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 sommations Pierre Lantagne \251 septembre 2000Coll\350ge de Maisonneuveplantag@edu.cmaisonneuve.qc.ca

Dans ce laboratoire, vous allez explorer la notation math\351matique S ( sigma majuscule est une lettre de l'alphabet grec) et sa transposition dans Maple. La notation sigma (S) a \351t\351 introduite par le math\351maticien Leonard Euler (1707-1783) pour symboliser une addition de termes cons\351cutifs.La somme de termes cons\351cutifs NiMmJSJhRzYjIiIi + NiMmJSJhRzYjIiIj + NiMmJSJhRzYjIiIk + ... + NiMmJSJhRzYjLCYlIm5HIiIiRighIiI= + NiMmJSJhRzYjJSJuRw== est symbolis\351e par l'expression NiMtJSRTdW1HNiQmJSJhRzYjJSJrRy9GKTsiIiIlIm5Ho\371 la lettre k est appel\351e variable de sommation. Le r\351f\351rentiel de la variable k est l'ensemble des entiers Z. La valeur 1 est la valeur initiale de la variable de sommation k, et n est la valeur finale qui est ici ind\351finie :NiMvLSUkU3VtRzYkJiUiYUc2IyUia0cvRio7IiIiJSJuRywoJkYoNiNGLUYtJkYoNiMiIiNGLSZGKDYjIiIkRi0= + ... + NiMsJiYlImFHNiMsJiUibkciIiJGKSEiIkYpJkYlNiNGKEYpLa macro-commande sum() de la biblioth\350que principale permet de transposer une sommation ind\351finie dans Maple.sum(a[k],k=1..n);Le choix de la lettre utilis\351e pour sp\351cifier la variable de sommation est arbitraire. Les lettres, i, j, k, et l servent le plus souvent comme variables de sommation. NiMvLSUkU3VtRzYkJiUiYUc2IyUia0cvRio7IiIiJSJuRy1GJTYkJkYoNiMlImlHL0YzRiw= = NiMmJSJhRzYjIiIi + NiMmJSJhRzYjIiIj + NiMmJSJhRzYjIiIk + ... + NiMmJSJhRzYjLCYlIm5HIiIiRighIiI= + NiMmJSJhRzYjJSJuRw==sum(a[i],i=1..6); sum(a[j],j=1..6); sum(a[k],k=1..6);La variable de sommation est en quelque sorte une variable muette.La valeur initiale de la variable de sommation peut \352tre un entier quelconque: NiMtJSRTdW1HNiQmJSJhRzYjJSJrRy9GKTsiIiQiIig= = NiMmJSJhRzYjIiIk + NiMmJSJhRzYjIiIl + NiMmJSJhRzYjIiIm + NiMmJSJhRzYjIiIn + NiMmJSJhRzYjIiIosum(a[k],k = 3 .. 7);NiMvLSUkU3VtRzYkJiUiYkc2IyUiaUcvRio7LCQiIiQhIiIiIiUsMCZGKDYjRi0iIiImRig2IywkIiIjRi9GNCZGKDYjLCRGNEYvRjQmRig2IyIiIUY0JkYoNiNGNEY0JkYoNiNGOEY0JkYoNiNGLkY0sum(b[i],i = -3 .. 4);REMARQUE NiMtJSRTdW1HNiQmJSJhRzYjJSJrRy9GKTslIm1HJSJuRw==Habituellement, en math\351matique, la valeur initiale de la variable de sommation est un entier inf\351rieur \340 la valeur finale de la variable, c'est-\340-dire que l'on a ordinairement m < n :NiMvLSUkU3VtRzYkJiUiYUc2IyUia0cvRio7LCQiIighIiIsJCIiIkYvLDAmRig2I0YtRjEmRig2IywkIiInRi9GMSZGKDYjLCQiIiZGL0YxJkYoNiMsJCIiJUYvRjEmRig2IywkIiIkRi9GMSZGKDYjLCQiIiNGL0YxJkYoNiNGMEYx Dans les cas inhabituels o\371 la valeur initiale est sup\351rieure \340 la valeur finale, soit m > n, l'\351valuateur donne pour r\351sultat la sommationNiMtJSRTdW1HNiQmJSJhRzYjJSJrRy9GKTslIm1HJSJuRw== = NiMsJC0lJFN1bUc2JCYlImFHNiMlImtHL0YqOywmJSJuRyIiIkYvRi8sJiUibUdGL0YvISIiRjI=Par exemple, soit la somme NiMtJSRTdW1HNiQmJSJhRzYjJSJrRy9GKTsiIigiIiI=sum(a[k],k = 7 .. 1);La macro-commande sum() poss\350de une forme inerte qui permet de bien documenter un \351ventuel d\351veloppement sous la forme d'une \351galit\351. Sum(a[k],k=3..7)=sum(a[k],k=3..7);Remarquez comment l'afficheur a pr\351sent\351 le r\351sultat pour sigma : le caract\350re sigma est en noir. Il en sera toujours ainsi lorsqu'on impose \340 l'afficheur de pr\351senter un r\351sultat qui inclus la forme inerte d'un \351l\351ment de syntaxe Maple. C'est le cas ici avec la macro-commande Sum(). Cela permet \340 l'usager de faire la diff\351rence entre la mise en forme impos\351e par la forme inerte et la pr\351sentation du r\351sultat lorsque l'\351valuateur n'a pu obtenir la simplification de la requ\352te. En effet, lorsqu'il n'y a pas simplification par l'\351valuateur, l'afficheur donne pour r\351sultat la requ\352te telle quelle. Il en sera de m\352me avec Diff(), Int(), Limit(), Product, etc. Par exempleSum(a[k],k=1..n)=sum(a[k],k=1..n);

