I want to create a polynomial ring which has float Coefficients like this. I can create with integers but, Floats does not work. using Oscar S, (a,b,c,d) = PolynomialRing(QQ,["a","b...

How do you write a Python code to check if the operation ∗ on the set {0,1,..,n−1} defined by a Cayley table is associative or not. My attempted code is: def is_associative_cayley_table(table): ...

I've been doing some light reading on functional programming concepts and ideas. So far, so good, I've read about three main concepts: algebraic structures, type classes, and algebraic data types. ...

A group extends the idea of a monoid to allow for inverses. This allows for: gremove :: (Group a) => a -> a -> a gremove x y = x `mappend` (invert y) But what about structures like natu...

There is a nice Free Alternative in the great free package, which lifts a Functor to a left-distributive Alternative. That is, the claim is that: runAlt :: Alternative g => (forall x. f x -&gt...

Number of binary operation on a set of 2 elements is 2^(2*2)=16. Number of associative binary operation on that set is only 8. Number of binary operation on a set of 3 elements is 3^(3*3)=19683....

I've written an extended Euclidean algorithm function xgcd :: FFElem -> FFElem -> (FFElem, FFElem) that, for nonzero finite field elements a,b ∈ GF(pm), calculates s and t such that sa + t...

Category theory and abstract algebra deal with the way functions can be combined with other functions. Complexity theory deals with how hard a function is to compute. It's weird to me that I haven'...

It is well-known that monoids are stunningly ubiquitous in programing. They are so ubiquitous and so useful that I, as a 'hobby project', am working on a system that is completely based on their pr...

The documentation for algebra/2.1.1.2/doc/html shows a colossal number of type classes. How do I declare that a structure in question must be equipped with a commutative associative operation and ...

How do you use GAP to identify the name of a group from its multiplication table? I know that you can define a group from a set of generators, and then look for the group in the set of internal tab...

I recently getting to know about functional programming (in Haskell and Scala). It's capabilities and elegance is quite charming. But when I met Monads, which makes use of an algebraic structure ...

With hammar's help I have made a template Haskell bit which compiles $(zModP 5) to newtype Z5 = Z5 Int instance Additive.C Z5 where (Z5 x) + (Z5 y) = Z5 $ (x + y) `mod` 5 ... I'm now facin...