JSFH

restart ;

2+2 ;

IiIl

a := sqrt(2) ;

KiQiIiMjIiIiRiM=

ic commentaire : cette fonction evalue a num\303\251riquement evalf(a) ;

JCIraU5AOTkhIio=

a^3 ;

LCQqJCIiIyMiIiJGJEYk

Manipulations symboliques. b :=(1+a)^2 ;

KiQsJiIiIkYkKiQiIiMjRiRGJkYkRiY=

expand(b);

LCYiIiQiIiIqJCIiIyNGJEYmRiY=

P:=x^3-x-1;

LCgqJEkieEc2IiIiJCIiIkYkISIiRihGJw==

Q:=2*(x-1)^2-3*x+3;

LCgqJCwmSSJ4RzYiIiIiISIiRiciIiNGKUYlISIkIiIkRic=

factor(Q) ;

KiYsJkkieEc2IiIiIiEiIkYmRiYsJkYkIiIjISImRiZGJg==

regroupe les coefficients suivant les puissances de x. collect(Q,x);

LCgqJEkieEc2IiIiI0YmRiQhIigiIiYiIiI=

calcul de P(a) : eval(P, x=a) ;

LCYqJCIiIyMiIiJGJEYmISIiRiY=

On peut d\303\251finir une FONCTION polyn\303\264me : f := x -> x^4-1 ;

Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJDkkIiIlIiIiISIiRi1GJUYlRiU=

f(x) ;

LCYqJEkieEc2IiIiJSIiIiEiIkYn

f(a) ;

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P1 := diff(P,x) ;

LCYqJEkieEc2IiIiIyIiJCEiIiIiIg==

int(P1,x);

LCYqJEkieEc2IiIiJCIiIkYkISIi

gcd(Q,f(x));

LCZJInhHNiIiIiIhIiJGJQ==

F:=f(x) ;

LCYqJEkieEc2IiIiJSIiIiEiIkYn

R2:=rem(F,Q,x); ### (ici commentaire : division euclidienne)

LCYjISQuIyIiKSIiIkkieEc2IiMiJC4jRiU=

R3:=rem(Q,R2,x);

IiIh

plot(Q, x=-3..3 ) ;

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

de l'aide ! help ?plot

n:=6; f:=1; for i from 2 to n do f:=f*i ; end do ;

IiIn

IiIi

IiIj

IiIn

IiND

IiQ/Ig==

IiQ/KA==

Le m\303\252me sans les r\303\251sultats interm\303\251diaires : utiliser ":" n:=6; f:=1: for i from 2 to n do f:=f*i ; end do : f;

IiIn

IiQ/KA==

On cr\303\251e une fonction factorielle. Entr\303\251e ; n, entier ; Sortie : f, entier qui vaut n! factorielle := proc(n) local f, i ; ## variables internes \303\240 la proc\303\251dure f:=1: for i from 2 to n do f:=f*i ; end do : RETURN(f); end proc ;

Zio2I0kibkc2IjYkSSJmR0YlSSJpR0YlRiVGJUMlPjgkIiIiPyg4JSIiI0YsOSRJJXRydWVHJSpwcm90ZWN0ZWRHPkYrKiZGK0YsRi5GLC1JJ1JFVFVSTkdGMjYjRitGJUYlRiU=

factorielle(12) ;

IiorOyt6JQ==

if /then/else if 3=2 then Ah; else Oh; end if;

SSNPaEc2Ig==

i:=1; while i<12 do i:=i+1; end do;

IiIi

IiIj

IiIk

IiIl

IiIm

IiIn

IiIo

IiIp

IiIq

IiM1

IiM2

IiM3

?asympt asympt(factorial(N),N);

