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Dec
8
comment Could a real curve symmetric across the line be defined only by polynomial that is not reflection-invariant?
The title asks for something not reflection-invariant, but the text inside asks for something invariant.
Nov
13
comment Is there a way to find out how many distinct roots a polynomial has?
This question has answers in textbooks on field theory as one of the results. Not ideal for Mathoverflow; better to be in math.stackexchange.
Oct
28
comment What are the necessary conditions for a real number to be a cyclotomic integers?
When we start with an irreducible polynomial over some field and regards its factorization into irreducible in a Galois extension are not the degrees of irreducible factors above equal (this follows from the transitive action of the Galois group on the primes lying above a given prime: Here the dedekind domains are the PIDs given by polynomial rings over the base and extension fields). So I don't fully understand what is special about cyclotomy here.
Oct
27
comment What are the necessary conditions for a real number to be a cyclotomic integers?
@Emil: Expanding on your comment integers of all quadratic fields, following Kronecker-Weber (or something simpler like quadratic reciprocity), are cyclotomic integers.
Oct
27
comment What are the necessary conditions for a real number to be a cyclotomic integers?
A real number $x$ is an algebraic integer if and only if $-x$ is. So positivity plays no role.
Sep
30
awarded  Quorum
May
9
answered Roots of not-necessarily reciprocal polynomials
Apr
28
comment Factoring a polynomial in a specific manner
Your definition of $d'$ involves an undefined $l$. Can you look into it.
Apr
25
comment Density of polynomials with a prescribed number field extension
or rather $(2N+1)^{n+1}$? (I missed zero!)
Apr
25
comment Density of polynomials with a prescribed number field extension
As the coefficients $a_i$ can lie between $-N$ and $N$, should not the definition of density have $(2N)^{n+1}$ in the denominator?
Apr
24
comment Open source mathematical software
OP wanted abstract mathematics, and plotting is mostly about numerical mathematics and applied mathematics.
Apr
17
comment Primes as uncorrelated random variables
I once saw a heuristic argument that the probability of two numbers being relatively prime is $6/\pi^2$, the computation involving calculating the value of Euler's zeta function value $\zeta(2)$. How does this gel with this?
Apr
15
comment How to handle a polynomial whose roots exhibit obvious symmetry
Can I assume all your polynomials are irreducible?
Apr
15
comment How to handle a polynomial whose roots exhibit obvious symmetry
You say you expect to reduce the polynomial because of cyclic group of order 3. What exactly do you mean by reducing? Your polynomials are not irreducible? And your plot needs info on how to interpret: are the dots hights represent roots (real numbers always?) Multiple dots at same level does that means roots of same modulus?
Apr
14
comment Decomposition space of $\mathbb{C}$ by concentric circles
Thats right; you gave the answer first; I gave an explanation justifyuing; I'd encourage you to rewrite your comment as answer, then I'll upvote that and delete my answer. OK?
Apr
13
awarded  Yearling
Apr
13
answered Decomposition space of $\mathbb{C}$ by concentric circles
Mar
26
answered Existence of functions on finite sets with specific propertise
Mar
16
comment Range of a trace preserving completely positive projection
Request Eckhardt to make the comment into an answer and H\'ector to accept it so that the question does not end up as showing unanswered.
Feb
20
accepted Do all algebraic number fields arise from Eisenstein polynomials?