2,(i,j)-&gt;[COL[i,j],STY[i,j],FSS[i,j]]):\012HL := [[&quot;Crimson&quot;,'solid',1],[&quot;BlueViolet&quot;,'solid',1]]:\012\012IJ := [2,8]: JOK := [&quot;#&quot;]: EPS := 0.05: HSPACE := 1.5: VSPACE := 1: BREAK := 3: MODE := &quot;T&quot;:\012OPT := table([ &quot;ij&quot; = IJ, &quot;eps&quot; = EPS, &quot;hs&quot; = HSPACE, &quot;vs&quot; = VSPACE, &quot;br&quot; = BREAK, &quot;mo&quot; = MODE ]): \012CHX := {1,2,3}:\012\012o0 := [0,0]:\012\012#Co11\012co11dt1X := Matrix (2,2):\012co11dt1Y := Matrix (2,2):\012co11dt1XY1 := Matrix(2,2):\012co11dt1XY2 := Matrix(2,2):\012\012#Co12\012co12dt1XY1 := Matrix(2,3):\012co12dt1XY2 := Matrix(3,4):\012\012#Co13\012co13dt1XY := Matrix(3,3):\012co13dt2XY := Matrix(3,4):\012\012#Co14\012co14dt1U1 := Matrix(2,3):\012co14dt1S1 := Matrix(2,3):\012co14dt1U2 := Matrix(2,2):\012co14dt1S2 := Matrix(2,4):\012\012co14dt2US1 := Matrix(3,5):\012\012#Co21\012co21dtX := Matrix (2,2):\012co21dtY := Matrix (2,2):\012co21dtXY := Matrix(2,2):\012Do(%co21TARXE = &quot;&quot;):\012Do(%co21TARYE = &quot;&quot;):\012Do(%co21TARXS = &quot;&quot;):\012Do(%co21TARYS = &quot;&quot;):\012\012Do(%co21TAR1XYC = &quot;&quot;):\012Do(%co21TAR1XYR = &quot;&quot;):\012\012co21dt2XY := Matrix(2,2):\012Do(%co21TAR2XYE = &quot;&quot;):\012\012#Co3\012co3dt2T := Matrix(2,4):\012\012#Ex121\012ex121dtXY := Matrix([[a,2*a,2*a],[3*a,a,a]]):\012\012#ExE2\012exE2dtCHI := Matrix([[p,q],[r,s]]):"/>
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<Input><Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><Font size="10" encoding="UTF-8" italic="true">Os links de exerc\303\255cios do WIMS se referem a uma compila\303\247\303\243o de exerc\303\255cios no site do WIMS, desenvolvido por XIAO Gang da Universidade de Nice.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal">1.O direito conjunto da <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font encoding="UTF-8"> \303\251 a lei</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal">do casal <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font encoding="UTF-8"> : \303\251 inteiramente determinado pelas probabilidades diferentes de zero</Font></Text-field>
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<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" bold="false" foreground="[0,51,0]" italic="false" size="10" layout="Heading 3"><Font size="10" underline="true" bold="true" foreground="[0,51,0]" encoding="UTF-8" italic="false">Observa\303\247\303\265es</Font></Text-field></Title><Presentation-Block>
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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">\303\200s vezes, usaremos a nota\303\247\303\243o </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"> e vamos resumir a distribui\303\247\303\243o por uma tabela de probabilidades </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"> quando \303\251 \303\272til.</Font></Text-field>
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<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" bold="false" foreground="[0,51,0]" italic="false" size="10" layout="Heading 3"><Font size="10" underline="true" bold="true" foreground="[0,51,0]" italic="false">Exemplos</Font></Text-field></Title><Presentation-Block>
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arrange := (n,p) -&gt; combinat[numbperm](n,p):
prX := r -&gt; binomial(3,r)*binomial(1,2-r)/binomial(4,2):
prY := r -&gt; arrange(1,r-1)*3*arrange(4-r,2-r)/arrange(4,2):

