Zobrazeno 1 - 10
of 17
pro vyhledávání: '"Manssour, Rida Ait El"'
Hilbert's Nullstellensatz is a fundamental result in algebraic geometry that gives a necessary and sufficient condition for a finite collection of multivariate polynomials to have a common zero in an algebraically closed field. Associated with this r
Externí odkaz:
http://arxiv.org/abs/2408.13027
The automatic generation of loop invariants is a fundamental challenge in software verification. While this task is undecidable in general, it is decidable for certain restricted classes of programs. This work focuses on invariant generation for (bra
Externí odkaz:
http://arxiv.org/abs/2407.09154
In this paper we introduce holonomic tree automata: a common extension of weighted tree automata and holonomic recurrences. We show that the generating function of the tree series represented by such an automaton is differentially algebraic. Converse
Externí odkaz:
http://arxiv.org/abs/2407.08218
Computational problems concerning the orbit of a point under the action of a matrix group occur in numerous subfields of computer science, including complexity theory, program analysis, quantum computation, and automata theory. In many cases the focu
Externí odkaz:
http://arxiv.org/abs/2407.04626
Autor:
Manssour, Rida Ait El, Pogudin, Gleb
The ideal of the arc scheme of a double point or, equivalently, the differential ideal generated by the ideal of a double point is a primary ideal in an infinite-dimensional polynomial ring supported at the origin. This ideal has a rich combinatorial
Externí odkaz:
http://arxiv.org/abs/2405.08964
Differentially-algebraic (D-algebraic) functions are solutions of polynomial equations in the function, its derivatives, and the independent variables. We revisit closure properties of these functions by providing constructive proofs. We present algo
Externí odkaz:
http://arxiv.org/abs/2301.02512
We study lines on smooth cubic surfaces over the field of $p$-adic numbers, from a theoretical and computational point of view. Segre showed that the possible counts of such lines are $0,1,2,3,5,7,9,15$ or $27$. We show that each of these counts is a
Externí odkaz:
http://arxiv.org/abs/2202.03489
Autor:
Manssour, Rida Ait El, Pogudin, Gleb
Publikováno v:
Alg. Number Th. 18 (2024) 947-967
The equation $x^m = 0$ defines a fat point on a line. The algebra of regular functions on the arc space of this scheme is the quotient of $k[x, x', x^{(2)}, \ldots]$ by all differential consequences of $x^m = 0$. This infinite-dimensional algebra adm
Externí odkaz:
http://arxiv.org/abs/2111.10446
We discuss practical methods for computing the space of solutions to an arbitrary homogeneous linear system of partial differential equations with constant coefficients. These rest on the Fundamental Principle of Ehrenpreis-Palamodov from the 1960s.
Externí odkaz:
http://arxiv.org/abs/2104.10146
We link $n$-jets of the affine monomial scheme defined by $x^p$ to the stable set polytope of some perfect graph. We prove that, as $p$ varies, the dimension of the coordinate ring of a certain subscheme of the scheme of $n$-jets as a $\mathbb{C}$-ve
Externí odkaz:
http://arxiv.org/abs/2102.03182