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Finding the group structure of a finite ring

Trying to construct an example I built up this finite ring: $$B=\mathbb{Z}/9\mathbb{Z}[x,y,z,w_1,w_2]/(x^3-1,y^3-1,(x-1)(z+3w_1),(y-1)(z+3w_2),w_1^2,w_2^2,z^2)$$ I need to know the structure of ...
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1answer
69 views

Numbers as sum of distinct squares

Yesterday Polish Olympiad of Information Science ended, one of the questions was purely mathematical, Squares (PL). In the task, we have defined square ...
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3answers
48 views

Proof of floor function [closed]

I want to proof $\forall x\in\mathbb R,\lfloor x+1 \rfloor =\lfloor x\rfloor+1$, I know it is true, but how to prove it?
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1answer
39 views

Understand a Maple output

My goal is to solve for $L$ in $\frac{(2k)!}{2^kk!}{2nL - L^2 \choose 2k} = \sum_{s=0}^k{L \choose s}{n-L \choose s}s!\frac{(2k-2s)!}{2^{k-s}(k-s)!)}{L-s \choose 2k-2s}.$ I tried to use the solve ...
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53 views

Can a Computer Algebra System 'experiment' with expressions?

I have recently been reading about software for symbolic manipulation, and I can see its use as a tool for performing large calculations that would be unfeasible otherwise. Given that these systems ...
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1answer
75 views

Where can I download the approx 1500 Appel-Haken reducible configurations in the Four-Color-Theorem proof?

Where can I download computer representations of the approximately 1500 Appel-Haken reducible configurations in the Four-Color-Theorem proof? The Wikipedia article ...
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100 views

Proof of Paper, Scissor, Rock as Monoid Instance in Coq

So while learning Coq I did a simple example with the game paper, scissor, rock. I defined a data type. Inductive PSR : Set := paper | scissor | rock. And three ...
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28 views

Computer program for decomposing a graph into subgraphs?

Obviously there are programs out there that can find perfect matchings. I am interested in finding out if there is a program that can, for instance, tell when graphs like the cube graph $Q_n$, has ...
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28 views

A conjecture on the product of digits of a number

Define $(m,n)$ to be a special pair if $n=m \cdot Pd(n)$. Where $Pd(n)$ is the product of digits $n$. Then I have the following conjecture - For every $m$ with no digit of $m$ being $0$ , there ...
5
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1answer
74 views

Math via Computers

What computer language is best for doing mathematics? That is, which of C or Ruby or whatever would generally be the widest applicable efficient computer language to master for doing mathematics? In ...
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0answers
72 views

Cut-off Subtraction in Coq

I am new to the world of computer assistant proof programs in general, and Coq in particular. As a result, I have sought to prove some elementary results about integers as a way to … At the moment, I ...
5
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1answer
117 views

What is the meaning of proof of a proof?

After reading about Curry-Howard corrsepondence and looking at some proofs written in coq i've thinked about meaning of proof of a proof. We can express proofs as a computer program Proof is correct ...
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0answers
63 views

An Auto-Generated Cartography of Mathematical Theories: Has it been done already?

While looking for a way to visualize the logical structure of mathematical theories a graph-like depiction came to my mind, where propositions are represented by vertices. An edge goes from ...
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0answers
185 views

Online math tool for equation visualisation

I am looking for a math editor that is able to present equations and relations between them. I am not searching for a traditional Latex / MathML editor (I know about various online services that allow ...
2
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3answers
161 views

Computer Assisted proofs apart from the 4 color theorem

I recently read about the 4 color theorem and that it was proved using help from computers. Does anybody know of some other 'good' computer-assisted proofs apart from the 4 color theorem?