Xv := [seq(k,k=1..2)]:
Xp := [seq(prX(k),k=1..2)]:
XX := Matrix([Xv,Xp]):
Yv := [seq(k,k=1..2)]:
Yp := [seq(prY(k),k=1..2)]:
YY := Matrix([Yv,Yp]):
XY1 := [1/4,1/4]:
XY2 := [1/2,0]:
XYXY2 := Matrix([XY1,XY2]):
XYXY1 := Matrix([[RB,BR],[RR,VIDE]]):

co11dt1X := copy(XX):
co11dt1Y := copy(YY):
co11dt1XY1 := copy(XYXY1):
co11dt1XY2 := copy(XYXY2):

end use; 
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aa := add(add(i*j,j=1..3),i=1..2):
XYXY1 := Matrix(2,3,(i,j)-&gt;i*j/aa):
XYXY2 := SMarg(XYXY1):

co12dt1XY1 := copy(XYXY1):
co12dt1XY2 := copy(XYXY2):

end use; 
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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">N\303\263s consideramos dois VA </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]"> e </Font><Equation executable="false" style="2D Math" input-equation="" 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XY1 := [1/4,1/4]:
XY2 := [1/2,0]:
XYXY1 := Matrix([XY1,XY2]):
XYXY2 := SMarg(XYXY1):

co13dt1XY := copy(XYXY2):

end use; 
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]">Tomamos os dados do Exemplo 1.1. Um resume os resultados obtidos pela tabela do direito conjunto e do direito marginal:</Font></Text-field>
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aa := add(add(i*j,j=1..3),i=1..2):
XYXY1 := Matrix(2,3,(i,j)-&gt;i*j/aa):
XYXY2 := SMarg(XYXY1):

co13dt2XY := copy(XYXY2):

end use; 
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<Input><Text-field style="Text" layout="Normal">2. A probabilidade <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font encoding="UTF-8"> pode ser calculado pela f\303\263rmula</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">3. A experan\303\247a  </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbWlHRiQ2KFEiRUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStleGVjdXRhYmxlR0Y0LyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y5LUkobWZlbmNlZEdGJDYlLUYjNiktRiw2JlEiWkYnL0YzRjFGNS9GOFEnaXRhbGljRidGRC8lK2ZvcmVncm91bmRHUStbMCwxNjAsODBdRidGNS8lLHBsYWNlaG9sZGVyR0YxLyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR0YxRkVGNS9GOFEnbm9ybWFsRictSSNtb0dGJDYuUSI9RidGNUZOLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGXm8tSSdtdW5kZXJHRiQ2JS1GIzYlLUZRNi9RJiZTdW07RidGNUZMRk5GVEZWL0ZZRjFGWi9GZ25GMS9GaW5GMUZqbi9GXW9RJjAuMGVtRicvRmBvUSwwLjE2NjY2NjdlbUYnRjVGTi1GIzYlLUYsNiZRInpGJ0ZERjVGRUY1Rk4vJSxhY2NlbnR1bmRlckdGNC1GUTYuUSJ+RidGNUZORlRGVkZYRlpGZm5GaG5Gam5GXHAvRmBvRl1wLUYsNihRI3ByRidGL0YyRjVGN0Y6LUY9NiUtRiM2J0ZBRlBGYnBGNUZORjVGTi1GUTYuUSgmdGltZXM7RidGNUZORlRGVkZYRlpGZm5GaG5Gam4vRl1vUSwwLjIyMjIyMjJlbUYnL0Zgb0ZmcUZicEY1Rk4=">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</Equation><Font encoding="UTF-8">  pode ser calculado pela f\303\263rmula</Font></Text-field>
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UU1 := Matrix(2,3,(i,j)-&gt;min(i,j)):
SS1 := Matrix(2,3,(i,j)-&gt;i+j):
Uv := [1,2]:
Up := [4/6,2/6]:
UU2 := Matrix([Uv,Up]):
Sv := [2,3,4,5]:
Sp := [1/6,2/6,2/6,1/6]:
SS2 := Matrix([Sv,Sp]):


co14dt1U1 := copy(UU1):
co14dt1S1 := copy(SS1):
co14dt1U2 := copy(UU2):
co14dt1S2 := copy(SS2):
Do(%co14TAR1UE = SMean(UU2)):
Do(%co14TAR1SE = SMean(SS2)):

