相关论文: A q-product tutorial for a q-series MAPLE package
We are developing a Maple package of functions related to Rota's Umbral Calculus. A Mathematica version of this package is being developed in parallel.
This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…
In this paper we present a new identity and some of its variants which can be used for finding solutions while solving fractional infinite and finite series. We introduce another simple identity which is capable of generating solutions for…
An algorithm is proposed to convert arbitrary unitary matrix to a sequence of $X$ gates and fully controlled $R_y, R_z$ and $R_1$ gates. This algorithm is used to generate Q# implementation for arbitrary unitary matrix. Some optimizations…
This manual describes a set of utilities developed for Lattice QCD computations. They are collectively called QCDUtils. They comprise a set of Python programs each of them with a specific function: download gauge ensembles from the public…
We introduce derivations on the algebra of multiple harmonic q-series and show that they generate linear relations among the q-series which contain the derivation relations for a q-analogue of multiple zeta values due to Bradley. As a…
We present a coordinate space version of the factorization formula for the connected tree part of the chronological products. We consider a general framework and then we apply it for the QCD case.
We give a new proof for a product formula of Jacobi which turns out to be equivalent to a $q$-trigonometric product which was stated without proof by Gosper. We apply this formula to derive a $q$-analogue for the Gauss multiplication…
In this paper we consider a $q$-analog of the Borel-Laplace summation process defined by Marotte and the second author, and consider two series solutions of linear $q$-difference equations with slopes $0$ and $1$. The latter are…
We offer a Maple package {\tt Poincare\_Series} for calculating the Poincar\'e series for the algebras of invariants/covariants of binary forms, for the algebras of joint invariants/covariants of several binary forms, for the kernel of…
The possibility of interaction between Maple and numeric compiled languages in performing extensive numeric calculations is exemplified by the Ndynamics package, a tool for studying the (chaotic) behavior of dynamical systems. Programming…
The software package developed in the MS thesis research implements functions for the intelligent guessing of polynomial sequence formulas based on user-defined expected sequence factors of the input coefficients. We present a specialized…
In this paper, the (infinite) direct product of fields is investigated. In particular, the finiteness of a given set is characterized in terms of some ring-theoretic observations. Next, a certain localization (whose multiplicative set…
These lecture notes were written for a mini-course that was designed to introduce students and researchers to {\it $q$-series,} which are also called {\it basic hypergeometric series} because of the parameter $q$ that is used as a base in…
The usual nonnegative modulus function is based on addition. A natural different modulus function on the set of positive reals is introduced. Arguments for results for series through the usual modulus function are transformed to arguments…
This Mathematica 5.2 package~\footnote{QDENSITY is available at http://www.pitt.edu/~tabakin/QDENSITY} is a simulation of a Quantum Computer. The program provides a modular, instructive approach for generating the basic elements that make…
We present the Maple package TDDS (Thomas Decomposition of Differential Systems). Given a polynomially nonlinear differential system, which in addition to equations may contain inequations, this package computes a decomposition of it into a…
In this paper, we intend to present a new algorithm to factorize large numbers. According to the algorithm proposed here, we prove that there is a common factor between p and q. With this procedure, the time of factorization considerably…
I give in this brief tutorial a short practical introduction to the Mathematica package SARAH. First, it is shown how an existing model file can be changed to implement a new model in SARAH. In the second part, masses, vertices and…
We introduce the combinatorial notion of a $q$-fatorization graph intended as a tool to study and express results related to the classification of prime simple modules for quantum affine algebras. These are directed graphs equipped with…