All Questions
Tagged with computer-algebra computer-science
15 questions
6
votes
0
answers
102
views
Computer program for free restricted Lie polynomial
I am conducting numerical experiments involving the Gröbner–Shirshov Basis for restricted Lie algebras. At each step of the computation, I need to work with restricted Lie polynomials. Specifically, I ...
- 63.9k
1
vote
0
answers
37
views
Computing all roots of a function with square-root terms
Given $3n$ positive numbers $a_1, \ldots, a_n$, $b_1, \ldots, b_n$, and $x_1, \ldots, x_n$, we are given a function
$$f(x) = \sum_{i = 1}^n \frac{a_i}{\sqrt{(x - x_i)^2 + b_i}}.$$
Can we find all the ...
- 11
3
votes
1
answer
315
views
About Shor's quantum algorithm
I know very little about quantum computing, and I've been trying to understand Shor's algorithm for the factorization of an integer $N$. I'm following Computational Complexity — a modern approach by ...
- 731
-5
votes
1
answer
79
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Application of Resultant in Computer Algebra [closed]
Can you guys give me some application of resultant in Computer Algebra, it will be amazing if you guys can give me some paper or book to read more. Thanks so much
- 2,992
7
votes
1
answer
352
views
About the complexity of some operation involving integers
There are two integers: $A, B$. Given the below four allowed operations (and only them):
$A+1$, $A-1$, $\sqrt{A}$, $A^2$
Also, it is only allowed to take the square root of $A$ when this square root ...
- 6,367
4
votes
1
answer
136
views
String compression algorithms for simplifying an expression by introducing variables
I have a very long algebraic expression computed with Maple, and when I inspect it visually, it is clear that it consists of a set of terms that appear over and over again. For purposes of human ...
- 11.8k
1
vote
1
answer
91
views
Algorithms for Polynomials Over a Real Algebraic Number Field, a reference
I need to find "Algorithms for Polynomials Over a Real Algebraic Number Field
Ph.D. thesis, University of Wisconsin, Madison (1974) by Rubald". However I cannot find it online nor in my ...
12
votes
2
answers
588
views
Ideal Membership without Certificate?
I have a homogeneous ideal $I=\langle f_1,\ldots,f_r\rangle$ of the polynomial ring $\mathbb C[X_1,\ldots,X_n]=:R$ where each of the $f_i$ is actually over $\mathbb Z$. My computations are usually ...
- 2,992
11
votes
1
answer
474
views
Representing field elements in a computer
I'm wondering if there is existing terminology to describe fields $F$ with the properties below. I don't have a completely precise description of the concept I have in mind, but hopefully this will be ...
- 4,727
9
votes
1
answer
2k
views
Efficient SVD of a matrix without some of the columns
I have a matrix $A \in \mathbb{R}^{p \times q}$ of rank $r$ and its SVD decomposition, i.e,
$$
A = U S V^\top,
$$
where $U \in \mathbb{R}^{p \times r}$ and $V \in \mathbb{R}^{q \times r}$ are ...
- 341
5
votes
2
answers
253
views
Can this way of comparing numbers of the form a+b sqrt(K) be generalized?
So I want to make a system for computing with various classes of numbers. One of those is a class of number closed under the standard arithmetic operators ($+$, $-$, $*$ and $/$) along with square ...
- 47.1k
0
votes
1
answer
2k
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AI / Machine Learning related to high/modern/front mathematics [closed]
I major math and cs. and i'm interested in ai/machine learning/data mining.
so i want to know what math subjects are used in frontier of these technology.
especially, high mathematical tool, like ...
- 28.6k
5
votes
2
answers
901
views
Given a formal power series ,decide whether there exists a polynomial the series satisfies and if it exists,how to write it down?
Given a formal power series $$y(x)=\sum_{i=0}^{\infty} a_i x^i$$ Is there an algorithm that decides whether there exists a polynomial$$ P(x,y)=p_n(x)y^n+p_{n-1}(x)y^{n-1}+\cdots+p_0(x)=0,p_j(x)\in F[x]...
- 6,397
1
vote
0
answers
206
views
Testing functional equivalence
We are looking for the most efficient (most recent, or best) techniques to check if two algebraic expressions (elementary, Calculus-type functions) are equivalent (or if an expression is equivalent to ...
- 6,210
0
votes
1
answer
182
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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