1
vote
0answers
31 views

Computer program to simplify formulas

What is the computer program that attempts to simplify sums of binomial coefficients, factorials, etc.? Possibly Zeilberger wrote it, but I'm unsure. If so, possibly it was talked about in his A=B ...
1
vote
1answer
66 views

another counting problem

There are $k$ warriors that participate in the Wars, which have happened for the past $n$ years. Each year there has been a victor. Further, a particular warrior $W$ has won the Wars an even number of ...
0
votes
1answer
44 views

Is there any algorithm (if possible, I need the codes) for Jordan normal form decomposition for large matrices in practice?

Although it is an ill-posed problem as B Kågström said in "An algorithm for numerical computation of the Jordan normal form of a complex matrix", I wonder what people do when they need to do Jordan ...
0
votes
1answer
47 views

Practical differences between a PRNG and a Markov chains

In computer programming you can easily find people describing both a PRNG, like a Mersenne Twister, and a Markov / Stochastic process as "pseudo random generators". I honestly never liked this ...
-2
votes
1answer
91 views

If P = NP, how would this allow us to cure diseases? [closed]

I have read a number articles on what the real-world ramifications would be if P = NP. One of these ramifications that is often repeated is that we 'could cure all sorts of diseases'. How or why ...
4
votes
1answer
230 views

“Opposite” of idempotent operation?

What is the adjective given to a mathematical operation/expression on a variable whose new value can only be described in terms of that variable's existing value? Sequential operation? Example: i = ...
0
votes
2answers
92 views

Existing Algorithm / Code to calculate exact values of the Riemann Zeta function at even natural numbers?

I wanted to know if there's any existing algorithm to compute exact values of the Riemann Zeta function at even natural numbers? For example, it should compute $\zeta(4)$ as exactly $\frac{\pi^4}{90}$ ...
0
votes
0answers
20 views

Echo State Network learning Mackey-Glass function, but how?

I got this example of a minimal Echo State Network (ESN) which I analyse while trying to understand Echo State Networks. Unfortunately I have some problems understanding why this really works. It all ...
2
votes
1answer
47 views

The “computability” of fundamental physical constants

I would like to ask if any of the fundamental physical quantities like the speed of light or plancks constant (all measured according to a common standard of of units) can be classified as computable ...
1
vote
0answers
51 views

What exactly is 'computer mathematics'?

I'm looking at some potential things to study next semester and I see a full B.sc. degree called 'Computer mathematics'. It says it's a hybrid between computer-science and mathematics. Does anyone ...
2
votes
0answers
41 views

LLL and factoring polynomials in $\Bbb Z[x]$

Given a degree $2k$ reducible polynomial $f(x)=\sum_{i=0}^{2k}a_ix^i\in\Bbb Z[x]$ with $gcd(a_{2k},\dots,a_0)=1$ that is known to be of the form $f_1(x)f_2(x)$ with $deg(f_i(x))=\frac{deg(f(x)}{2}=k$ ...
1
vote
0answers
26 views

Nonlinear optimization using parallel input/output

I have a system that accepts a vector and returns a function value. The goal is to change the elements of the vector such that the function value is minimized using a derivative-free solver, eg. using ...
1
vote
1answer
62 views

Ackermann function and primitive recursiveness

If we define $b_n(m) := a(n,m)$ for all $n$ and $m \in \mathbb{N}$. For which $n$ is the function $b_n$ primitive recursive and for which $n$ it is not a primitive recursive function? Can anyone ...
0
votes
1answer
180 views

Simultaneous recursion

I have no idea how to even start proving the following theorem: If $f_0, f_1: \mathbb{N}^r \rightarrow \mathbb{N}$ and $g_0, g_1: \mathbb{N}^{r+3} \rightarrow \mathbb{N}$ are primitive recursive, ...
5
votes
2answers
922 views

Fast Matlab Code for hypergeometric function $_2F_1$

I am looking for a good numerical algorithm to evaluate the hypergeometric function $_2F_1$ in Matlab (hypergeom in Matlab is very slow). I looked across the ...
0
votes
2answers
49 views

Generating a random number of higher range

I had a discussion with my friend about writing a function (a computer program) which generates 9 values randomly using a random number generator which generates 4 values, i.e I have a PRNG rand(4) ...
2
votes
1answer
137 views

Is there a computer programm or CAS (maybe GAP?) that can calculate with projective (indecomposable) A-modules (A is a finite dimensional k-algebra)?

