Commutative Property

This 'deceptively simple' question demands a dip into the murky waters of quantum physics.

What do the integers have in common with the symmetries of a triangle? In the 19th century, mathematicians invented groups as an answer to this question.

When pursuing an education in mathematics and algebra, one of the earliest and most important concepts to understand is the associative property, also known as the associative law.

As I toil to finish a book, mean reviews often pop into my head. As I wrapped up My Quantum Experiment , this line came to mind: "John Horgan's book is one long humblebrag." Usually my innate cockiness propels me past spasms of self-doubt, but the sting of "humblebrag" lingered. When bullied by

Are there maths where the Pythagorean triples don't exist? I ask because of the following: Let A,B,C, and K be elements of the Natural Numbers 1.∃K(K≤1)∧∃A,B,C(A^K+B^K=C^K ) 2.∃A,B,C(A^K+B^K=C^K )∧∃K(K≤1) 3.∃A,B,C(A^K+B^K=C^K )→∃K(K≤1) 4.∀K(K>1)→∀A,B,C(A^K+B^K≠C^K ) Premise 1 is true because at K equal to 1 I can find natural numbers A,B, and C such that A+B=C. Premise 2 is true because of the commutative property.…

Main repository of SageMath. Now open for Issues and Pull Requests. - sagemath/sage

New fold algorithms in C++23, what they do, how to use them.

Developing automatic Math Word Problem (MWP) solvers is a challenging task that demands the ability of understanding and mathematical reasoning over the natural language. Recent neural-based approaches mainly encode the problem text using a language model and decode a mathematical expression over quantities and operators iteratively. Note the problem text of a MWP consists of a context part and a question part, a…

N-COHESIVE RINGS Definition: Letnbe a positive integer. We define ann-cohesive ring to be a commutative ringSsuch that, for every primepdividing the characteristic ofS,pndivides the order of the mult…

Article URL: https://andrea.corbellini.name/2015/05/17/elliptic-curve-cryptography-a-gentle-introduction/ Comments URL: https://news.ycombinator.com/item?id=33488459 Points: 2 # Comments: 0

In which integration brings simplification.

A team of researchers from the U.S. Department of Energy's (DOE) Brookhaven National Laboratory and Stony Brook University have devised a new quantum algorithm to compute the lowest energies of molecules at specific configurations during chemical reactions, including when their chemical bonds are broken. As described in Physical Review Research, compared to similar existing algorithms, including the team's previous…

I keep hearing this term tossed around in several different contexts. What is it?

Scroll along the number line, and explore hundreds of interesting curious properties and facts. Then zoom in and out to discover even more!

It is well established that quantum error correction can improve the performance of quantum sensors. But new theory work cautions that unexpectedly, the approach can also give rise to inaccurate and misleading results—and shows how to rectify these shortcomings.

A study led by Dr. Guancong Ma (Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China) and Dr. Kun Ding (Department of Physics, Fudan University, Shanghai 200438, China) provides a new perspective for the study of non-Abelian phenomena and states permutations.

Physicists have proposed a new model of space-time that may provide the 'first observational evidence supporting string theory,' a new preprint suggests.

Scientists propose "fuzzy gravity"—adding extra dimensions and non-commutative spacetime—to reconcile general relativity with quantum mechanics.

Defining schema to communicate an API or standard.

Table of Contents In this article we'll implement a global optimization pass, and show how to use the dataflow analysis framework to verify the results of our optimization. The code for this …