KigsMCooIiIjIyIiIkYlSSNQaUclKnByb3RlY3RlZEdGJiokSSJORzYiISIiI0YtRiVGJyooRiVGJkYoRiZGKkYmI0YnIiM3KihGJUYmRihGJkYqIyIiJEYlI0YnIiQpRyooRiVGJkYoRiZGKiMiIiZGJSMhJFIiIiZTPSYqKEYlRiZGKEYmRiojIiIoRiUjISRyJiIoPyQpWyMqKEYlRiZGKEYmRiojIiIqRiUjIid6UTsiKiEpKT0hNCMtSSJPR0YpNiMqJEYqIyIjNkYlRidGJylGKkYrRi0tSSRleHBHNiRGKUkoX3N5c2xpYkdGLDYjRitGLQ==

series( factorial(m), m=infinity, 1);

KigsJiooIiIjIyIiIkYlSSNQaUclKnByb3RlY3RlZEdGJiokSSJtRzYiISIiI0YtRiVGJy1JIk9HRik2IyokRipGJkYnRicpRipGK0YtLUkkZXhwRzYkRilJKF9zeXNsaWJHRiw2I0YrRi0=

s\303\251quences ("suite" finie) S := 2,3,1,a,Pi,ln(5),x, 3,2,1 ;

NiwiIiMiIiQiIiIqJEYjI0YlRiNJI1BpRyUqcHJvdGVjdGVkRy1JI2xuRzYkRilJKF9zeXNsaWJHNiI2IyIiJkkieEdGLkYkRiNGJQ==

S[5] ;

SSNQaUclKnByb3RlY3RlZEc=

Liste : L := [S] ;

NywiIiMiIiQiIiIqJEYjI0YlRiNJI1BpRyUqcHJvdGVjdGVkRy1JI2xuRzYkRilJKF9zeXNsaWJHNiI2IyIiJkkieEdGLkYkRiNGJQ==

nombre d'\303\251l\303\251ments de la liste ; nops(L) ;

IiM1

L[1];

IiIj

L[12];

Error, invalid subscript selector

Ajouter un \303\251l\303\251ment ; on passe en s\303\251quence, et on ajoute l'\303\251l\303\251ment : S2:= op(L) ;

NiwiIiMiIiQiIiIqJEYjI0YlRiNJI1BpRyUqcHJvdGVjdGVkRy1JI2xuRzYkRilJKF9zeXNsaWJHNiI2IyIiJkkieEdGLkYkRiNGJQ==

L2 := [ S2, 67,42];

Ny4iIiMiIiQiIiIqJEYjI0YlRiNJI1BpRyUqcHJvdGVjdGVkRy1JI2xuRzYkRilJKF9zeXNsaWJHNiI2IyIiJkkieEdGLkYkRiNGJSIjbiIjVQ==

L2 := [ op(L), 67,42];

Ny4iIiMiIiQiIiIqJEYjI0YlRiNJI1BpRyUqcHJvdGVjdGVkRy1JI2xuRzYkRilJKF9zeXNsaWJHNiI2IyIiJkkieEdGLkYkRiNGJSIjbiIjVQ==

Ensemble : presque pareil, mais sans ordre et sans r\303\251p\303\251titions ; ensemble := {S} ;

PCkiIiIiIiMiIiRJI1BpRyUqcHJvdGVjdGVkR0kieEc2IiokRiQjRiNGJC1JI2xuRzYkRidJKF9zeXNsaWJHRik2IyIiJg==

nops(ensemble) ;

IiIo

ensemble union {4} ;

PCoiIiIiIiMiIiQiIiVJI1BpRyUqcHJvdGVjdGVkR0kieEc2IiokRiQjRiNGJC1JI2xuRzYkRihJKF9zeXNsaWJHRio2IyIiJg==

ensemble minus {3,8,x} ;

PCciIiIiIiNJI1BpRyUqcHJvdGVjdGVkRyokRiQjRiNGJC1JI2xuRzYkRiZJKF9zeXNsaWJHNiI2IyIiJg==

On peut charger des librairies en m\303\251moire :

with(LinearAlgebra);

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

Pour enlever la valeur de a; a := 'a' ;

SSJhRzYi

a^2 ;

KiRJImFHNiIiIiM=