L'\351valuateur conna\356t bien s\373r les r\350gles \351l\351mentaires de la sommation. L'extension student va nous aider \340 le montrer.with(student):R\310GLE 1Sum(1,k=1..n)=sum(1,k=1..n);R\310GLE 2Sum(c,k=1..n)=sum(c,k=1..n);R\310GLE 3Sum(A*b[k],k=1..n)=expand(Sum(A*b[k],k=1..n));R\310GLE 4Sum(A*b[k]+B*b[k],k=1..n)=expand(Sum(A*b[k]+B*b[k],k=1..n));Enfin, une sommation peut \352tre scind\351e en deux sommations contigu\353s pour tout entier m tel que 1 < m < n :R\310GLE 5Sum(b[k],k=1..n)=Sum(b[k],k=1..m)+Sum(b[k],k=m+1..n);R\351ciproquement, deux sommations contigu\353s peuvent \352tre unifi\351es en une seule sommation avec la macro-commande combine()de la biblioth\350que principale. Sum(b[k],k=-5..12)+Sum(b[k],k=13..36); ``=combine(%);L'\351valuateur est capable de simplifier automatiquement un tr\350s grand nombre de sommations ind\351finies. Par exemple, demandez \340 l'\351valuateur les sommes suivantes:NiQtJSRzdW1HNiQlImtHL0YmOyIiIiUibkctRiQ2JCokRiYiIiNGJw== et NiMtJSRzdW1HNiQqJCUia0ciIiQvRic7IiIiJSJuRw==.Sum(k,k = 1 .. n)=sum(k,k = 1 .. n);Sum(k^2,k = 1 .. n)=sum(k^2,k = 1 .. n);Sum(k^3,k = 1 .. n)=sum(k^3,k = 1 .. n);Toutes les r\351ponses pr\351c\351dentes peuvent, \351videmment, \352tre simplifi\351es - sous la forme d\351velopp\351e avec normal( ,expanded()) et - sous la forme factoris\351e avec factor(). Par exemple:Sum(k^3,k = 1 .. n)=sum(k^3,k = 1 .. n); ``=normal(sum(k^3,k = 1 .. n),expanded); ``=factor(sum(k^3,k = 1 .. n));Pour obtenir la formule de la somme ind\351finie NiMtJSRTdW1HNiQsKComIiIkIiIiKiQlImtHIiIlRilGKSokRisiIiMhIiJGKUYpL0YrO0YpJSJuRw==, il n'est pas n\351cessaire de faire intervenir explicitement les propri\351t\351s du symbole de sommation. L'\351valuateur donnera directement le r\351sultat:Sum(3*k^4-k^2+1,k = 1 .. n)=factor(sum(3*k^4-k^2+1,k = 1 .. n));Si on d\351sire obtenir la d\351composition d'une sommation \340 l'aide des propri\351t\351s du symbole de sommation, il faut utiliser la macro-commande expand()(Il est n\351cessaire que l'extension student ait \351t\351 rendu disponible).# with(student): Sum(3*k^4-k^2+1,k = 1 .. n)=expand(Sum(3*k^4-k^2+1,k = 1 .. n));

