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  
stats  profile views  12,640 
I'm just here for asking stupid questions.
1d

comment 
Coquasitriangular Hopf algebra  notation
Such questions are always better with a link/reference to the article, btw. 
1d

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Coquasitriangular 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 nonpolynomial is.) 
2d

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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

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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 
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An equality for the dimension of the sum of subspaces (in the nondegenerate 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 nondegenerate case)
Hmm. I fear this is becoming more and more a question about indecomposable representations of the foursubspaces quiver... 
Jul 28 
revised 
An equality for the dimension of the sum of subspaces (in the nondegenerate case)
added 23 characters in body 
Jul 28 
comment 
An equality for the dimension of the sum of subspaces (in the nondegenerate case)
Take my counterexample $\left(U_1, U_2, U_3, U_4\right)$, and take a nondegenerate 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 nondegenerate 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 45 definitions, but often there are 1520. A certain kind of reader (often it is me) has troubles following a large pile of definitions without getting "handson experience" (such as solving exercises or reading examples or proofs of lemmas) after every two or three of them. 
Jul 12 
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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 
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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 (minusplus) elementary symmetric functions of the x'es. 
Jul 12 
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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! 