# definition of types. To be taken randomly.
# Format:
# line 1 = description
# line 2 = name_y
# line 3 = fn_yx
# line 4 = derivee_yx

du produit $$namei_y = $namei_x*$namei_z
 V
 $a2*$$x^2/($$x-$a1)
 2*$a2*$$x/($$x-$a1)-$a2*$$x^2/($$x-$a1)^2

:de l'aire $$namei_y du triangle <i>OAB</i>
 V
 $a2*$$x^2/($$x-$a1)/2
 $a2*$$x/($$x-$a1)-$a2*$$x^2/($$x-$a1)^2/2

:de la somme $$namei_y = $$namei_x+$$namei_z
 S 
 $$x*(1+$a2/($$x-$a1))
 1+$a2/($$x-$a1)-$a2*$$x/($$x-$a1)^2

:de la longueur $$namei_y du segment <i>AB</i>
 S
 $$x*sqrt(($$x-$a1)^2+$a2^2)/($$x-$a1)
 ($$x+$$a2^2*$$x/($$x-$a1)^2-$a2^2*$$x^2/($$x-$a1)^3)/sqrt($$x^2+($a2*$$x/($$x-$a1))^2)
  