  In this paper, we study linear forms \[\lambda =
\beta_1\mathrm{e}^{\alpha_1}+\cdots+\beta_m\mathrm{e}^{\alpha_m},\] where
$\alpha_i$ and $\beta_i$ are algebraic numbers. An explicit lower bound for the
absolute value of $\lambda$ is proved, which is derived from "th\'eor\`eme de
Lindemann--Weierstrass effectif" via constructive methods in algebraic
computation. Besides, the existence of $\lambda$ with an explicit upper bound
is established on the result of counting algebraic numbers.
