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# 8,672 Comments

 Jun22 comment Using Gröbner bases for solving polynomial equations This is quite nice! I do some amount of work on equations of state (e.g. the Redlich-Kwong EOS and modifications thereof) so this is interesting to me. I recall tediously deriving $\Delta H$ and $\Delta G$ and inversion temperatures by hand... Jun21 comment Using Gröbner bases for solving polynomial equations @jbc, would you consider writing an answer demonstrating this? Jun20 comment Find closed form for $1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 10, \ldots$ Nevertheless, the OP should have visited the OEIS first for his sequence... Jun17 comment Mathematica: How to convert scales to frequencies? Sure, but that site you speak of didn't exist at the time you asked this question (otherwise, you'd have asked it there to begin with ;) ). Anyway... Jun17 comment Mathematica: How to convert scales to frequencies? To those voting to close: this topic is too old to be migrated anymore; go easy, y'all. Jun13 comment Help find hard integrals that evaluate to $59$? Ah, shoot; let me look for my notes on this... if memory serves, I trolled through OEIS and looked for generating functions. Jun12 comment Parallel to line on $f(x)=1+\sin(x)/x$ Well, since the discontinuity at $0$ is of the removable kind, I went ahead and defined the value of the function at $0$ to be the same as the value of an appropriate limit. Or, did you not tackle that limit while learning calculus? Jun12 comment Parallel to line on $f(x)=1+\sin(x)/x$ ...the function you were asking about. What else could it have been? Jun12 comment Any four points on the space curve given by the parametrization $(t,t^2,t^3)$ are noncolinear After noting that the matrix is Vandermonde, recall particular conditions on the rows for a matrix to be singular. Interpret geometrically. Jun11 comment My sister absolutely refuses to learn math @Kolyunya, " She probably wants to become an artist or something" so, ratio and proportions aren't important to artists? How about geometry? I'm not even counting those people who use actual math to make sculptures, e.g. Bathsheba Grossman or George Hart. Jun11 comment My sister absolutely refuses to learn math @Love, your suggestion of "treat it like a Foreign language" is quite sound; the symbols were invented precisely to compress what would take a lot of English/whatever words to describe. 'course, some people don't want to bother with learning foreign languages either. Jun11 comment My sister absolutely refuses to learn math @Love, "I was always confident I could solve the problem if I knew what the words meant..." - I'd say that applies not only to math, but to programming as well, and to any subject of some complexity in general. Jun9 comment Goldberg polyhedra coordinates You might want to see this. Jun8 comment Moore-Penrose pseudo inverse algorithm implementation in Matlab @justik, as long as your computing environment allows you to compute the singular value decomposition of a matrix, then it is not too hard to construct the Moore-Penrose inverse. Jun8 comment Laplace, Legendre, Fourier, Hankel, Mellin, Hilbert, Borel, Z…: unified treatment of transforms? You might be interested in things like the FHA cycle... Jun8 comment Eigenvectors of inverse complex matrix @Sharkos, certainly true, but I suspect that OP might not have noticed that his eigenvectors can look a bit different, since MATLAB does no normalization of eigenvectors, if memory serves. Jun8 comment Eigenvectors of inverse complex matrix You are aware that if $\mathbf v$ is an eigenvector of $\mathbf A$ corresponding to an eigenvalue $\lambda$, then $c\mathbf v$ ($c\neq 0$) is an equally valid eigenvector as well? Jun8 comment Switch place of 2 infinite summations A related question. Jun8 comment How to evaluate $\lim\limits_{s\to\infty}\log s$? @JMC, after excluding the bases $0$ and $1$, the logarithm remains sensible, no? Jun7 comment Generation of unimodular matrices with bounded elements I suppose a nice alternative would be to grab the unimodular factor from the Hermite decomposition of a random integer matrix, and then apply your "fix" to the unimodular matrix thus generated. Thanks for the elaborate answer!