En math\351matique, on rencontre dans le calcul matriciel des sommations o\371 interviennent deux variables de sommation : NiMtJSRzdW1HNiQtRiQ2JComJiUieEc2IyUiaUciIiImJSJ5RzYjJSJqR0YtL0YxO0YtJSJtRy9GLDtGLSUibkc=.La double sommation est en fait une sommation d'une sommation. Dans les textes math\351matiques, les doubles sommations s'\351crivent habituellement sans parenth\350ses. Cela est la cons\351quence de la r\350gle 1 qu'on verra \340 la sous-section suivante.Dans la sommation imbriqu\351e NiMtJSRzdW1HNiQqJiYlInhHNiMlImlHIiIiJiUieUc2IyUiakdGKy9GLztGKyUibUc=, les variables indic\351es NiMmJSJ4RzYjJSJpRw== jouent un r\364le de constante face \340 la sommation sur j. On a donc l'\351galit\351 : NiMtJSRzdW1HNiQqJiYlInhHNiMlImlHIiIiLUYkNiQmJSJ5RzYjJSJqRy9GMTtGKyUibUdGKy9GKjtGKyUibkc=.Sum(Sum(x[i]*y[j],j=1..m),i=1..n)=Sum(x[i]*Sum(y[j],j=1..m),i=1..n);Et on \351crit``=Sum(x[i],i=1..n)*Sum(x[j],j=1..m);Obtenons ce dernier d\351veloppement \340 l'aide de expand() appliqu\351e directement sur la double sommation.Sum(Sum(x[i]*y[j],j=1..m),i=1..n)=expand(Sum(Sum(x[i]*y[j],j=1..m),i=1..n));On rencontre donc rarement, en math\351matique, la multiplication de deux sommations car il s'agit en fait d'une double sommation. La preuve est assez simple \340 faire. Illustrons plut\364t ici la v\351racit\351 de cette affirmation avec le d\351veloppement limit\351 suivant : NiMtJSRTdW1HNiQtRiQ2JComJiUieEc2IyUiaUciIiImJSJ5RzYjJSJqR0YtL0YxO0YtIiIjL0YsO0YtIiIl. D'une part, le d\351veloppement de la double sommation donne ceci :Sum(Sum(x[i]*y[j],j=1..2),i=1..4)=sum(sum(x[i]*y[j],j=1..2),i=1..4);Et d'autre part, le d\351veloppement de la multiplication des deux sommation donne ceci :Sum(y[j],j = 1 .. 2)*Sum(x[i],i = 1 .. 4)=sum(y[j],j = 1 .. 2)*sum(x[i],i = 1 .. 4);expand(%);On a donc bien, ici, l'\351galit\351 NiMvLSUkU3VtRzYkLUYlNiQqJiYlInhHNiMlImlHIiIiJiUieUc2IyUiakdGLi9GMjtGLiIiIy9GLTtGLiIiJSomLUYlNiRGL0YzRi4tRiU2JEYqRjZGLg== qui est v\351rifi\351e.