end use; 
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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">Pode ser interessante fazer uma tabela de valores, pois fornece informa\303\247\303\265es sobre os c\303\241lculos a serem feitos para obter as probabilidades:</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]" encoding="UTF-8">Poder\303\255amos completar as tabelas anteriores pela tabela de interse\303\247\303\265es </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"> mas a independ\303\252ncia do VA torna esta tabela in\303\272til.</Font></Text-field>
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US1 := Matrix([[X1Y1,X1Y2*X2Y1,X1Y3,VIDE],[VIDE,VIDE,X2Y2,X2Y3]]):
US2 := Matrix([[1/6,2/6,1/6,0],[0,0,1/6,1/6]]):
US2 := SMarg(US2):

co14dt2US1 := copy(US1):
co14dt2US2 := copy(US2):

end use; 
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\303\251 a covari\303\242ncia das vari\303\241veis \342\200\213\342\200\213centralizadas reduzidas </Font><Equation executable="false" style="2D Math" input-equation="" 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<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" bold="false" foreground="[0,51,0]" italic="false" size="10" layout="Heading 3"><Font size="10" underline="true" bold="true" foreground="[0,51,0]" encoding="UTF-8" italic="false">Observa\303\247\303\265es</Font></Text-field></Title><Presentation-Block>
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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">1. O coeficiente de correla\303\247\303\243o \303\251 independente das unidades de medida, diferentemente da covari\303\242ncia.
2. O caso </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"> corresponde a uma aus\303\252ncia de correla\303\247\303\243o, o que n\303\243o significa que o VA </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]"> e </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> s\303\243o independentes: por outro lado, a independ\303\252ncia de </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]"> e </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> resulta em correla\303\247\303\243o zero.
Existe, no entanto, um caso em que uma correla\303\247\303\243o zero leva \303\240 independ\303\252ncia: quando </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEiWEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEiWEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn</Equation><Font size="10" foreground="[0,51,0]"> e </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEiWUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEiWUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> s\303\243o vari\303\241veis \342\200\213\342\200\213caracter\303\255sticas.</Font></Text-field>
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arrange := (n,p) -&gt; combinat[numbperm](n,p):
prX := r -&gt; binomial(3,r)*binomial(1,2-r)/binomial(4,2):
prY := r -&gt; arrange(1,r-1)*3*arrange(4-r,2-r)/arrange(4,2):

Xv := [seq(k,k=1..2)]:
Xp := [seq(prX(k),k=1..2)]:
XX := Matrix([Xv,Xp]):
Yv := [seq(k,k=1..2)]:
Yp := [seq(prY(k),k=1..2)]:
YY := Matrix([Yv,Yp]):
muX := SMean(XX):
muY := SMean(YY):
sX := SEct(XX):
sY := SEct(YY):
XY1 := [1/4,1/4]:
XY2 := [1/2,0]:
XYXY := Matrix([XY1,XY2]):
cXY := SCov(XX,YY,XYXY):
rXY := SCor(XX,YY,XYXY):

co21dtX := copy(XX):
co21dtY := copy(YY):
co21dtXY := copy(XYXY):
Do(%co21TARXE = muX):
Do(%co21TARYE = muY):
Do(%co21TARXS = evalf(sX,3)):
Do(%co21TARYS = evalf(sY,3)):

end use; 
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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">Recordamos tamb\303\251m o direito conjunto de </Font><Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkobWZlbmNlZEdGJDYnLUYjNistSSNtaUdGJDYoUSJYRicvJSVzaXplR1EjMTBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUSlbMCw1MSwwXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2MFEifkYnRjRGOkY9L0ZBUSdub3JtYWxGJy8lJmZlbmNlR0Y/LyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlktRkQ2MFEiLEYnRjRGOkY9RkdGSS9GTEY5Rk1GT0ZRRlNGVUZXL0ZlblEsMC4zMzMzMzMzZW1GJ0ZDLUYxNihRIllGJ0Y0RjdGOkY9RkBGNEY6Rj1GR0Y0RjpGPUZHRjRGOkY9Rkc=</Equation><Font size="10" foreground="[0,51,0]"> :</Font></Text-field>
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arrange := (n,p) -&gt; combinat[numbperm](n,p):
prX := r -&gt; binomial(3,r)*binomial(1,2-r)/binomial(4,2):
prY := r -&gt; arrange(1,r-1)*3*arrange(4-r,2-r)/arrange(4,2):

