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Macaulay2 is built around fast implementations of algorithms useful for computation in commutative algebra and algebraic geometry. This core functionality includes arithmetic on rings, modules, and matrices, as well as algorithms for Gröbner bases, free resolutions, Hilbert series, determinants and Pfaffians, factoring, and similar.
[1] [2] [3] The memory order is said to be strong or sequentially consistent when either the order of operations cannot change or when such changes have no visible effect on any thread. [1] [4] Conversely, the memory order is called weak or relaxed when one thread cannot predict the order of operations arising from another thread.
In category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the colimit of a diagram consisting of two morphisms f : Z → X and g : Z → Y with a common domain.
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
E_2={d,e}. d is labeled 3, and has one edge to f. e is labeled 1, and has one edge to f and one to g. E_3={f,g}. f is labeled 4. g is labeled 1. Etc. An ordered Bratteli diagram is a Bratteli diagram together with a partial order on E n such that for any v ∈ V n the set { e ∈ E n−1 : r(e) = v } is totally ordered. Edges that do not share ...
The Fano matroid, derived from the Fano plane.Matroids are one of many kinds of objects studied in algebraic combinatorics. Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra.
A nondeterministic algorithm for determining whether a 2-satisfiability instance is not satisfiable, using only a logarithmic amount of writable memory, is easy to describe: simply choose (nondeterministically) a variable v and search (nondeterministically) for a chain of implications leading from v to its negation and then back to v. If such a ...
The Z-ordering can be used to efficiently build a quadtree (2D) or octree (3D) for a set of points. [4] [5] The basic idea is to sort the input set according to Z-order.Once sorted, the points can either be stored in a binary search tree and used directly, which is called a linear quadtree, [6] or they can be used to build a pointer based quadtree.
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