# Tagged Questions

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 ...
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 ...
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 ...
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 ...
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 ...
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 = ...
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 $\frac{\pi^4}{90}$ ...
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 ...
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 ...
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 ...
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 $deg(f_i(x))=\frac{deg(f(x)}{2}=k$ ...
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 ...
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 ...
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, ...
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 ...
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) ...
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 ...
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 ...
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 ...
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 ...
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.
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?
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 ...