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 m2 numbers by adding minimal numbers ℓi 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 ui = 0 must be respectively differentiated ℓi 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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