# Tagged Questions

Using a computer to implement mathematics.

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### Basic maths on python [on hold]

I'm getting an invalid syntax error on the l of the diagonal = I can't figure out the issue. polygon = int(input("How many sides are on your polygon?") diagonal = 2 ** (polygon) print ("There ...
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29 views

### Applications of calculus in competitive programming and algorithms [duplicate]

I was learning calculus 1 and 2 this year and I was wondering what is the usage of calculus in competitive programming and algorithms, what techniques and algorithms are commonly used and what are ...
2answers
197 views

### Count all numbers up to X that are divisible by at least two of their digits

I want to count how may numbers are there in range [1,X] which are divisible by at least two of their digits, different and >1. I found a sequence on OEIS, but this will take lot of time to generate ...
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57 views

### Why did the Mathematica Language choose term rewriting instead of the Lambda Calculus as its basis? [closed]

Now we can see that Church was associated with the Simply Typed Lambda Calculus. Indeed, it seems he explained the Simply Typed Lambda Calculus in order to reduce misunderstanding about the Lambda ...
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### Number of N Shaped figures formed from the set of points

Given k points on 2d plane and i need to find the number of N shaped figures from these k points. lets consider four different points from the set and name them A,B ,C ,and D (in that order). These ...
1answer
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### Good resources for understanding semidefinite relaxation for combinatorial problems

I am looking for good, complete and understandable resources in the field of semidefinite programming and combinatorial optimization. Especially I have a combinatorial problem which I want to relax as ...
1answer
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### ordered uniform distribution

We are given $n$ objects with individual weights $w_1 , w_2 , \ldots , w_n$ and $m$ buckets in which these objects are to be inserted but in order. Here order means if object $i$ goes in bucket $m_i$ ...
1answer
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### Algorithm to convert rendered number back into symbolic form

If you have a number such as $3.14626437$ and you need to know what symbols create it, as far as I know, there are two tools: 1- ISC 2- wolframalpha and the answer is $\sqrt2+\sqrt3$ I am ...
1answer
39 views

### Approximate a float using a minimal fraction

This sounds like it's probably a well-known problem, but I haven't been able to find references to it by searching. Given a floating point value $x$ and an error range $\varepsilon$, how can I ...
0answers
15 views

### RINS: start - incumbent and relaxation solution have all different values

RINS: Relaxation induced neighborhood search, firstly introduced by Danna et.al in 2004 in "Exploring relaxation induced neighborhoods to improve MIP solutions" I wanted to design an example how the ...
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### Symmetric Roles of the two problem solutions in RINS

Currently, I am reading the paper "Exploring relaxation induced neighborhood to improve MIP solutions" by Danna et.al. from 2004 and they are talking about a symmetric role of incumbent and the ...
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52 views

### Research in realtime computational physics?

I am aware that there is a considerable amount of interest in computational mechanics for simulation of cloth, hair and other elastica, particularly for animation films. The methods developed by ...
2answers
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### Which types of mathematical functions are the least complex for a computer to compute ?

Let's consider these four function types : Polynomial, Exponential, Logarithmic and Trigonometric. Considering that both input and output values are floating point numbers. How do they rank in ...
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### What is the Necessary math to understand books?

I have many problems understanding algorithms described in the books. Well, I'm talking about the mathematical description of a problem. For example: I don't understand how the math of Unscented ...
1answer
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### How to find a subset of numbers such that its average is close to the average of the full set?

I have a set of n numbers whose average (arithmetic mean) is x. I have to choose a subset of k numbers from n such that its average is closest to x. Please note that k is the upper bound. If the ...
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39 views

### Representing Computations on Transcendental Numbers

Consider the set of transcendental numbers that are not compressible to a finite base-2 representation. How can I compute multiples (more generally, any algebraic computation) of one of these numbers,...
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### Pedagogic reference on cut generating functions

Can you recommend an introduction to the topic of cut generating functions? I am looking for introductory or review-like material. I did find the following survey paper, but it seems to be addressed ...
1answer
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### The symbolic differentiation of univariate expressions

I was reading "Doug McIlroy: McCarthy Presents Lisp" and the phrase "symbolic differentiation of univariate expressions" triggered a faint memory of a demonstration of differentiation done in haskell ...
1answer
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### Fastest nth root algorithm to a lot of digits?

