Questions tagged [magma]
A magma is a set together with a binary operation on this set. (For questions about the computer algebra system named Magma, use the [magma-cas] tag instead.)
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Compilation of Phenomena Modeled by an Operation Table
It seems like there would be utility in a search engine or database through which the user inputs the operation table of a magma (I think that's the right level of algebraic structural generality) to ...
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Counting the number of points on a curve over a finite field by calculators
I want to count the number of points on a algebraic curve $C:y^2=x^5-x+1$ over $\mathbb{F}_{3^n} (n=2,3,4,...)$ by calculators (Pari/GP, Sage, Magma,...).
Can you give me a command that solves the ...
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Generalization of free magmas for nested structures
Consider a nonempty set $X$. What is the name / concept that gives rise to (the set of) all $X$ labeled planar trees e.g.
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Does the percentage of associative operations on a finite set decrease monotonically towards zero?
In this answer, André Nicolas proves that it is rare for a binary operation on a finite set to be associative, in the following sense: if $A_n$ denotes the number of semigroups that can be defined on ...
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How to define the non-commutative ring $\mathbb{F}_{4}+e\mathbb{F}_{4}$, $e^2=1$, $ae=ea^2$ in MAGMA(Computational Algebra System)?
I'm trying to learn to use MAGMA(Computational Algebra System) for research in coding theory over non-commutative rings, but it's been slow going. I feel like it's hard to find anything in the ...
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Is there a model of this equational theory which is not power-associative?
This is a follow up to my previous question, here: Two questions regarding equational axiomatizations of power-associative magmas.. As before, let $t$ be a term, in the sense of universal algebra. I ...
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Two questions regarding equational axiomatizations of power-associative magmas.
A power-associative magma is a magma $(M;*)$ where the submagma generated by any single $x$ in $M$, is associative. I have two questions regarding power-associative magmas. First, some terminology. ...
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Eckmann–Hilton Argument and magma homomorphisms
The Eckmann-Hilton result is as follows:
Let $X$ be a set equipped with two binary operations $\circ$ and $\otimes$, and suppose
$\circ$ and $\otimes$ are both unital, meaning there are identity
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Which axiom can almost determine the magma with one element?
The axiom $((a * b) * c) * (a * ((a * c) * a)) = c$ uniquely determines Boolean algebra, an example of a single axiom giving a magma an "interesting" structure. What is the fewest number of ...
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intersection of point stabilisers is trivial
Let $G=\operatorname{GL}_{n}(2)$. Let $v_{i}$ be the basis elements of the natural module of $G$. I observed by computing with Magma that the intersection of all Stabiliser($G, v_{i}$) is trivial for ...
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An equational basis for the variety generated by the following class of magmas.
Let $(M;*)$ be a magma, and define a binary relation $R$ on $M$ by saying that $aRb$ iff there exists a $c$ in $M$ such that $a*c=b$. I call $R$ the left-divisor relation associated with $(M;*)$. I ...
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An example of a binary operation which is neither idempotent nor has a right identity, but has a reflexive "left-divisor" relation.
Let $A$ be a set with a binary operation $*$. I define a binary relation $R$ on $A$ by defining $xRy$ to hold if there exists a $z$ in $A$ such that $x*z=y$, and in that case I call $x$ a "left-...
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Is class number the always the degree of [Hilbert class field of discriminant $D:K=\mathbb{Q}(\sqrt{d})]$
I was going through https://services.math.duke.edu/~schoen/discriminants.html where the minimal polynomial whose quotient over $K=\mathbb{Q}(\sqrt{d})$ is equal to the Hilbert class field for ...
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non-commutative algebraic structure with 16 elements, need help categorizing it and finding a representation
We have an abstract algebraic structure with the following multiplication table, has anyone seen this structure before and can anyone give it a proper name and a simple (possibly matrix) ...
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Program to calculate homology of a Koszul complex involving univariate polynomials
Let $R = \mathbb{Z}[x_1,...,x_6]$ be a polynomial ring. Then we may form the Koszul complex $K(x_1,...,x_6)$ which looks something like:
$$ R \xrightarrow{d_6} R^6 \xrightarrow{d_5} R^{15} \...
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