Questions tagged [computer-algebra]

Using computer-aid approach to solve algebraic problems. Questions with this tag should typically include at least one other tag indicating what sort of algebraic problem is involved, such as ac.commutative-algebra or rt.representation-theory or ag.algebraic-geometry.

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95 views

IntersectInP bug of Macaulay2 [closed]

I am trying to use the intersectInP command in Macaulay2, inside package ReesAlgebra. However, I tried to follow the exact code in the user-guide, but it doesn't run in my Ubuntu app (of win 10). Can ...
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1answer
466 views

Polynomial of degree N with integer coefficient for a given root.

Is it possible to construct a polynomial of degree N, with all of them as integer coefficient have a root as the given value. ...
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1answer
98 views

Quantifier elimination and where is this quantified convex program in the polynomial hierarchy?

I have a quantified convex program of the form that I need to solve $$\exists(x_{1,1},\dots,x_{1,n})\in\mathbb R^n\quad\forall(x_{2,1},\dots,x_{2,n})\in\mathbb R^n$$ $$\vdots$$ $$\exists(x_{2t-1,1},\...
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1k views

What program/language can I use to handle large numbers (over 10^300) [closed]

I'm trying to multiply together a set of numbers. However, the programs I have tried (Excel, R, FreeMat) do not allow numbers above around 300 digits. This limits me to sets of a few hundred numbers ...
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1answer
600 views

Does MAGMA have a function to decide if two indefinite, integral quadratic forms are isometric?

Let's say we have two $n$-dimensional lattices $(V,b)$ and $(W,b_1)$ equipped with integral bilinear forms $b$ and $b_1$ respectively. Is there an implemented function in MAGMA that decides whether $(...
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1answer
176 views

the maximal length of a special dicksonian sequence

First, we define a sequence $t_{1},t_{2},\cdots,t_{k}$ of n-tuples dicksonian, if $\forall 1\leq i < j\leq k,$ there does not exist a non-negative n-tuple t such that $t_{i}+t=t_{j}.$ For example, ...
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2answers
111 views

Properties of adjacent submatrixes [closed]

Hi! I've encountered a matrix problem when designing an algorithm, which I cannot seem to figure out. I have a (square) matrix with the following properties: j<k → aij<aik, aji<aki aij&...
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95 views

Stabilizers in the action of $\mathrm{GL}(n, \mathbb Z)$ on $\mathbb Z^n$

How can we calculate effectively the subgroups of $G: = \mathrm{GL}(n, \mathbb Z)$ which fix pointwise a given submodule $S$ of $\mathbb Z^n$ in the action of $G$ on $\mathbb Z^n$ by left ...
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54 views

Low rank approximation

Can we solve low rank approximation problem by using concept of Gröbner basis? I was trying to find it by Macaulay2 but didn't find the answer. I was trying to do by toric ideals as for them Gröbner ...
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54 views

Quadrics over the univariate function field with discriminant of minimal degree

Consider a non-degenerate quadric $Q(x,y,z) \subset \mathrm{P}^2$ over the univariate function field $\mathbb{F}_p(t)$, where $\mathbb{F}_p$ is a prime finite field, $p > 2$. For simplicity assume ...
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119 views

lcalc and the Analytic Rank of $y^2 = x^3 + 432764797 x^2 + 332896 x$

I'm looking at elliptic curves associated with $a/(b+c) + b/(a+c) + c/(a+b) = N$. For the case $N=10400$, Michael Rubinstein's lcalc gives the analytic rank of the associated elliptic curve $y^2 = x^3 ...
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24 views

Limit/Expansion Problems for Benchmarking

I am interested in collections of ‘interesting’ problems involving limits and/or asymptotic expansions of univariate real-valued functions. The purpose is to test a particular algorithm that I ...
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1answer
281 views

Computational Algebra and Symbolic Computation - Where? [closed]

Following the line of this question, I'm in my last year of M.Sc., and I'm looking for a place where I can start my PHD. Since that question has been asked 4 years ago, I thought it may be wise to ask ...
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539 views

Systems of linear modular equations with unknowns in the moduli

I am interested in systems of linear modular equations, where the unknowns also appear in the moduli. The general form would be: $A \vec{x}= \vec{b} \;\textrm{mod} \; (C \vec{x}+\vec{d})$ where A ...
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329 views

Understanding a program for computing Khovanov homology

I would like to understand how a computer program for computing Khovanov homology works. The particular program I have in mind is by John Baldwin: https://web.math.princeton.edu/~baldwinj/Kh.cpp The ...
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111 views

What is the largest computed summatory liouville interval ?

I am interested to know the largest computed summatory liouville interval, an implementation of which is detailed in Section 4.1 of [1]. The wikipedia page [2] for the function charts summatory ...
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1answer
80 views

Perform a univariate integral, involving a Gauss hypergeometric function

This is a follow-up question to the one posed in Compute the two-fold partial integral, where the three-fold full integral is known . (I hope that doing so is viewed as a legitimate step. If not so, I ...
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1answer
430 views

Mul + div using only add/sub ? [closed]

In an algorithm book once the first example was how to compute a multiplication in a loop (only that, so I just remembered, and wanted to do it programmatically but with all operations) ...

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