**TI92**Group file dated 01/08/00, 11:19nranlnumirbissecichkmisiKdifdiviSdifdivs elimgaus@ fixgaus gausjacb gausseidjacobidlagrangelegendremisndre/newtoneortopolypminquadquadgauskreplace9secante)Z:(fun,var,a,b,erro) Prgm Local fa,fb,mdp,fmid,sgn Define sgn(num)=when(num=0,"0",when(num>0,"+","-")) fix(approx(a))a fix(approx(b))b fix(approx(fun|var=a))fa fix(approx(fun|var=b))fb ClrIO Disp "f(a)=",fa Disp "f(b)=",fb If fa*fb>0 Then Disp f(a)*f(b)>0 Stop EndIf Disp " a("&sgn(fa)&") b("&sgn(fb)&") mid fmid +/-" Loop fix(approx((a+b)/2))mdp If fix(approx((b-a)/2))0 Then mdpa Else mdpb EndIf EndLoop EndPrgm A(g,var,a,b) Prgm Local dg,mx,mode,grph setMode("Graph","SEQUENCE")mode setGraph("Seq Axes","WEB")grph 1.nmin 32.nmax 1.plotStrt 1.plotStep axmin bxmax 1.xscl expr(string(g)&"|"&string(approx(fMin(g,var)|vara and varb)))ymin expr(string(g)&"|"&string(approx(fMax(g,var)|vara and varb)))ymax 1.yscl DelVar u1 expr(replace(string(g),string(x),"u1(n-1)")&"u1(n)") (a+b)/2ui1 (g,var)dg expr(string(var)&"|"&string(approx(fMax(abs(dg),var)|vara and varb)))mx ClrIO Disp "g("&string(var)&")=",g Disp "min(g("&string(var)&"))=",ymin Disp "max(g("&string(var)&"))=",ymax Pause Disp "g'("&string(var)&")=",dg Disp "max|g'("&string(var)&")|=",approx(abs(dg|var=mx)) Pause ClrDraw Style 1,"THICK" ZoomSqr LineHorz a LineHorz b LineVert a LineVert b LineTan limit(g,var,x),mx Trace DelVar u1 DelVar ui1 setGraph("Seq Axes",grph) setMode("Graph",mode) setMode("Split 1 App","Home") EndPrgm #(xxx,yyy) Func Local sublist,nn dim(xxx)nn Define sublist(ll,i1,i2)=seq(ll[ii],ii,i1,i2) If nn=1 Return fix(yyy[1]) Return fix(difdiv(sublist(xxx,2,nn),sublist(yyy,2,nn))-difdiv(sublist(xxx,1,nn-1),sublist(yyy,1,nn-1)))/(xxx[nn]-xxx[1]) EndFuncU/(xxx,yyy) Prgm Local ii,nn,aa,tmp dim(xxx)nn fix(xxx)xxx fix(yyy)yyy ({xxx,yyy})aa ClrIO Disp xxx,yyy For ii,1,nn-1 seq(fix(approx((aa[jj+1,ii+1]-aa[jj,ii+1])/(aa[jj+1,1]-aa[jj,1]))),jj,1,nn-ii)tmp Disp tmp augment(aa,listmat(augment(tmp,newList(ii)),1))aa EndFor aaanswer EndPrgm ܓb(mat,flag) Prgm Local i,j,k,n,m rowDim(mat)n fix(mat)mat ClrIO Disp mat Pause For i,1,n-1 If when(flag,true,false,false) Then ik For j,i+1,n If abs(mat[j,i])>abs(mat[k,i]) jk EndFor If ki rowSwap(mat,i,k)mat EndIf For j,i+1,n fix(approx(mat[j,i]/(mat[i,i])))m fix(approx(mRowAdd(m,mat,i,j)))mat 0.mat[j,i] EndFor Disp mat Pause EndFor fix(approx(rref(mat)))mat Disp mat EndPrgmĄY(var) Func If getType(prec)"NUM" Return var Local ffix Define ffix(num)=expr(format(num,"S"&string(prec-1))) approx(var)var If getType(var)="NUM" Return ffix(var) If getType(var)="LIST" Return seq(ffix(var[i]),i,1,dim(var)) If getType(var)="MAT" Return seq(seq(ffix(var[i,j]),j,1,colDim(var)),i,1,rowDim(var)) Return var EndFunc p(a,b,emr,) Prgm Local j,e,n,0 ClrIO 0j rowDim(a)n Loop j+1j 0 approx(seq((b[i,1]-(0[k]*a[i,k],k,1,i-1)-(0[k]*a[i,k],k,i+1,n))/(a[i,i]),i,1,n)) fix() approx(max(abs(-0))/(max(abs())))e fix(e)e Disp j,,e If eabs(mat[k,i]) jk EndFor If ki rowSwap(mat,i,k)mat EndIf For j,i+1,n fix(approx(mat[j,i]/(mat[i,i])))m fix(approx(mRowAdd(m,mat,i,j)))mat 0.mat[j,i] EndFor For j,1,i-1 fix(approx(mat[j,i]/(mat[i,i])))m fix(approx(mRowAdd(m,mat,i,j)))mat 0.mat[j,i] EndFor Disp mat Pause EndFor fix(approx(rref(mat)))mat Disp mat EndPrgm ӥp(kk,xxx) ((x-xxx[ii])/(xxx[kk]-xxx[ii]),ii,1,kk-1)*((x-xxx[ii])/(xxx[kk]-xxx[ii]),ii,kk+1,dim(xxx)) %(nn) Prgm Local ii,tmp,,,pp,px {1}pp ClrIO Disp pp[1] For ii,1,nn Pause (2*ii-1)/ii (ii-1)/ii Disp {,} *x*pp[ii]-when(ii=1,0,*pp[ii-1])tmp Disp tmp augment(pp,{tmp})pp EndFor ppanswer EndPrgm J(gfn,var,emr,) Prgm Local n,e,0 ClrIO 0n Loop n+1n 0 approx(gfn|var=) approx(abs(-0))e Disp n,,e If e-->