Relative Invariants from 1879 Onward:: Their Evolution for Differential Equations - Softcover

Inhaltsangabe

During the years 1879-1889, there were differential equations for which mathematicians found remarkable combinations of the coefficients that possessed an invariant character under unrestricted transformations. In fact, specific examples of basic relative invariants were discovered by E. Laguerre in 1879, G.H. Halphen in 1881-1884, A. R. Forsyth in 1888, and P. Appell in 1889. However, there was little progress about such matters after 1889 until the subject was completely redeveloped during 1989-2013. All of the basic relative invariants are now known for the differential equations that interested the researchers of 1879-1889, and they are also known for many other types of differential equations. Moreover, the explicit formulas presented for them in this monograph can be immediately incorporated into systems of computer algebra. The task of discovering how particular relative invariants can be expressed as explicit combinations of basic ones required solving a difficult problem of central importance. Namely, this monograph presents a general technique for combining two relative invariants of respective weights p and q to explicitly construct a relative invariant of weight p + q + r, when r is any given nonnegative integer. Numerous applications are presented.

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