En ce qui concerne la double sommation, l'\351valuateur reconna\356t la r\350gle suivante. R\310GLE 1Dans une double sommation, on peut sans faute, permuter les deux \240\253 S \273 : NiMvLSUkc3VtRzYkLUYlNiQqJiYlInhHNiMlImlHIiIiJiUieUc2IyUiakdGLi9GMjtGLiUibUcvRi07Ri4lIm5HLUYlNiQtRiU2JEYpRjZGMw==.Sum(Sum(x[i]*y[j],j = 1 .. m),i = 1 .. n) = Sum(Sum(x[i]*y[j],i = 1 .. n),j = 1 .. m);Illustrons la r\350gle 1 par le d\351veloppement limit\351 suivant : NiMtJSRTdW1HNiQtRiQ2JComJiUieEc2IyUiaUciIiImJSJ5RzYjJSJqR0YtL0YxO0YtIiIlL0YsO0YtIiIj .Sum(Sum(x[i]*y[j],j = 1 .. 4),i = 1 .. 2)=sum(sum(x[i]*y[j],j = 1 .. 4),i = 1 .. 2);Sum(Sum(x[i]*y[j],i = 1 .. 2),j = 1 .. 4)=sum(sum(x[i]*y[j],i = 1 .. 2),j = 1 .. 4);Terminons la liste des r\350gles en ajoutant les quatres r\350gles suivantes.R\310GLE 2# with(student):Sum(Sum(a[i,j]+b[i,j],j = 1 .. m),i = 1 .. n) = expand(Sum(Sum(a[i,j]+b[i,j],j = 1 .. m),i=1..n));R\310GLE 3Sum(Sum(k*a[i,j],j = 1 .. m),i = 1 .. n) = expand(Sum(Sum(k*a[i,j],j = 1 .. m),i = 1 .. n));R\310GLE 4Sum(Sum(x[i],j = 1 .. m),i = 1 .. n) = expand(Sum(sum(x[i],j = 1 .. m),i = 1 .. n)); Sum(Sum(y[j],j = 1 .. m),i = 1 .. n) = expand(sum(Sum(y[j],j = 1 .. m),i = 1 .. n));R\310GLE 5Sum(Sum(k,j = 1 .. m),i = 1 .. n) = sum(sum(k,j = 1 .. m),i = 1 .. n);

La macro-commande sum()est la macro-commande \340 utiliser pour obtenir formellement l'expression d'une somme ind\351finie, qu'elle soit finie ou infinie. D\351velopper, sous la forme d'une \351galit\351, la somme ind\351finie NiMtJSRTdW1HNiQpIiImLCYlImtHIiIiRiohIiIvRik7RiolIm5H.Sum(5^(k-1),k = 1 .. n)=sum(5^(k-1),k = 1 .. n);``=simplify(sum(5^(k-1),k = 1 .. n),symbolic);La somme ind\351finie pr\351c\351dente est une somme finie. Avec la macro-commande sum(), il est possible aussi d'obtenir une somme infinie.Sum((-1)^k*1/k,k=1..infinity)=sum((-1)^k*1/k,k=1..infinity); Un tel r\351sulat d\351coule de l'\351tude des s\351ries infinies, ce qui d\351borde le niveau du cours EED.Dans certains cas, la formulation du r\351sultat est exprim\351e avec des expressions math\351matiques inconnues du niveau coll\351gial.Sum(k/(k+1),k=0..n) = sum(k/(k+1), k=0..n);O\371 le nombre NiMlJmdhbW1hRw== (gamma) est la constante d'Euler valant approximativement:gamma=evalf(gamma,20);et la fonction d'Euler NiMlJFBzaUc= (Psi) \351tant d\351finie par NiMtJSVEaWZmRzYkLSUjbG5HNiMtJSZHYW1tYUc2IyUieEdGLA== o\371 NiMvLSUmR2FtbWFHNiMlInhHLSUkSW50RzYkKiYtJSRleHBHNiMsJCUidEchIiIiIiIpRjAsJkYnRjJGMkYxRjIvRjA7IiIhJSlpbmZpbml0eUc=.Ne soyez pas effray\351 par tous ces d\351tails, c'est seulement pour \351pater la galerie...Lorsqu'il s'agit d'obtenir la somme d'un nombre fini de valeurs num\351riques, c'est-\340-dire lorsqu'on cherche explicitement une somme num\351rique plut\364t qu'une formule, il est recommand\351 d'utiliser la macro-commande add()m\352me si la macro-commande sum() pourrait donner explicitement la somme.Calculer NiMtJSRTdW1HNiQsJiomIiIkIiIiKiQlImtHIiIjRilGKUYpRikvRis7IiIlIiNQ.add(3*k^2+1,k = 4 .. 37);Il est quand m\352me n\351cessaire d'utiliser la forme inerte de sum() afin de documenter la somme avec une \351galit\351: Sum(3*k^2+1,k = 4 .. 37)=add(3*k^2+1,k = 4 .. 37);R\351sumons. Pour op\351rer symboliquement une sommation ind\351finie, on utilise sum() tandis que pour op\351rer num\351riquement une sommation d\351finie, on utilise add().Sur les intervalles num\351riques sum() et add() donne la somme:add(k,k=1..12); sum(k,k=1..12); Tandis que sur les intervalles symboliques, add() est inop\351rante:add(k,k=1..n); sum(k,k=1..n);En fait, la macro-commande add() est une petite proc\351dure d\351finie \340 l'aide d'une structure de contr\364le appel\351e boucle for: add(Formule, k=m..n) \326 S := 0; Valeur := i; for i from m to n do S := S+Formule end do; i := Valeur; S; # Affichage du r\351sultat Tandis que la macro-commande sum() fait appel \340 un ensemble de r\351sulats d\351coulant de l'\351tude des polyn\364mes.C'est ce qui explique son usage lorsqu'on effectue un traitement analytique d'une sommation.