What is that fastest algorithm that can calculate a lot of digits of a decimal root? For example: 10,000 digits of the 3.56th root of 60.1?
1answer
211 views

### Can a computer count to infinity? [closed]

So, could a computer count to infinity assuming it was a super computer and had near unlimited amounts of ram and hard drive/solid state drive storage? I am being serious when I ask this. [This is ...
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50 views

### Number of ways to connect sets of $k$ vertices in a perfect $n$ -gon [closed]

This is a copy of my post at Mathexchange.com, as my question is still not fully answered and I really wanna find a solution to this. Feel free to refer to there for useful comments and partial ...
3answers
1k views

### Are there any compression algorithms based on PI?

What we know is that Ï€ is infinite and quite likely it contains every possible finite string of digits (disjunctive sequence). I've seen recently some prototype of Ï€fs which assume that every file ...
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57 views

### Exponential maths operator

I have written a math library which handles really big numbers with good precision. Each digit is stored in a nibble and a 'nibble array' makes up the number. There is no epsilon portion, as for ...
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6 views

### Decimal exponents [duplicate]

I've written a library which stores numbers as an array of nibbles. You set the digits and decimal places at compile time. I've written all basic math +-*/% but I'm not sure how to do exponentiation (...
1answer
59 views

### What advanced math topics are recommended for computer science? [closed]

I am enrolled in a computer science degree at the moment. I have looked around trying to find answers, but people tend to ask 'what is the minimum math needed for computer science' as opposed to what ...
1answer
323 views

### Matrix Multiplication Algorithms for Non-Square Matrices

I'm interested in learning about some of the algorithms available for multiplying non-square matrices, yet despite exhaustive Googling efforts I have been unable to find any discussions of such ...
1answer
148 views

### Implementing the Schur decomposition of a matrix

I'm trying do implement the Schur decomposition of a matrix, but I can't find any good articles for the theory. Could someone share one?
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131 views

### C++: Minimization Using Levenberg Marquardt to Solve for Two Variables [closed]

I am trying to solve this equation using C++: X and Y are both given sets of data. X = [x1, x2, ... , xn], Y = [y1, y2, ... , yn] a is a given integer. The goal is to find a pair z and k that ...
2answers
216 views

### Japanese Multiplication simulation - is a program actually capable of improving calculation speed? Or am I doomed from the start?

On SuperUser, I asked a (possibly silly) question about processors using mathematical shortcuts and would like to have a look at the possibility at the software application of that concept. I'd like ...
3answers
133 views

### Is it possible to accurately determine the number of instructions required to multiply or add two integers in a modern processor?

I'm not nearly at the experience level in computer science to be able to properly determine the number of instructions involved in basic ALU calculations, and I'm interested in a certain software ...
1answer
30 views

### Solving for the matrix $W$ in an equation involving $W \cdot W^{T}$

Having large matrices, $W$ (the unknown) and $M$ (known), is it possible to solve for $W$ in this equation $$W \cdot W^{T} = M,$$ where $M$ can have negative entries.
1answer
453 views

### Euclidean Algorithm in Coq

Question How do I write more intuitive proofs of the two following results in Coq? ...
2answers
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### Theorem Proofs in Coq

Background I am learning assistance, Coq, on my own. So far, I have completed reading Yves Bertot's Coq in a Hurry. Now, my goal is to prove some basic results concerning the natural numbers, ...
1answer
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### Known facets of the Travelling Salesman Problem polytope

For the branch-and-cut method, it is essential to know many facets of the polytopes generated by the problem. However, it is currently one of the hardest problems to actually calculate all facets of ...