  Given a rank $n$ irreducible finite reflection group $W$, the $W$-invariant
polynomial functions defined in ${\mathbb R}^n$ can be written as polynomials
of $n$ algebraically independent homogeneous polynomial functions,
$p_1(x),\ldots,p_n(x)$, called basic invariant polynomials. Their degrees are
well known and typical of the given group $W$. The polynomial $p_1(x)$ has the
lowest degree, equal to 2. It has been proved that it is possible to choose all
the other $n-1$ basic invariant polynomials in such a way that they satisfy a
certain system of differential equations, including the Laplace equations
$\triangle p_a(x)=0,\ a=2,\ldots,n$, and so are harmonic functions. Bases of
this kind are called canonical. Explicit formulas for canonical bases of
invariant polynomials have been found for all irreducible finite reflection
groups, except for those of types $E_6$, $E_7$ and $E_8$. Those for the groups
of types $E_6$, $E_7$ and $E_8$ are determined in this article.
