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Feb
21
comment Can every rational function be represented in barycentric form?
@JohnHughes You mean because $y_j$ is not just a coefficient, but also identical to $r(x_j)$? Maybe you have a good point, and it could be related to my troubles understanding the cited statement.
Feb
21
comment Can every rational function be represented in barycentric form?
In Barycentric Lagrange Interpolation. Jean-Paul Berrut, Lloyd N. Trefethen., the earliest references seem to be from 1997 of Jean-Paul Berrut. This is a case of an author citing another paper of himself as reference, so "it is known" might only refer to a very small set of people...
Feb
21
asked Can every rational function be represented in barycentric form?
Feb
16
accepted Is the 3d Schwartz space isomorphic to a subspace of the 1d Schwartz space?
Feb
16
revised Is the 3d Schwartz space isomorphic to a subspace of the 1d Schwartz space?
Clarified the isomorphism means isomorphism of topological vector spaces, and added information I found in the meantime
Feb
16
asked Is the 3d Schwartz space isomorphic to a subspace of the 1d Schwartz space?
Feb
15
answered Notable examples of “impossible” results ruled out by earlier barrier or no-go theorems or widespread beliefs
Feb
13
reviewed Leave Open Real Analysis, using Zorns Lemma
Jan
26
reviewed Close Logic - how to write $\exists !x$ without the $\exists !$ symbol
Dec
23
comment What's behind the Banach-Tarski paradox?
The physical world doesn't deal with sets at all!
Dec
19
awarded  Constituent
Dec
8
awarded  Caucus
Nov
29
comment Which associative and commutative operations are defined for any commutative ring?
@ThomasAndrews Yes, in case of addition the corresponding condition is that $b$ has to be in the range of $x\to ax$. What I like less is that $a$ and $b$ are currently not true parameters, but are restricted to the free commutative ring without generators, i.e. $\mathbb Z$. But I'm not sure how to extend Martin Brandenburg's "natural" argument to the case with parameters.
Nov
29
comment Which associative and commutative operations are defined for any commutative ring?
@ThomasAndrews It certainly won't be in the range of $\phi_{ab}$ if $b(b-1)/a$ is not defined, i.e. when $b(b-1)$ is not in the range of $x\to ax$. If on the other hand $b(b-1)$ is in the range of $x\to ax$, then the laws of commutative rings are sufficient to show that also the other expression will work.
Nov
29
comment How to show distributivity in a ring, and what is wrong with my algebra?
See also the appendix of math.stackexchange.com/questions/1001186/…
Nov
27
awarded  Nice Answer
Nov
12
revised Which associative and commutative operations are defined for any commutative ring?
Added an appendix with a more intuitive explanation/description of the found operations
Nov
6
comment Graph-Minor Theorem for Directed Graphs?
@Denis My guess would be that the other answer was the first answer by a new user, and got its votes through the corresponding review queue. In the review queue, you can only see the answer and the question, but not the other answers. The main claim I make in this answer is that the definition "A directed graph is a minor of another if the first can be obtained from a subgraph of the second by contracting edges." is equivalent to the definition given in the question. If you want to challenge this claim, or think I should it explain it in more detail, please let me know.
Nov
3
comment Example of a commutative ring which is not a subring of a commutative ring where every non-invertible element is a zero-divisor
Thanks for the link. So instead of "every non-invertible element is a zero-divisor", I could say "every regular element is a unit". Sweet, short and positive...
Nov
3
accepted Example of a commutative ring which is not a subring of a commutative ring where every non-invertible element is a zero-divisor