Using a computer to implement mathematics.

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31 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 ...
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1answer
57 views

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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34 views

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 ...
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1answer
95 views

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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34 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 ...
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21 views

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 ...
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1answer
21 views

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 ...
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1answer
117 views

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?
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1answer
124 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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48 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 ...
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2answers
550 views

Are there any compression algorithms based on PI?

What we know is that π is infinite and quite likely it contains every possible finite string of digits (disjunctive sequence). I've seen recently some prototype of πfs which assume that every file ...
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55 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 ...
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1answer
55 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 ...
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1answer
242 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 ...
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1answer
89 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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95 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 ...
3
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2answers
212 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 ...
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3answers
97 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 ...
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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.
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1answer
376 views

Euclidean Algorithm in Coq

Question How do I write more intuitive proofs of the two following results in Coq? ...
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2answers
387 views

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, ...
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1answer
69 views

Solving a graph problem by Gaussian elimination

I have been given a graph with n nodes. Now, I have to color every node of this graph by k colors, number from 0 to k-1. Now, there is a rule. For a node $x$ with adjacent nodes $y_1 , y_2, y_3, ...
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What is the fastest algorithm for multiplication of two n-digit numbers?

I want to know which algorithm is fastest for multiplication of two n-digit numbers? Space complexity can be relaxed here!
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1answer
67 views

Finding number of numbers dividing n^m exactly p times

Suppose I am given a number $n$ (less than $10^8$) and $m$ (less than $10^7$) and $p$ (less than $10^4$), I have to write a program to find number of numbers that divide $n^m$ exactly $p$ times. ...
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3answers
135 views

Writing a program to find polynomial $f(x)$ from $f(1)$ and $f(f(1))$

Let $f(x)=a_0+a_1x+a_2x^2+\dots+a_nx^n$, where $a_i\ge0$ and $a_i$ is integer. Given $f(1)=p$ and $f(f(1))=q$, we have to find $a_0$, $a_1$, $a_2$, $a_3$, $\dots$, $a_n$, where such $f(x)$ exists. Or ...
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124 views

Drawing Zonotopes from an Adjacency Matrix

I'm conflicted whether to post this here or in either math.stackexchange or mathematica.stackexchange. Define a "simple zonotope" to be a regular $2n$-gon which is tiled by the following rule: all ...
2
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1answer
293 views

Permuting natural numbers

We have two integers $z, k$ We form a sequence now of first z natural numbers. i.e. $1, 2, 3, 4, \ldots z$. Now we have to find total number of permutations of this sequence such that the sum of ...
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1answer
590 views

Calculating Binet's formula for Fibonacci numbers with arbitrary precision

Binet's formula for the nth Fibonacci numbers is remarkable because the equation "converts" via a few arithmetic operations an irrational number $\phi$ into an integer sequence. However, using finite ...
8
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2answers
784 views

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 ...