Xv := [seq(k,k=1..2)]:
Xp := [seq(prX(k),k=1..2)]:
XX := Matrix([Xv,Xp]):
Yv := [seq(k,k=1..2)]:
Yp := [seq(prY(k),k=1..2)]:
YY := Matrix([Yv,Yp]):
muX := SMean(XX):
muY := SMean(YY):
sX := SEct(XX):
sY := SEct(YY):
XY1 := [1/4,1/4]:
XY2 := [1/2,0]:
XYXY := Matrix([XY1,XY2]):
cXY := SCov(XX,YY,XYXY):
rXY := SCor(XX,YY,XYXY):

Do(%co21TAR1XYC = cXY):
Do(%co21TAR1XYR = evalf(rXY,3)):

end use; 
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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">Para calcular a covari\303\242ncia de </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]"> e </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> n\303\263s usamos a f\303\263rmula  </Font></Text-field>
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XYv := [1,2]:
XYp := [1/4,3/4]:
XY := Matrix([XYv,XYp]):
muXY := SMean(XY):

co21dt2XY := copy(XY):
Do(%co21TAR2XYE = muXY):

end use; 
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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">Para calcular a covari\303\242ncia de </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]"> e </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiWUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> n\303\263s usamos a f\303\263rmula  </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal" alignment="right"><Hyperlink linktarget="http://wims.unice.fr/~wims/wims.cgi?session=QXA06CAC6B.4&amp;lang=fr&amp;cmd=new&amp;module=U2%2Fproba%2Foefvad2.fr&amp;exo=couple4&amp;qnum=1&amp;qcmlevel=3&amp;scoredelay=&amp;special_parm2=&amp;special_parm4=" hyperlink="true"><Font size="10" style="Hyperlink" foreground="[153,51,102]">Covariance 1</Font></Hyperlink></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">Portanto, usamos a f\303\263rmula de probabilidades condicionais</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal" alignment="centred"><EC-RadioButton id="co3RAB2" caption="2. Tirage sans remise" groupname="co3RAB" fontcolor="[0,0,0]" fillcolor="[255,255,255]" enabled="true" visible="true" selected="true"><MapleCode action="click-event-handler">use DocumentTools in 

p0 := r -&gt; 7/(10-r+1):
q0 := r -&gt; (3-r+1)/(10-r+1):
prT := r -&gt; p0(r)*mul(q0(k),k=1..r-1):

Tv := [1,2,3,4]:
Tp := [seq(prT(k),k in Tv)]:
TT := Matrix([Tv,Tp]):

co3dt2T := copy(TT):

