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Apr
3
comment A Conjecture based on the Complex Conjugate Root Theorem.
I agree, I was just thinking aloud
Apr
3
comment A Conjecture based on the Complex Conjugate Root Theorem.
so you can get polynomials of degree n with n prescribed roots...
Apr
3
comment A Conjecture based on the Complex Conjugate Root Theorem.
every monic polynomial f(z) is the product of $z-\alpha_k$, where $\alpha_k$ are its roots.
Mar
5
comment On Hyper-geometric Functions and its recurrence relation
right, just replace $a$ by $a+n$
Mar
5
comment On Hyper-geometric Functions and its recurrence relation
$a$ is just a parameter; nothing will become invalid if you change it to $a+n$.
Feb
25
comment Eigenvalues of Symmetric Pseudo-Toeplitz Matrix
I suppose you checked en.wikipedia.org/wiki/Tridiagonal_matrix#Determinant and noticed that due to this, you can write down the characteristic polynomial quickly.
Apr
5
comment Dominated convergence theorem and fundamental lemma
this looks like a meaningful question...
Mar
26
comment Proving that $(e^x+1)^{1/3}$ has no elementary antiderivative
well, consider my answer being done by computer, not me :-)
Mar
22
comment Determinant of a Vandermonde matrix of roots of monic polynomial with integer coefficients
the square of the Vandermonde is a symmetric function, and thus Per's argument applies.
Mar
18
comment Nauty software package and weighted graphs
There is no such command in dreadnaut. You will have to supply it the already prepared non-weighted graph.
Mar
18
comment Nauty software package and weighted graphs
Well, how you represent weights is an entirely different question. In the setting of computing automorphisms and isomorphisms all what matters is that different weights are represented by different integer numbers (or colours).
Jan
21
comment How unitarize an irreducible representation of a finite group?
In fact you don't need to compute eigenvalues and eigenvectors. Although you will still need to compute square roots of real cyclotomics at the end, as I mentioned in GAP forum.
Sep
29
comment What is the second least non prime order of a simple group?
PSL(3,2), not PSL(7,2)
Sep
28
comment divisibility of number of solutions of $x_1+\cdots+x_k=n$
I'm not 100% sure, but it seems that if $\gcd(n,k)=1$ then all the $k$ cyclic $k$-shifts of a solution are different. This means that the number of solutions is divisible by $k$.
Dec
4
comment Complexity of multiplying Cauchy matrix by a vector
I've edited the question. Hopefully someone reviews the changes.
Nov
29
comment Complexity of multiplying Cauchy matrix by a vector
this is the problem of multiplying a vector by a matrix, not solving linear equations...
Sep
17
comment a question about odd cycle
isn't a proof for $k=1$ trivial? Take 2 vertices $u_0,u_2$ at distance 2 (say, $u_0u_1u_2$ is a path connecting them). Then there should be a length $2k+1=3$ path $u_0v_1v_2u_2$ between them, too. Now take all the vertices $u_i$ and $v_j$ - they form a 5-path, right?