An Algorithm to Compute the Equations of Tangent Cones
EUROCAM '82 Proceedings of the European Computer Algebra Conference on Computer Algebra
A generalization of reduction rings
Journal of Symbolic Computation
Journal of Symbolic Computation
Standard bases and geometric invariant theoryI. Initial ideals and state polytopes
Journal of Symbolic Computation
Constructive lifting in graded structures: A unified view of Buchberger and Hensel methods
Journal of Symbolic Computation
On the computation of generalized standard bases
Journal of Symbolic Computation
On the construction of Gröbner bases using syzygies
Journal of Symbolic Computation
A geometric consistency theorem for a symbolic perturbation scheme
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
The concept of Gröbner algebras
Journal of Symbolic Computation
Standard bases and some computations in rings of power series
Journal of Symbolic Computation
A new notion of reduction: Generating universal Gröbner bases of ideals in K[x, y]
Journal of Symbolic Computation
Geometry theorem proving in vector spaces by means of Gröbner bases
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
Exponential space computation of Gröbner bases
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Groebner basis under composition II
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Families of ideals in statistics
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Remarks on Gröbner basis for ideals under composition
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation
Admissible orderings and finiteness criteria for differential standard bases
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
A Gröbner fan method for biochemical network modeling
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
On the Structure of Order Domains
Finite Fields and Their Applications
Finite Fields and Their Applications
On The Diversity Of Orderings On Strings
Fundamenta Informaticae
On the complexity of computing gröbner bases for quasi-homogeneous systems
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Converting subalgebra bases with the Sagbi walk
Journal of Symbolic Computation
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It is well known that various notions of distinguished bases of ideals, such as standard and Grobner bases, and algorithms for constructing them, play a central role in solving algorithmic problems in polynomial ideal theory and related algebraic theories. In this paper a new structural algebraic framework is given for the concept and the construction of the so-called generalised standard bases. Although the spirit of this paper is more structural than algorithmic, the general results achieved should also help to shape and direct future research in the algorithmic aspects of commutative algebra.