\300 l'aide de la macro-commande add(), obtenez la somme des 100 premiers nombres impairs1 + 3 + 5 + 7 + 9 + ... + 199avec comme valeur initale de la variable de sommation, a) la valeur 0b) la valeur 1

\300 l'aide de la macro-commande sum(), obtenez la formule factoris\351e de la somme des n premiers nombres impairs cons\351cutifs avec comme valeur initiale de la variable de sommation,a) la valeur 0b) la valeur 1

\300 l'aide de la macro-commande sum(), v\351rifiez que la somme des n premier termes donne, (Vous devez touver le terme g\351n\351ral de la sommation.) a) 1 + 2 + 3 + 4 + 5 + ... = NiMqKCUibkciIiIsJkYkRiVGJUYlRiUiIiMhIiI=b) NiMqJCIiIiIiIw== + NiMqJCIiI0Yk + NiMqJCIiJCIiIw== + NiMqJCIiJSIiIw== + NiMqJCIiJiIiIw== + ... = NiMqKiUibkciIiIsJkYkRiVGJUYlRiUsJiomIiIjRiVGJEYlRiVGJUYlRiUiIichIiI=c)NiMqJCIiIiIiJA== + NiMqJCIiIyIiJA== + NiMqJCIiJEYk + NiMqJCIiJSIiJA== + NiMqJCIiJiIiJA== + ... = NiMqKCUibkciIiMsJkYkIiIiRidGJ0YlIiIlISIic) NiMsKComIiIiRiUqKEYlRiUiIiNGJSIiJEYlISIiRiUqJkYlRiUqKEYnRiVGKEYlIiIlRiVGKUYlKiZGJUYlKihGKEYlRixGJSIiJkYlRilGJQ==+ ... = NiMqKCUibkciIiIsJkYkRiUiIiRGJUYlKigiIiVGJSwmRiRGJUYlRiVGJSwmRiRGJSIiI0YlRiUhIiI=d) 1 + 7 + 13 + 19 + ... = NiMqJiUibkciIiIsJiomIiIkRiVGJEYlRiUiIiMhIiJGJQ==e) NiMsKiokIiImIiIhIiIiKiRGJUYnRicqJEYlIiIjRicqJEYlIiIkRic= + ... = NiMqJiwmKSIiJiUibkciIiJGKCEiIkYoIiIlRik=

Pour les exercices ci-dessous, documentez votre solution comme l'exemple suivant. ExempleObtenez la somme infinie NiMqJiIiIkYkIiIkISIi + NiMqJiIiIkYkIiM6ISIi + NiMqJiIiIkYkIiNOISIi + NiMqJiIiIkYkIiNqISIi + NiMqJiIiIkYkIiMqKiEiIg== + NiMqJiIiIkYkIiRWIiEiIg== + ... + NiMqJiIiIkYkKiYsJiomIiIjRiQlImtHRiRGJEYkISIiRiQsJkYnRiRGJEYkRiRGKg== + ... de deux mani\350res diff\351rentes - en posant directementNiMtJSRTdW1HNiQmJSJhRzYjJSJrRy9GKTsiIiIlKWluZmluaXR5Rw== et - en posantNiMtJSZMaW1pdEc2JC0lJFN1bUc2JCYlImFHNiMlImtHL0YsOyIiIiUibkcvRjAlKWluZmluaXR5Rw==.et v\351rifiez si l'\351valuateur a, dans chaque cas, donn\351 un r\351sultat \351quivalent.SolutionP:=k->1/((2*k-1)*(2*k+1));seq(P(k),k=1..6);Sum(P(k),k=1..infinity)=sum(P(k),k=1..infinity);Sum(P(k),k=1..infinity)=Limit(Sum(P(k),k=1..n),n=infinity); ``=Limit(sum(P(k),k=1..n),n=infinity); ``=limit(sum(P(k),k=1..n),n=infinity); Dans les deux cas, l'\351valuateur a donn\351 un r\351sultat \351quivalent.a) NiMsLComIiIiRiUiIiQhIiJGJSomRiVGJSIiKUYnRiUqJkYlRiUiIzpGJ0YlKiZGJUYlIiNDRidGJSomRiVGJSIjTkYnRiU= + ... + NiMqJiIiIkYkKiYlImtHRiQsJkYmRiQiIiNGJEYkISIi + ...b) NiMsLiomIiIiRiUiIiUhIiJGJSomRiVGJSIjNUYnRiUqJkYlRiUiIz1GJ0YlKiZGJUYlIiNHRidGJSomRiVGJSIjU0YnRiUqJkYlRiUiI2FGJ0Yl + ... + NiMqJiIiIkYkKiYlImtHRiQsJkYmRiQiIiRGJEYkISIi + ...c) NiMsLiomIiIiRiUiIiMhIiJGJSomRiVGJSIiJEYnRiUqJkYlRiUiIilGJ0YlKiZGJUYlIiNJRidGJSomRiVGJSIkVyJGJ0YlKiZGJUYlIiRTKUYnRiU= + ... + NiMqJiUia0ciIiItJSpmYWN0b3JpYWxHNiMsJkYkRiVGJUYlISIi + ...

