Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics pp 93-99 | Cite as
Differential-Algebraic and Differential-Geometric Approach to the Study of Involutive Symbols
Chapter
Abstract
Any system of partial differential equations after a finite number of prolongations becomes either inconsistent or involutive. The Hilbert function of any homogeneous ideal becomes polynomial beginning from a certain value of its argument. Any system of generators of a polynomial ideal becomes its Gröbner basis when multiplied by all monomials of sufficiently big degree. We discuss the interrelations between the number of steps required in these three procedures, for systems of partial differential equations with constant coefficients.
Keywords
Polynomial Ideal Hilbert Function Homogeneous Ideal Hilbert Polynomial Reducible Modulo
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© Springer Science+Business Media Dordrecht 1993