\def{integer a1=random(1,-1)*random(1..5)}
\def{integer a2=random(1,-1)*random(1..5)}
\def{integer a3=random(1,-1)*random(1..5)}
\def{integer a4=random(1,-1)*random(1..5)}
\def{integer =random(1,-1)*random(1..5)}
\def{integer u=random(-2..2)}
\def{integer v=random(1,-1)*random(3..4)}
\def{integer w=random(1,-1)*random(5..7)}
\def{text mult=shuffle(3,3,2,2,2)}
\def{integer m1=item(1,\mult)}
\def{integer m2=item(2,\mult)}
\def{integer m3=item(3,\mult)}
\def{text data=pari( [Pol([\a1,\a2, \a3,\a4],x),
(x-(\u))^(\m1)*(x-(\v))^(\m2),(x-(\v))^(\m2)
,(x-(\u))^(\m1),
x-(\u),x-(\v)])}

\def{text P=item(1,\data)}
\def{text Q=item(2,\data)}
\def{text Q1=item(3,\data)}
\def{text Q2=item(4,\data)}
\def{text xu=item(5,\data)}
\def{text xv=item(6,\data)}

\def{text tayl=wims(lines2items  maxima(taylor((\P)/(\Q1),x,\u,\m1-1); 
taylor((\P)/(\Q2),x,\v,\m2-1);taylor((\P)/(\Q1),x,\u,\m1-1)/(x-(\u))^(\m1)
;taylor((\P)/(\Q2),x,\v,\m2-1)/(x-(\v))^(\m2);)
)
}
\def{text tayl1=item(1,\tayl)}
\def{text tayl2=item(2,\tayl)}
\def{text tayl3=item(3,\tayl)}
\def{text tayl4=item(4,\tayl)}
Exemple \reload{<img src="gifs/doc/etoile.gif" alt=" recharger" width="20" height="20">} :
<p>
Soit \(Q = \Q = (\xu)^\m1*(\xv)^\m2) et \(P = \P). Calculons le dveloppement en lments simples de P :
<ul>
<li> en \(x = \u) : 
<p><center> \(\frac{(\xu)^\m1 P}{Q}) = \((\P)/(\Q1))
</center>
<center>\(= (\tayl1)/(1) + (\xu)^\m1 *H_1)
</center>
</li>
<li> en \(x = \v) : 
<p><center> \(\frac{(\xv)^\m2 P}{Q}) = \((\P)/(\Q2))
</center>
<center>\( = (\tayl2)/(1) + (\xv)^\m2 *H_2)
</center>
</li>
</ul>
Comme le degr de P est strictement infrieur au degr de Q, <p>
<center>
\(\frac{P}{Q} =)\( \tayl3 +  \tayl4)
</center>

