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Questions tagged [mathematical-programming]

Using a computer to implement mathematics. For questions about (mathematical) optimization, (also) use the optimization tag.

168 questions
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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!
Andy
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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 you've created (or anybody else) or you will create,…
kenorb
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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 such polytopes as they rapidly grow in size. For…
stefan
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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, culminating with the so-called division algorithm.…
user11942
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7
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2 answers

Is global non-convex optimization NP-complete?

Assume I have some non-convex function $f(x_1, x_2, ...)$ and I want to optimize it to find a global minimum. I feel like it is easy to show that this problem is in the class NP with the decision problem Is there a set of points such that f < C?…
wjmccann
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1 answer

How did the Logic Theorist prove the Pons Asinorum?

I was reading about the Logic Theorist proving many of the Whitehead and Russell's Principia's theorems. However, I cannot find any technical explanation on how the program proved those theorems and specifically what method did it use to solve the…
Nir Levy
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Count number of pairs $(a,b)$ in an array such that $(a + b)$ divides $(a * b)$

We are given an array of size $N$ with integer entries $> 0$. We have to count the number of all such pairs $(a,b)$ with $a \leq b$ such that $a*b$ is divisible by $a + b$. The obvious naive way is to check every pair and it takes…
chelsea
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5
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Is the $x$ in $\frac{\mathrm{d}}{\mathrm{d}x}$ a symbol in the sense of Harper's PFPL?

The role of $x$ in $\frac{\mathrm{d}}{\mathrm{d}x} y$ not only confuses my calculus students, it has also puzzled some well known mathematicians. Questions one might ask are: Does the $x$ in the denominator bind the $x$ in $y$? (Clearly no, since…
Michael Bächtold
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5
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n! mod p Fast Factorial

I need to find N! (mod 232-5) such that 0 ≤ N ≤ 264 for i cases, 0 ≤ i ≤ 1000 in 1 sec. Credits: https://dmoj.ca/problem/factorial2 I am aware that I only have to handle 0 ≤ N ≤ 2 ≤ 232-6 because once N ≥ 232-5, N!≡0 (mod 232-5) . A naive solution…
WIR3D
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Why did the Mathematica Language choose term rewriting instead of the Lambda Calculus as its basis?

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 Calculus. Now when John McCarthy created Lisp - he…
hawkeye
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Euclidean Algorithm in Coq

Question How do I write more intuitive proofs of the two following results in Coq? Theorem Course_of_values_ind: InductiveRel N less Theorem DivRem: (forall d n:N, (Sigma N (fun q => (Sigma N (fun s => and (I N n (add…
user11942
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5
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Usefulness of Differential Geometry

I recently came across these books: Differential Geometry and Lie Groups: A Computational Perspective Differential Geometry and Lie Groups: A Second Course Their subject matter really intrigues me, as I really enjoy topology/geometry/analysis, but…
user37344
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Fermat's last theorem: How to (partially) solve by programs

No three distinct positive integers $a, b, c$ can satisfy the equation : $a^n + b^n=c^n$, if $n$ is an integer greater than two. The above statement, known as the Fermat's last theorem is proven with rigorous mathematics. I happened to stumble…
hola
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Can this system of polynomial equations be solved in polynomial time?

I have these $n$ equations, with $n$ variables. Variables are first $n$ positive integers, constants can be any rational number including zero. Given that there is always a solution, how do we find a solution to the…
user101371
4
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3 answers

Is it possible to make a language that can build upon itself perfectly?

First of all, note that I'll have to explain my thoughts in a layman's terms. There are so many high-level programming languages out there that compete with each other. This means we have to build the same functionality over and over again in each…
MetaStack
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