research
∙
06/01/2023
Some New Non-Commutative Matrix Multiplication Algorithms of Size (n,m,6)
For various 2≤ n,m ≤ 6, we propose some new algorithms for multiplying a...
share
research
∙
03/05/2023
Some D-finite and Some Possibly D-finite Sequences in the OEIS
In an automatic search, we found conjectural recurrences for some sequen...
research
∙
02/13/2023
Transcendence Certificates for D-finite Functions
Although in theory we can decide whether a given D-finite function is tr...
research
∙
02/09/2023
Hermite Reduction for D-finite Functions via Integral Bases
Trager's Hermite reduction solves the integration problem for algebraic ...
research
∙
02/08/2023
Order bounds for C^2-finite sequences
A sequence is called C-finite if it satisfies a linear recurrence with c...
research
∙
12/02/2022
Flip Graphs for Matrix Multiplication
We introduce a new method for discovering matrix multiplication schemes ...
research
∙
10/08/2022
The FBHHRBNRSSSHK-Algorithm for Multiplication in ℤ_2^5×5 is still not the end of the story
In response to a recent Nature article which announced an algorithm for ...
research
∙
06/01/2022
A Normal Form for Matrix Multiplication Schemes
Schemes for exact multiplication of small matrices have a large symmetry...
research
∙
05/12/2022
Order-Degree-Height Surfaces for Linear Operators
It is known for linear operators with polynomial coefficients annihilati...
research
∙
02/16/2022
Guessing with Little Data
Reconstructing a hypothetical recurrence equation from the first terms o...
research
∙
02/12/2021
Lazy Hermite Reduction and Creative Telescoping for Algebraic Functions
Bronstein's lazy Hermite reduction is a symbolic integration technique t...
research
∙
06/02/2020
Good pivots for small sparse matrices
For sparse matrices up to size 8 × 8, we determine optimal choices for p...
research
∙
02/07/2020
Integral P-Recursive Sequences
In an earlier paper, the notion of integrality known from algebraic numb...
research
∙
02/04/2020
Separating Variables in Bivariate Polynomial Ideals
We present an algorithm which for any given ideal I⊆𝕂 [x,y] finds all el...
research
∙
05/24/2019
New ways to multiply 3 x 3-matrices
It is known since the 1970s that no more than 23 multiplications are req...
research
∙
05/21/2019
Lonely Points in Simplices
Given a lattice L in Z^m and a subset A of R^m, we say that a point in A...
research
∙
03/27/2019
Local Search for Fast Matrix Multiplication
Laderman discovered a scheme for computing the product of two 3x3 matric...
research
∙
02/09/2019
On the maximal minimal cube lengths in distinct DNF tautologies
Inspired by a recent article by Anthony Zaleski and Doron Zeilberger, we...
research
∙
05/23/2018
A Simple Re-Derivation of Onsager's Solution of the 2D Ising Model using Experimental Mathematics
In this case study, we illustrate the great potential of experimental ma...
research
∙
04/04/2018
Short Proofs for Some Symmetric Quantified Boolean Formulas
We exploit symmetries to give short proofs for two prominent formula fam...
research
∙
02/12/2018
Symmetries of Quantified Boolean Formulas
While symmetries are well understood for Boolean formulas and successful...
research
∙
05/02/2017
Apparent Singularities of D-finite Systems
We generalize the notions of singularities and ordinary points from line...
research
∙
01/26/2017
Bounds for Substituting Algebraic Functions into D-finite Functions
It is well known that the composition of a D-finite function with an alg...
research
∙
11/22/2016
Reduction-Based Creative Telescoping for Fuchsian D-finite Functions
Continuing a series of articles in the past few years on creative telesc...
research
∙
11/17/2016
D-finite Numbers
D-finite functions and P-recursive sequences are defined in terms of lin...
research
∙
09/13/2016
Some Open Problems related to Creative Telescoping
Creative telescoping is the method of choice for obtaining information a...
research
∙
06/09/2016
Hypergeometric Expressions for Generating Functions of Walks with Small Steps in the Quarter Plane
We study nearest-neighbors walks on the two-dimensional square lattice, ...
research
∙
02/01/2016
Reduction-Based Creative Telescoping for Algebraic Functions
Continuing a series of articles in the past few years on creative telesc...
research
∙
01/12/2016
Factorization of C-finite Sequences
We discuss how to decide whether a given C-finite sequence can be writte...
research
∙
09/29/2015