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Questions tagged [algebra]

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2
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1answer
37 views

Decidability of factoring algebraic equations

Given an arbitrary algebraic equation, say for example the likelihood of the bernoulli distribution: $$\prod_{i}^{n}\theta^{x_i}(1-\theta)^{1-x_i}$$ And some arbitrary factorization constraints, say:...
1
vote
2answers
33 views

Dominance Law in Boolean Algebra

The dominance law states that x + 1 = 1 If we go by that logic, does that mean that x' + 1 = 1? Please just tell me if it's a yes(as I think that this is the answer but I just want to clear my ...
0
votes
1answer
25 views

Boolean Algebra Simplifying complex equation

I am trying to simplify the following equation and I am getting stuck on a line and I can't cut it down any further. I'm not sure if certain 'moves' are legal or not. F(A,B,C,D) = A'B'C' +ACD + A’BCD ...
2
votes
1answer
45 views

How to Apply Elementary Axioms from Kleene Star to an Inequality

Axioms For * \begin{align} 1 + aa^* &\leq a^* \\ 1 + a^*a &\leq a^* \\ b + ax &\leq x \to a^*b \leq x \\ b + xa &\leq x \to ba^* \leq x \\ \end{align} Elementary Results \begin{...
6
votes
1answer
65 views

What is the fastest algorithm to check whether input table is a group?

Given an input table with binary operation $\circ$. I want to check whether given input table represents a group or not. I need to verify the four axioms of a group. The identity I can find it by ...
3
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0answers
41 views

A book introducing proof theory needed (many-sorted FOL, classical non-Gentzen calculus, satisfiability in partial algebras, induction)

We define a signature as a triple $$\Sigma\ =\ (S,F,\mathrm{type})$$ where $S$ is a set of sorts, $F$ a set of $n$-ary function symbols $f$ of the type $\mathrm{type}(f)$ $=$ $(M_1,\dotsc,M_n\...
2
votes
1answer
79 views

What is the difference between Boolean Algebra and Boolean Lattice?

What is the difference between Boolean Algebra and Boolean Lattice? I have already searched on Google but could not find a reasonable answer?
1
vote
1answer
43 views

What's the theory behind the operator precedences of common operators?

Could for example the precedence ordering of addition, multiplication, exponentiation, boolean and/or and zip/cross product be inferred from a few rules?
2
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0answers
54 views

Optimal vector decomposition

I have a vector $v \in \mathbb{N}^k$ and a set of vectors $R \subset \mathbb{N}^k$, with $k \ll \left\vert R \right\vert $. I would like to find a way to obtain all the possible bases of $\mathbb{N}^...
18
votes
2answers
634 views

Is there a non-trivial type which is equal to its own derivative?

An article called The Derivative of a Regular Type is its Type of One-Hole Contexts shows that the "zipper" of a type—its one hole contexts—follow the differentiation rules in type algebra. We have: ...
1
vote
1answer
58 views

Isomorphism of finite dimensional polynomial algebras over finite fields

For a prime power $q$, consider polynomials $f_1,f_2 \in \mathbb{F}_q[x]$. Then, do we have an efficient way of checking whether there exists an algebra isomorphism between: $$\frac{\mathbb{F}_q[x]}{\...
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0answers
17 views

Is there evidence to suggest Macsyma was directed at the Diophantine equations in the Entscheidungsproblem?

I'm reading the book The Annotated Turing by Charles Petzold. In it he mentions the Diophantine equations - which was a joy to read. This then lead to Hilbert's 10th problem - finding an algorithm ...
4
votes
0answers
6k views

Convert HSV to RGB colors

HSV colors are composed of a triple of numbers: hue $\in [0, 360)$ (in degrees), saturation $\in [0, 1]$ and value or brightness $\in [0, 1]$. RGB colors instead are more well-known and are also ...
4
votes
1answer
181 views

Solving systems of linear equations over semirings

So I have come across an issue where it would be very nice to solve systems of linear equations over semirings but I have no clue how to do that. Over a field I would use Gaussian elimination but I'm ...
1
vote
1answer
27 views

Producing an algebric equation from a graph

I'm writing a computer game and one of my game's objects must follow a movement path that is very similar to the following graph. The bold lines are the Y and X axis. In order to be able to code this ...
5
votes
1answer
75 views

Complexity of covering subset of the monoid $(\{0,1\}^n, \text{OR})$

(At the very bottom of this, I will shortly describe the motivation for this question.) Assume we have a commutative monoid $(G,\circ)$, i.e. a set $G$ with a commutative binary operation $\circ$ ...