end use; 
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size="10" foreground="[0,51,0]" encoding="UTF-8"> primeiras impress\303\265es: existe </Font><Equation executable="false" style="2D Math" input-equation="" 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size="10" foreground="[0,51,0]"> bolas brancas em </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbW5HRiQ2J1EjMTBGJy8lJXNpemVHRi4vJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNjBRKCZtaW51cztGJ0YvRjFGNEY3LyUmZmVuY2VHRjYvJSpzZXBhcmF0b3JHRjYvJSlzdHJldGNoeUdGNi8lKnN5bW1ldHJpY0dGNi8lKGxhcmdlb3BHRjYvJS5tb3ZhYmxlbGltaXRzR0Y2LyUnYWNjZW50R0Y2LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGTi1JI21pR0YkNihRImtGJ0YvLyUnaXRhbGljR1EldHJ1ZUYnRjFGNC9GOFEnaXRhbGljRictRjs2MFEiK0YnRi9GMUY0RjdGPkZARkJGREZGRkhGSkZMRk8tRiw2J1EiMUYnRi9GMUY0RjdGL0YxRjRGNw==">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</Equation><Font size="10" foreground="[0,51,0]"> bolas no total, ou seja, uma probabilidade</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]">Filmamos sem desconto </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JlEiM0YnRjJGNUY/RjJGNUY/">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JlEiM0YnRjJGNUY/RjJGNUY/</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> bolas em uma urna que cont\303\251m </Font><Equation executable="false" style="Text" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]"> bolas vermelhas e </Font><Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUkjbW5HRiQ2JVEiMkYnRjUvRjlRJ25vcm1hbEYnRjJGNS8lLHBsYWNlaG9sZGVyR0Y0RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRk4vJSlzdHJldGNoeUdGTi8lKnN5bW1ldHJpY0dGTi8lKGxhcmdlb3BHRk4vJS5tb3ZhYmxlbGltaXRzR0ZOLyUnYWNjZW50R0ZOLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGZ24tRj42JVEiNEYnRjVGQUY1RkE=">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</Equation><Font foreground="[153,51,102]"> bolas pretas: notamos </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2J1EiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRRjJGNUY/">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2J1EiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRRjJGNUY/</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> &quot; n\303\272mero de bolas vermelhas desenhadas &quot;e </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2J1EiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRRjJGNUY/">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2J1EiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRRjJGNUY/</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> &quot; classifica\303\247\303\243o da primeira bola preta &quot;.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]">1. Determine as leis marginais de </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]"> .</Font></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">Um aluno faz 2 exames, supostamente independentes. N\303\263s notamos </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]"> e </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]"> suas notas no primeiro e no segundo exame: essas notas podem assumir os valores equivalentes </Font><Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUkjbW5HRiQ2JlEiMEYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2L1EifkYnRi9GMkY1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GOTYvUSIsRidGL0YyRjVGPC9GP1EldHJ1ZUYnRkBGQkZERkZGSEZKL0ZOUSwwLjMzMzMzMzNlbUYnRjgtRjk2L1EoJmN0ZG90O0YnRi9GMkY1RjxGPkZARkJGREZGRkhGSkZNRjhGT0Y4LUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR0ZTRi9GMi9GNlEnaXRhbGljRidGL0YyRjU=</Equation><Font foreground="[153,51,102]"> , com aqui </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JlEiM0YnRjJGNUY/RjJGNUY/">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JlEiM0YnRjJGNUY/RjJGNUY/</Equation><Font foreground="[153,51,102]">.</Font></Text-field>
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2. Calcule as probabilidades </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]"> , </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]"> e </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]"> .</Font></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">3. Determine a lei e a experan\303\247ade  </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]"> e </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]"> . </Font></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">Uma carta \303\251 desenhada duas vezes com entrega em uma urna contendo as letras A, B, C.
N\303\263s notamos </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> o n\303\272mero de vogais, </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> o n\303\272mero de consoantes e </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> o n\303\272mero de B's obtidos.</Font></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">2. Calcular os coeficientes de correla\303\247\303\243o </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]"> , </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]"> e </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]">.</Font></Text-field>
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1. Calcule as probabilidades</Font></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">Uma pessoa procura um objeto em uma sala: se uma primeira pesquisa n\303\243o produz nada, ela come\303\247a novamente e assim por diante. Assumimos que a probabilidade de sucesso diminua a cada vez, seja por fadiga ou porque a pessoa tem cada vez menos certeza de que o objeto est\303\241 na sala: notamos </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2J1EiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRRjJGNUY/">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2J1EiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRRjJGNUY/</Equation><Font foreground="[153,51,102]">  &quot; tempo de espera antes de encontrar o objeto &quot;e damos</Font></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.Mostre que, se a covari\303\242ncia </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEnJiM5Njc7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdGNC8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdRJXRydWVGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2KS1GLzYnUSJBRicvRjNGPEY1RjgvRj5RJ2l0YWxpY0YnRkVGNUY4LyUscGxhY2Vob2xkZXJHRjwvJTBmb250X3N0eWxlX25hbWVHUSVUZXh0RidGRi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2MFEifkYnRjVGOEY6Rj0vJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0Zeb0Y1RjhGSkY9">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</Equation><Font foreground="[153,51,102]"> e </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW9HRiQ2MFEifkYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSy1JJW1zdWJHRiQ2JS1JI21pR0YkNihRJyYjOTY3O0YnLyUnaXRhbGljR0Y0Ri9GMkY1RjgtRiM2KS1GUjYnUSJCRicvRlZGN0YvRjIvRjlRJ2l0YWxpY0YnRmZuRi9GMi8lLHBsYWNlaG9sZGVyR0Y3LyUwZm9udF9zdHlsZV9uYW1lR1ElVGV4dEYnRmduLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGL0YyRltvRjg=">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</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> \303\251 zero, ent\303\243o esses dois VA s\303\243o independentes.
2. Conceder a lei conjunta de </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> quando os dois VAs s\303\243o independentes.</Font></Text-field>
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