12,193 reputation
340114
bio website mit.edu/~darij/www
location Karlsruhe (home), Munich (until summer 2011), Cambridge/MA (2011-)
age 26
visits member for 5 years, 7 months
seen 1 hour ago
I'm just here for asking stupid questions.

1d
comment Co-quasitriangular Hopf algebra - notation
Such questions are always better with a link/reference to the article, btw.
1d
comment Co-quasitriangular Hopf algebra - notation
Maybe it means $r \circ T$, where $T$ is the twist? (This is just a guess motivated by the fact that $\sigma_{ij}$ often means "$\sigma$ acting on the tensorands $i$ and $j$ in this order".)
2d
comment Divisibility among discriminants
Oops, I think I cannot read... I thought of $f$ and $g$ being polynomials. Is it true then? (I actually don't know what the discriminant of a non-polynomial is.)
2d
comment Divisibility among discriminants
And as preliminary work, any results about $\operatorname{Res}\left(f\circ h, g\circ h\right)$ and $\operatorname{Res}\left(f\circ g, f\circ h\right)$ would be useful. It is a pity that the world has forgotten the art of resultants :/
2d
comment Divisibility among discriminants
Have you tried generalizing to something like $D\left(f\right) D\left(g\right) = D\left(f \circ g\right)$ ?
Jul
28
comment An equality for the dimension of the sum of subspaces (in the non-degenerate case)
It isn't (e.g., daim.idi.ntnu.no/masteroppgave?id=4316 ), but the characterization is beyond my understanding.
Jul
28
comment An equality for the dimension of the sum of subspaces (in the non-degenerate case)
Hmm. I fear this is becoming more and more a question about indecomposable representations of the four-subspaces quiver...
Jul
28
revised An equality for the dimension of the sum of subspaces (in the non-degenerate case)
added 23 characters in body
Jul
28
comment An equality for the dimension of the sum of subspaces (in the non-degenerate case)
Take my counterexample $\left(U_1, U_2, U_3, U_4\right)$, and take a non-degenerate quadruple $\left(V_1, V_2, V_3, V_4\right)$ for which equality holds (e.g., pick a $4$-dimensional vector space with basis $e_1,e_2,e_3,e_4$, and let $V_i$ be the span of $e_1,e_2,\ldots,\widehat{e_i},\ldots,e_4$). Now $\left(U_1\oplus V_1,U_2\oplus V_2,U_3\oplus V_3,U_4\oplus V_4\right)$ (in the direct sum of the ambient spaces of the two quadruples) should be a non-degenerate counterexample.
Jul
24
revised Eigenvalues of principal minors Vs. eigenvalues of the matrix
edited title
Jul
19
comment Books you would like to read (if somebody would just write them…)
@LennartMeier: Link is broken for me.
Jul
17
comment Commutative algebra books representing the edge of research
Swanson's books ( people.reed.edu/~iswanson/papers.html ), particularly the one with Huneke on integral closure, come to my mind.
Jul
17
comment In modules over finite rings $Rv = Rw \iff R^\times v = R^\times w$
Why is $R/Re \cong R/Rf $ ?
Jul
16
answered What are examples of good toy models in mathematics?
Jul
14
awarded  Nice Answer
Jul
13
awarded  Nice Answer
Jul
13
comment When to postpone a proof?
@EmanueleTron: Example 1 has its own downsides. It forces the authors to introduce all notations necessary to state all important results right away in the introduction. This is fine if there are only 4-5 definitions, but often there are 15-20. A certain kind of reader (often it is me) has troubles following a large pile of definitions without getting "hands-on experience" (such as solving exercises or reading examples or proofs of lemmas) after every two or three of them.
Jul
12
comment Searching a specific matrix whose determinant is a product which is similar to the Vandermonde determinant
Also I think there is a dissonance in the question: Either $A$ and $B$ should be subsets of $\left\{1,2,\ldots,n\right\}$ (rather than of the set of pairs you wrote), or the products should run over $\left(i,j\right)\in A$. I supposed you want the former.
Jul
12
comment Searching a specific matrix whose determinant is a product which is similar to the Vandermonde determinant
What surely works is the Sylvester matrix of the monic polynomial $\prod_{i\in A}\left(X - x_i\right)$ and the monic polynomial $\prod_{j\in B}\left(X - x_j\right)$". Its entries will be certain (minus-plus) elementary symmetric functions of the x'es.
Jul
12
comment What technical and/or theoretical challenges are involved in automatically extracting proofs from books and papers into Coq code?
"We're now trying to write an updated and more comprehensive document." That's wonderful news, thank you!