Live briefing
Everything about Modulo
Computational operation
In mathematics and computing, modulo is the binary operation of which the value is the remainder or signed remainder of a division of one number by another, the latter being called the modulus of the operation. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: ModuloA 5-minute orientation
- Skim a recent paper: Modulo-addition operation enables terahertz programmable metasurface for high-resolution two-dimensional beam steeringInfluential work since 2022
- Pick up a classic book: Advanced number theoryThe most-reprinted book on the subject
- Read the landmark paper: New automatic equaliser employing modulo arithmeticCited 770 times
- Go sideways: RemainderA closely related topic
- Go sideways: Floor and ceiling functionsA closely related topic
📖 Definitions
Preposition Given a specified modulus of.
Preposition Except for differences accounted for by.
Preposition (The addition of quotations indicative of this usage is being sought:) With due allowance for (a specified exception or particular detail).
Noun The operation or function that returns the remainder of one number divided by another.
🏆 Landmark papers (most cited)
New automatic equaliser employing modulo arithmetic
Solving SAT and SAT Modulo Theories
Satisfiability modulo theories
Fibonacci Series Modulo m
Random numbers generated by linear recurrence modulo two
How to encode the modulo-two sum of binary sources (Corresp.)
Secure State Estimation for Cyber-Physical Systems Under Sensor Attacks: A Satisfiability Modulo Theory Approach
Completion of a Set of Rules Modulo a Set of Equations
🆕 Influential since 2022
Modulo-addition operation enables terahertz programmable metasurface for high-resolution two-dimensional beam steering
Image Encryption Based on Fourier-DNA Coding for Hyperchaotic Chen System, Chen-Based Binary Quantization S-Box, and Variable-Base Modulo Operation
An n-dimensional modulo chaotic system with expected Lyapunov exponents and its application in image encryption
An n-dimensional polynomial modulo chaotic map with controllable range of Lyapunov exponents and its application in color image encryption
Computational Array Signal Processing via Modulo Non-Linearities
📚 Books worth reading
Advanced number theoryHarvey Cohn · 1980- 📕Propriétés statistiques de suites arithmétiquesGérard Rauzy · 1976
- 📕Asymptotic distribution modulo 1NUFFIC International Summer Session in Science (1962 Breukelen, Utrecht, Netherlands) · 1965
- 📕Integration in locally compact spaces by means of uniformly distributed sequencesKarel Albertus Post · 1967
- 📕Répartition modulo 1 dans un corps de séries formelles sur un corps finiGeorges Rhin · 1972
- 📕Distribution modulo one and diophantine approximationYann Bugeaud · 2012
- 📕Répartition modulo 1 · 1975
Répartition modulo 1Colloque sur la répartition modulo 1 Marseille 1974. · 1975
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Remainder In mathematics, the remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after…
- Floor and ceiling functions Floor and ceiling functions In mathematics, the floor function is the function that takes a real number x as input and returns the greatest integer less…
- −1 In mathematics, −1 (negative one or minus one) is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element…
- Modular arithmetic In mathematics, modular arithmetic is a system of arithmetic operations for integers, differing from the usual ones in that numbers "wrap around" when…
- Montgomery modular multiplication In modular arithmetic computation, Montgomery modular multiplication, more commonly referred to as Montgomery multiplication, is a method for performing…
- Java (programming language) Java is a high-level, general-purpose, memory-safe, object-oriented programming language. It is intended to let programmers write once, run anywhere (WORA)…
- Short-circuit evaluation Short-circuit evaluation, minimal evaluation, or McCarthy evaluation (after John McCarthy) is the semantics of some Boolean operators in some programming…
- Gaussian integer In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition…