Using a computer to implement mathematics.

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3
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1answer
79 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?
-1
votes
1answer
74 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 ...
1
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0answers
43 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 ...
3
votes
2answers
352 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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0answers
53 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 ...
1
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0answers
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 ...
-1
votes
1answer
47 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 ...
2
votes
1answer
111 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 ...
0
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1answer
59 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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0answers
59 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
votes
2answers
193 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 ...
0
votes
3answers
76 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 ...
2
votes
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.
4
votes
1answer
316 views

Euclidean Algorithm in Coq

Question How do I write more intuitive proofs of the two following results in Coq? ...
8
votes
2answers
306 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, ...
0
votes
1answer
65 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, ...
11
votes
2answers
5k views

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!
2
votes
1answer
65 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. ...
2
votes
3answers
129 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 ...
3
votes
0answers
116 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
votes
1answer
292 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 ...
1
vote
1answer
499 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
votes
2answers
702 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 ...