I have the following question(s): I have an "Algebra-With-One" $R$ as a subalgebra of a full matrix algebra in GAP. Furthermore, I have 5 primitive orthogonal idempotents $e_1,...,e_5$, which sum up ...
2
votes
1answer
92 views

What does noncomputable really mean?

I believe I understand the definition of a noncomputable problem from an introductory computer science class, but I don't understand what it really means. One of my hypothesis was that a ...
4
votes
1answer
193 views

What is the fastest computational graph theory package?

What is the fastest computational graph theory package with respect to executing algorithms and computing graph theoretic data? I am aware of this related question, which requests graph theory ...
3
votes
3answers
559 views

Understanding recursive definitions of a language.

I am having difficulty understanding the recursive definition of a language. The problem asked how to write this non recursively. But I want to understand just how a recursive definition of a ...
0
votes
2answers
113 views

floating point binary arithmetic

Prove that the decimal number $\displaystyle \frac{1}{5}$ cannot be represented by a finite expansion in the binary system.
1
vote
2answers
183 views

Finite representation in the binary $\implies$ finite representation in the decimal system

Any number that has a finite representation in the binary system have a finite representation in the decimal system. Why?
1
vote
0answers
173 views

Power sums, fast algorithm

I know some schemes to compute power sums (I mean $1^k + 2^k + ... + n^k$) (here I assume that every integer multiplication can be done in $O(1)$ time for simplicity): one using just fast algorithm ...
2
votes
1answer
455 views

Computational Complexity of Modular Exponentiation

The following was posted from a lecture: "($a^n \bmod N$) has a runtime complexity of $\mathcal{O}(n*|a|*|N|)$ using the brute force method. $Z_1 = a \bmod N$ $Z_2 = (aZ_1) \bmod N$ $Z_3 = (aZ_2) ...
2
votes
1answer
588 views

radial basis function and neural networks

actually i need a simple explanation consider it for dummies about what is Radial basis function are?and what is the relation between radial basis function and neural networks ?and is there's any ...
1
vote
1answer
160 views

Solve equation on the PC

A friend of mine asked me to help him and make a small application to solve a problem. This problem can be reduced to this equation system: aX = Yb; Y > c; Y < d; X is a whole number (X has ...
1
vote
1answer
72 views

Finding the computational complexity of an algorithm

Algorithm: for (int i = 0; i < 2*n; i += 2) for (int j = n; j >i; j--) foo(); I want to find the number of times foo() is called. ...
1
vote
1answer
89 views

Regarding the definition of a problem

I recently noted from http://rjlipton.wordpress.com/2010/11/07/what-is-a-complexity-class/ that a problem is defined as a mere set of strings. So, here is the point: If I say the following: "Find ...
17
votes
5answers
875 views

What interesting open mathematical problems could be solved if we could perform a “supertask” and what couldn't?

If we had a computer that could perform a countably infinite number of steps of a Turing machine, what currently open problems could we solve? I guess a lot of number theory problems could be solved ...
2
votes
6answers
866 views

Gödel's Proof as a proof strategy for P = NP or P != NP

I have had this thought for quite a while. Gödel proved the incompleteness of arithmetic by creating a one-to-one correspondence with a number and certain numerical relationships to create a statement ...
1
vote
2answers
145 views

Sequences of a computable function

Is there any computable function $f(n)$, which given any integer $n$ has been proven to return either $0$ or $1$ in finite time, and for which the statement "$f(1), f(2), f(3),\ldots$ contains ...