-2
votes
1answer
116 views

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 ...
1
vote
2answers
385 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 ...
1
vote
0answers
74 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 ...
8
votes
2answers
205 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 ...
0
votes
1answer
155 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, ...