An extension of Buchberger's algorithm and calculationsin enveloping fields of lie algebras
Journal of Symbolic Computation
“One sugar cube, please” or selection strategies in the Buchberger algorithm
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Involutive bases of polynomial ideals
Mathematics and Computers in Simulation - Special issue: Simplification of systems of algebraic and differential equations with applications
The theory of involutive divisions and an application to Hilbert function computations
Journal of Symbolic Computation
Computational ideal theory in finitely generated extension rings
Theoretical Computer Science
Dynamical aspects of involutive bases computations
SNSC'01 Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
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The objective of this article is to enlighten the relationship between the two classical theories of passive complete orthonomic systems of PDEs on the one hand and Gröbner bases of finitely generated modules over polynomial rings on the other hand. The link between both types of canonical forms are the involutive bases which are both, a particular type of Gröbner bases which carry some additional structure and a natural translation of the notion of passive complete orthonomic systems of linear PDEs with constant coefficients into the language of polynomial modules. We will point out some desirable applications which a "good" notion of involutive bases could provide. Unfortunately, these desires turn out to collide and we will discuss the problem of finding a reasonable compromise.