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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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Generate all polynomials with coefficients 0 or 1 given degree n

I am trying to enumerate in 'C#' all the possible polynomials given the degree. Is there any algorithm to enumerate all possible polynomials given degree n? Maybe I don't know how to ask this question precisely but these are the examples: For…
Rebin
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Using Leo II to prove Theorems in Frobenius Algebras

Using the ATP Leo II with the TPTP thf language it is possible to prove many theorems in Frobenius algebras and open-closed cobordisms. I an using the following code thf(alpha_decl,type,(alpha: $aaxa > $axaa)). thf(invalpha_decl,type,(invalpha:…
Juan Ospina
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How to prove theorems for one-parameter groups using Z3

Using Z3 it is possible to prove that forms a one-parameter group. The proof is performed using the following Z3 code: (declare-sort S) (declare-fun carte (Real Real) S) (declare-fun h (Real S) S) (declare-fun a () Real) (declare-fun b ()…
Juan Ospina
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Z3 is the only system that is able to refute REL051+1.p?

The problem in relational algebra REL051+1.p reads File : REL051+1 : TPTP v6.1.0. Released v4.0.0. % Domain : Relation Algebra % Problem : Dense linear ordering Using TPTP syntax with fof the corresponding code is fof(f01,axiom,( ! [A]…
Juan Ospina
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The context between Abstract Algebra and programming

I'm a computer science student among the things I'm learning Abstract Algebra, especially Group theory. I'm programming for about 5 years and I've never used such things as I learn in Abstract Algebra. what is the context between programming and…
Billie
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Learning Cyclical Redundancy Check Failure Cases

I am trying to understand how likely a Cyclic Redundancy Check is to fail, given a particular divisor P(x). I am specifically interested in failures resulting from an odd number of bit flips in my message, an example to follow. Some prerequisite…
J. Moll
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How to define a specific field in Coq

I am trying to construct GF(2) in Coq using the standard library definition of a field over the standard library's boolean implementation. to be clear: "true" should be the field's "1" element. "false" should be the field's "0" element. "xorb"…
firstname gklsodascb
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Algebird HyperLogLog - Register Index and Register Value Bits

I am new to HyperLogLog and Scala, and am trying to use the Twitter Algebird's HyperLogLog implementation - https://github.com/twitter/algebird/blob/develop/algebird-core/src/main/scala/com/twitter/algebird/HyperLogLog.scala. In other…
DJElbow
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What is this signature { zero : α; append : α -> β -> α; } name?

I have Monoid and Builder interfaces: interface IMonoidFor { T Zero { get; } T Append(T a, T b); } interface IBuilderFor { IBuilderFor Append(T value); T Result(); } And want to implement from Monoid to Builder converting…
Valentyn Zakharenko
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Conditions for interchange modulos

I've been working on a problem and hope someone can help me with this (probably this has already been studied, I don't know). For a given a and to numbers m and n, are there any special conditions for the equality (a (mod m))(mod n)=(a (mod n))(mod…
liwuen
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Use Canvas to draw thousands of Rects

I am trying to make a native Android version of http://arapaho.nsuok.edu/~deckar01/Zvis.html So, I made a custom View that draws all the squares needed. Of course, this drawing ends up taking 10s of seconds once the number becomes large enough to…
Eric Cochran
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C: Convert big number from string to int modulo n

I'm trying to convert realy big numbers (>100 digits) from string to integer in Zn additive group (modulo n). n is guaranteed to be in standard C int range (say n=12345). Neither the simple approach of atoi then "%", nor BigIntiger works here. Any…
Dave
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