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Questions tagged [abstract-algebra]

Abstract algebra is the subject area of mathematics that studies algebraic structures such as groups, rings, fields, modules, vector spaces, and algebras. It is heavily used in several programming related fields, such as cryptography. Any math questions on this site should be programming related.

In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebra over a field. The term abstract algebra was coined in the early 20th century to distinguish this area of study from the other parts of algebra.

Any math questions on this site should be programming related.

References:

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Randomly generating associative operations

In abstract algebra, the notion of a group is fairly fundamental. To get a group, we need a set of objects, and an binary operation with 3 properties (4 if you count closure). If we want to randomly generate a group given a finite set, (that is,…
deontologician
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Proper Carmichael Function

I'm creating all the necessary functions for RSA algorithm. Unfortunately i can't seem to a make proper Carmichael function. These are the functions that i've written: def gcd(a, b): # Greatest Common Divisor Generator (Euclidean Algorithm) …
ShellRox
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Do notation and Monad composition

Im a Haskell beginner and I'm still learning about Category Theory and its practical use in computer science. I've spent last day watching couple lectures from Berkley's university about category theory, most of its content was showing a…
Pablo Parada
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Is it good to design object according to mathematical group theory

For example, suppose you are designing a class of object called Car, which support a binary operation denoted by the sign, +, i.e. you can do car1 + car2 where car1 and car2 are instances of Car As you just finish an abstract algebra course, you try…
asinkxcoswt
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How to change The Ring of the polynomial in Julia

Main using AbstractAlgebra include("./lib.jl"); S, (a,b,c) = PolynomialRing(QQ,["a","b","c"]) RR = AbstractAlgebra.RealField s1 = S(b^2*a + c*a - 1) s2 = S(c*a^2 + -b*a - c^4*a) s3 = S(b*a + a + b) poly_list =…
Ahmet Yusuf
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Monad: Why does Identity matter, what's going to happen if there's no such special member in a set?

I'm trying to learn the concept of monad, I'm watching this excellent video Brian Beckend trying to explain what is monad. When he talks about monoid, it's a collection of types, it has a rule of composition, and this composition has to obey 2…
Aaron Shen
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Z3 is not able to prove the equivalence between two simple programs using Kleene algebras with test but Mathematica and Reduce are able

Our problem here is to show that using Kleene algebras with test. In the case when the value of b is preserved by p, we have the commutativity condition bp = pb; and the equivalence between the two programs is reduced to the equation In the case…
Juan Ospina
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How to use Z3 SMT-LIB to prove theorems in Frobenius Algebras

We prove the following theorem in Frobenius Algebras The proof is performed using the following code ;; Frobenius algebra object (A,mu,eta,delta, epsilon) (declare-sort A) (declare-sort AA) (declare-sort A_AA) (declare-sort AA_A) (declare-sort…
Juan Ospina
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Operator overloading and class definition in R: Use a different base field/corpus

(I'm using the word "field" in the mathematical sense; base fields/corpora which R already uses include the real and complex numbers.) I'm interested in allowing some other base fields/corpora (like F₅, which is modular arithmetic in base 5). To do…
isomorphismes
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How to constrain associated type synonyms?

I'm (relatively) new to Haskell and want to code some math. For example, abelian groups. I would like to write the following code: {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE TypeSynonymInstances #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE…
TheMadHaberdasher
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Representation & Behaviour - Rational Tangle Dance

Four people stand at positions A, B, C and D and hold two ropes in the initial configuration shown. These folk may “dance” with these ropes by performing just two moves, multiple times, in any order they like: Rotate as a group 90 degree…
overexchange
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Permutations distinct under given symmetry (Mathematica 8 group theory)

Given a list of integers like {2,1,1,0} I'd like to list all permutations of that list that are not equivalent under given group. For instance, using symmetry of the square, the result would be {{2, 1, 1, 0}, {2, 1, 0, 1}}. Approach below…
Yaroslav Bulatov
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Wreath Product Of Groups In Sagemath

Can anyone help me with taking Wreath Products of Groups in Sagemath? I haven't been able to find a online reference and it doesn't appear to be built in as far as I can tell.
Sam H
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Python: finding all generators for a cyclic group

Take a cyclic group Z_n with the order n. The elements are: Z_n = {1,2,...,n-1} For each of the elements, let us call them a, you test if a^x % n gives us all numbers in Z_n; x is here all numbers from 1 to n-1. If the element does generator our…
Heinrich Jensen
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Shortcut for all the possible permutation of a set of numbers for m digits

I have been working on finite field. Suppose I have a prime number p=7. So I get a list q=[0,1,2,3,4,5,6]. Now I want all the possible permutation of the elements of set q for 7 places. For example [1,1,1,4,6,3,1] is one of the possible…
Shashank Ranjan
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