II. Memoir on the symmetrical functions of the roots of systems of equations

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Abstract
The object of the present memoir is the extension to systems of algebraical quantities of the new theory of symmetric functions which has been developed by the author in regard to a single system in Volume 11 and succeeding volumes of the ‘American Journal of Mathematics.’ In the theory of the single system the conceptions and symbolism are to a large extent arithmetical, and are based upon the properties of single integral numbers and their partitions into single integral parts. In this sense the theory may be regarded as being unipartite. In the present generalisation to the case of m systems of quantities the fundamental ideas proceed, not from a single number, but from a collection of m single numbers. In regard to number, weight, degree, part, and suffix, the collection of m numbers invariably replaces the single number of the theory of the single system. In this view the theory of the m systems is m -partite.

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