To form a conception of this problem it is to be noted that since the position of the body in space can be computed from the six elements of the orbit at any time we may ideally conceive the coordinates of the body to be algebraically expressed as functions of the six elements and of the time.
Dodgson periodically published mathematical works - An Elementary Treatise on Determinants (1867); Euclid, Book V., proved Algebraically (1874); Euclid and his Modern Rivals (1879), the work on which his reputation as a mathematician largely rests; and Curiosa Mathematica (1888).
One more covariant is requisite to make an algebraically complete set.
The general equation of degree 5 cannot be solved algebraically, but the roots can be expressed by means of elliptic modular functions.
(2), (3), (4),...(n), and say that with ao, we have an algebraically complete system.