  The problem of finding independent components of an indexed object (e.g., a
tensor) with arbitrary number of indices and arbitrary linear symmetries is
discussed. It is proved that the number of independent components $f(k)$ is a
polynomial of degree not greater than the number of indices $n$, $k$ being the
dimension of the space. Several algorithms to compute $f(k)$ for arbitrary $k$
are described and discussed. It is shown that in the worst case finding $f(k)$
for arbitrary $k$ requires solving at most P(n) systems of linear equations
with at most $(n!)^2$ equations for at most of $n!$ unknowns, P(n) being the
number of partitions of $n$. As a by-product, an efficient algorithm to
parametrize all components of the object through its independent components is
found and implemented in \Mathematica.
