The reduction to normal form of a non-normal system of differential equations
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This paper was edited by Sigismund Cohn, C. W. Borchardt and A. Clebsch from posthumous manuscripts of C. G. J. Jacobi. The solution of the following problem: “to transform a square table of m 2 numbers by adding minimal numbers ℓ i to each horizontal row, in such a way that it possess m transversal maxima”, determines the order and the shortest normal form reduction of the system: the equations u i = 0 must be respectively differentiated ℓ i times. One also determines the number of differentiations of each equation of the given system needed to produce the differential equations necessary to reduce the proposed system to a single equation.
KeywordsDifferential algebra Order of a differential system Jacobi’s bound Assignment problem Differential resolvent Shortest reduction in normal form
Mathematics Subject Classification (2000)12H05 65-03 65L80 65L08 90C05 90C27
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