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23h
answered Expectation of minimum discrete and continious random variable
1d
comment Borel Measurable Function 3
Yes, but note that you also need $X$ to be a topological space in order for the Borel sigma algebra (the sigma generated by the open sets) to be defined.
1d
answered $\arg\max$ of an increasing function grows as the region grows.
1d
answered Reasoning behind method of steepest descent
1d
comment Finding a One Step Transition Matrix for a Markov Process? (Gambling Application)
To set up the transition matrix you need to describe the gambling itself (Is it a a toss of a fair coin, a slot machine with $N$ different outcome and probabilities $\mu(n)$ of outcome $n$, etc?
1d
answered non-stationary Markov chain n-step
1d
comment Book recommendation needed: asymptotic behavior of non-stationary Markov chain
Continuous-time or discrete-time chains?
Feb
11
revised How to efficiently represent and manipulate polynomials in software?
added 428 characters in body
Feb
11
revised How to efficiently represent and manipulate polynomials in software?
added 256 characters in body
Feb
11
comment How to efficiently represent and manipulate polynomials in software?
Thank you, this is a nice and sound suggestion. As a attempt I've implemented something along these lines. I gave the bounty to Respawned Fluff because of his great references, hope you do not mind to much.
Feb
11
accepted How to efficiently represent and manipulate polynomials in software?
Feb
11
comment How to efficiently represent and manipulate polynomials in software?
Thank you for the detailed reply and the references. This is exactly the type of thing I was looking for.
Feb
10
comment How to efficiently represent and manipulate polynomials in software?
@RespawnedFluff yes for the examples I've included it really does not matter. However, ideally I'd like to manipulate polynomials in the low tens of variables and degrees in which I've found it really does matter.
Feb
5
comment How to efficiently represent and manipulate polynomials in software?
@AlexR you're right. However, this would only help in some cases (for instance, it wouldn't make a difference in your example).
Feb
5
comment How to efficiently represent and manipulate polynomials in software?
@AlexR However if no one else posts another suggestion and you copy paste one of your comments into a reply I'll give the bounty to you.
Feb
5
comment How to efficiently represent and manipulate polynomials in software?
@AlexR Thank you for the suggestion, using tensors would get rid of the headache of trying to decide what number corresponds to which monomial. However, without further tweaking, I'd end up using more memory than I need to (in your example you need to store 9 numbers to represent a polynomial with only 3 non-zero coefficients). In general, even if all coefficients are non-zero, to save a polynomial of degree $d$ in $n$ variables I'd need to save $n^d$ numbers while the polynomial only has $n+d$ choose $d$ coefficients. So for the time being I'd like to leave the question open.
Feb
5
revised How to efficiently represent and manipulate polynomials in software?
added 91 characters in body
Feb
2
revised How to efficiently represent and manipulate polynomials in software?
edited title
Feb
2
asked How to efficiently represent and manipulate polynomials in software?
Jan
26
awarded  Nice Question