chapter  Chapter 7
24 Pages

Characteristic Polynomial

WithLorentz Jäntschi, Sorana D. Bolboacă

A topological description of a molecule requires storing the adjacencies (the bonds) between the atoms and the identities. The characteristic polynomial (ChP) is the natural construction of a polynomial in which the eigenvalues of the [Ad] are the roots of the ChP as it follows: The characteristic polynomial is a polynomial in ++ of degree the number of atoms. First reports relating to the use of the characteristic polynomial in relation with the chemical structure appears shortly after the discovery of wave-based treatment of microscopic level in Hückel. The main inconvenient of the previous given method is that it requires the tridiagonalization of the adjacency, which it means that a series of operations including divisions are involved and the resulted matrix no more contains only integers, and therefore is lost the feature to work with arbitrary-precision integers and to extract the exact values of the coefficients.