\300 l'aide de la macro-commande add(), \351valueza) NiMtJSRzdW1HNiQtRiQ2JComLCYqJCUiaUciIiMiIiJGLSEiIkYtLCYlImpHRi1GLUYtRi0vRjA7Ri0iIiUvRitGMg==b) NiMtJSRzdW1HNiQtRiQ2JCwmKiYlImlHIiIiJSJqR0YrRisqJiIiI0YrRipGK0YrL0YsO0YrIiInL0YqO0YrIiIl

Montrez formellement que NiMvKiQtJSRzdW1HNiQmJSJ4RzYjJSJpRy9GKzsiIiIlIm5HIiIjLUYmNiQtRiY2JComRihGLiZGKTYjJSJqR0YuL0Y4Ri1GLA==

Montez formellement que NiMvKiQtJSRzdW1HNiQsJiYlInhHNiMlImlHIiIiRi1GLS9GLDtGLSUibkciIiMsKC1GJjYkLUYmNiQqJkYpRi0mRio2IyUiakdGLS9GOkYvRi5GLSooRjFGLUYwRi0tRiY2JEYpRi5GLUYtKiRGMEYxRi0=

Similairement \340 ce qu'on fait avec le symbole S, la lettre NiMlI3BpRw== majuscule de l'alphabet grec, soit P, est utlilis\351e pour symboliser une multiplication de facteurs cons\351cutifs : NiMtJShwcm9kdWN0RzYkJiUiYUc2IyUia0cvRik7IiIiJSJuRw== = NiMqKCYlImFHNiMiIiJGJyZGJTYjIiIjRicmRiU2IyIiJEYn ... NiMqJiYlImFHNiMsJiUibkciIiJGKSEiIkYpJkYlNiNGKEYp.Product(a[k],k=1..n);Product(a[k],k=1..7)=product(a[k],k=1..7);D\351veloppez les multiplications suivantes.a) NiMtJShQcm9kdWN0RzYkJSJrRy9GJjsiIiIiIig=b) NiMtJShQcm9kdWN0RzYkKigsJiUia0ciIiJGKUYpRikiIiMhIiJGKEYpL0YoOyIiJCIiKg== c) NiMtJShQcm9kdWN0RzYkKiQqJiUia0ciIiIsJkYoRikiIiNGKSEiIiIiJC9GKDtGKSIjPw==d) NiMtJShQcm9kdWN0RzYkKiQqJiUieEciIiIsJkYoRikiIiNGKSEiIiIiJC8lImtHO0YpIiM/e) NiMtJShQcm9kdWN0RzYkLCYqJiIiIyIiIiUia0dGKUYpIiM6ISIiL0YqOywkIiImRixGMA==f) NiMtJShQcm9kdWN0RzYkLCYqKCIiIyIiIiUia0dGKSUjcGlHRilGKUYpRikvRio7LCQiIiYhIiJGLw==

Pierre Lantagne \251, septembre 2000