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Calcul formel: mode d'emploi: exemples en Maple by Claude Gomez, Bruno Salvy, Paul Zimmermann

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By Claude Gomez, Bruno Salvy, Paul Zimmermann

Gomez C., Salvy B., Zimmermann P. Calcul formel (Dunod, 1995)(ISBN 2225847800)

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Extra info for Calcul formel: mode d'emploi: exemples en Maple

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Voici comment elle pourrait s’´ecrire en Maple: simple member:=proc(a,l:list,pos:name) local i, nb elts; nb elts:=nops(l); for i to nb elts while a<>l[i] do od; if i=nb elts+1 then false else pos:=i−1; true fi end: Il nous reste ` a d´ecrire la seconde fa¸con d’utiliser la boucle do : l’appel avec in. Dans ce cas, la variable d’indice, au lieu de prendre des valeurs enti`eres dans une progression arithm´etique, prend pour valeurs successives les sousexpressions de l’expression donn´ee. La d´efinition pr´ecise de ce que l’on entend par sous-expression sera donn´ee en §2, disons simplement pour l’instant qu’il s’agit des op´erandes de l’expression.

7. Exercices. Ces exercices visent essentiellement `a faire ex´ecuter des calculs simples en apprenant progressivement `a se d´ebrouiller `a l’aide de la documentation en ligne. Pour chaque exercice, sont indiqu´es entre crochets les items de la documentation en ligne `a consulter. √ 1. Calculer la valeur num´erique de eπ 163 −262537412640768744 avec successivement 10, 20, 30, 40 et 50 chiffres significatifs. Commentaires. [evalf] 2. Montrer que (z + 1)(z + j)(z + j 2 ) = (1 + z)(1 + jz)(1 + j 2 z) o` u j est une racine cubique de l’unit´e.

Celles qui suivent cr´eent des expressions `a partir d’expressions existantes. Combin´ees avec les primitives de la premi`ere section, elles forment tout l’arsenal du programmeur Maple. Les principales proc´edures qui cr´eent de nouveaux objets `a partir d’expressions existantes sont : subsop, convert, subs, select. Il faut noter que ces proc´edures ne modifient pas leur argument. La plupart des objets que manipule Maple ne peuvent en effet pas ˆetre modifi´es. Les proc´edures que nous allons pr´esenter cr´eent des copies alt´er´ees de leur argument.

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