Related papers: Grobner fan for analytic D-modules with parameters
In this article we compute a minimal Groebner basis for the symmetric algebra for certain affine Monomial Curves, as an R-module. Keywords: Monomial Curves, Groebner Basis, Symmetric Algebra. Mathematics Subject Classification 2000: 13P10,…
The paper is mainly devoted to systematic developments and applications of geometric aspects of second-order variational analysis that are revolved around the concept of parabolic regularity of sets. This concept has been known in…
The $g$-fan of a finite dimensional algebra is a fan in its real Grothendieck group defined by tilting theory. We give a classification of complete $g$-fans of rank 2. More explicitly, our first main result asserts that every complete…
Following DeMeyer, Ford & Miranda [DFM93], we define a topology on a fan by declaring open sets to be its subfans. Then, like Kato [Kat94], we make our fans into monoided spaces by associating a sheaf of monoids to each fan. (Our sheaf of…
In this paper we describe an efficient involutive algorithm for constructing Groebner bases of polynomial ideals. The algorithm is based on the concept of involutive monomial division which restricts the conventional division in a certain…
Several known constructions relate initial degenerations of projective toric varieties and Grassmannians to regular subdivisions of appropriate point configurations. We define a general framework which allows for partial generalizations of…
We announce a new four parameter partition theorem from which the (big) theorem of Gollnitz follows by setting any one of the parameters equal to 0. This settles a problem of Andrews who asked whether there exists a result that goes beyond…
We derive a graded character formula for the action of any finite group on the Artinian reduction of the Stanley--Reisner ring of any complete simplicial fan, which is given by an equivariant version of the classical h-polynomial. This…
The paper has two goals: the study the associated graded ring of contracted homogeneous ideals in $K[x,y]$ and the study of the Groebner fan of the ideal $P$ of the rational normal curve in ${\bf P}^d$. These two problems are, quite…
Computing Gr\"obner bases is known to have a very high upper bound on computation time with respect to input length. Due to the connection between polyhedral geometry and Gr\"obner bases through the Gr\"obner fan, one can attempt an…
D. Bayer and M. Stillman showed that Grobner bases can be used to compute the Castelnuovo-Mumford regularity, which is a measure for the vanishing of graded local cohomology modules. The aim of this paper is to show that the same method can…
The theme of symbolic computation in algebraic categories has become of utmost importance in the last decade since it enables the automatic modeling of modern algebra theories. On this theoretical background, the present paper reveals the…
In this work we develop the theory of Gr\"obner bases for modules over the ring of univariate linearized polynomials with coefficients from a finite field.
Let $G$ be a linearly reductive group acting on a vector space $V$, and $f$ a (semi-)invariant polynomial on $V$. In this paper we study systematically decompositions of the Bernstein-Sato polynomial of $f$ in parallel with some…
The Bernstein-Sato polynomial (or global b-function) is an important invariant in singularity theory, which can be computed using symbolic methods in the theory of D-modules. After surveying algorithms for computing the global b-function,…
Let $(R, \mf, k_R)$ be regular local $k$-algebra satisfying the weak Jacobian criterion, such that $k_R/k$ is an algebraic field extension. Let $D_R$ be the ring of $k$-linear differential operators of $R$. We give an explicit decomposition…
Let $A=K[a_1,\ldots,a_n]$ be a weighted $\mathbb{N}$-filtered solvable polynomial algebra with filtration $FA=\{ F_pA\}_{p\in\mathbb{N}}$, where solvable polynomial algebras are in the sense of (A. Kandri-Rody and V. Weispfenning,…
Let $I$ be an ideal of the polynomial ring $A[x]=A[x_1,...,x_n]$ over the commutative, noetherian ring $A$. Geometrically $I$ defines a family of affine schemes over $\Spec(A)$: For $\p\in\Spec(A)$, the fibre over $\p$ is the closed…
In this paper, we introduce the notion of an admissible partition of a simplicial polyhedral fan and define the category of a partitioned fan as a generalisation of the $\tau$-cluster morphism category of a finite-dimensional algebra. This…
Estimating the temperature field of a building envelope could be a time-consuming task. The use of a reduced-order method is then proposed: the Proper Generalized Decomposition method. The solution of the transient heat equation is then…