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12h
revised Relation between continuous maps and convergence of sequences
\bar made f(A') and f(A)' indistinguishable
1d
comment Surjective functions and cal'
$f$ surjective means $f\left(\Bbb R\right)=\Bbb R$. That's true for $x\mapsto x$ and $x\mapsto -x$ but not $x\mapsto 0$ because $\left(x\mapsto 0\right)\left(\Bbb R\right)=\{0\}\not= \Bbb R$. In other words, your friend is right.
1d
comment Minimal polynomial of a matrix whose elements have a certain form
If you're missing just one eigenvalue, since the trace is the sum of the eigenvalues, ...
Jul
2
awarded  Curious
May
25
comment How to find the ideals of $\Bbb{Z}_n$
They are all of the form $n\Bbb Z$. To prove it, take $n=$ the smallest positive element of an ideal and prove both inclusions. One is trivial. The other is done using Euclidean division.
May
17
comment Sufficient conditions for convexity using the right derivative
math.stackexchange.com/questions/418737/…
May
15
comment Numeric Analysis Interpolation of $f(x) , f'(x) $
You should have linear equations. Try to put them in matrix form.
May
15
comment Numeric Analysis Interpolation of $f(x) , f'(x) $
$P_2$ is a polynomial of degree $2$? If it is, just write $P_2(x)=ax^2+bx+c$ and use that in your equations.
May
15
comment Canonical representation of finite field
It's not terribly inconvenient. But since I want to use Shamir secret sharing, it triples the size of parts... So since I'm going to write those on paper, I'd rather keep them short :) $p=2$ and $n=$"number of bits" and can be determined just by looking at the paper (because I'll leave non-significant $0$s). But I think it'll take the smallest $p>2^n$ that's prime.
May
14
accepted Canonical representation of finite field
May
14
comment Canonical representation of finite field
I was wondering how to find it algorithmically but I found papers explaining that. And I know that $k<n$ but you said $a\in\Bbb F_{p^k}$. Anyway, it's far too complicated for what I had in mind so I'll just take a $\Bbb F_{p'}$ with $p'>p^n$ and prime.
May
14
comment Canonical representation of finite field
And, assuming I want to do some computation where I need to represent the elements as polynomials modulo another polynomial. How do I get from those ireducibles polynomials to my element? I just try all elements and the only one on which the evaluation of the polynomial yields $0$ is the good one?
May
14
comment Canonical representation of finite field
Hm. Why is it not true? This wikipedia page seems to say it is en.wikipedia.org/wiki/Finite_field#Cyclic
May
14
comment Canonical representation of finite field
Will this polynomial have coefficients in $\Bbb F_p$? It feels like it should be but it's not that obviously. If you apply the Frobenius automorphism, you get $X^{p^k}\pm a^{p^k}$ and unless I'm mistaken, that's $X^{p^k}\pm a$. How does that help representing $a$? Or should I extend the polynomial and it'll magically have coefficients in $\Bbb F_p$?
May
14
comment Canonical representation of finite field
I wanted to represent my elements of $\Bbb F_{p^n}$ by polynomials of $\Bbb F_p[X]$. And I assumed there would be many ways to do so.
May
14
asked Canonical representation of finite field
May
13
comment Derivatives and functions
math.stackexchange.com/questions/792089/…
May
10
comment Using matrices to calculate fibonacci?
You diagonalize the matrix so then, computing the $n$-th power is easy and you get it back in the right basis with two matrix multiplications.
May
10
comment Using matrices to calculate fibonacci?
math.stackexchange.com/questions/342096/…
May
10
comment Math Competition Question Singapore
@SanathDevalapurkar : I noticed. For some reason I had imagined a $+\dots$ at the end. Doesn't change much though.