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2022-01-21 03:01:38 +0200 | asked a question | Can sage automatically find singular points of a function? Can sage automatically find singular points of a function? When computing the asymptotics of a series, a common idea is |
2021-09-01 02:57:55 +0200 | commented answer | Change Valuation to do Series Reversion Thank you! I don't know how the idea of solving for a series in one variable, then reversing that and substituting the o |
2021-09-01 02:48:42 +0200 | marked best answer | Change Valuation to do Series Reversion I've run into the problem of doing series reversion with symbolic power series a few times now, and while in the past I was able to hack together a solution (by using some inelegant combination of Concretely, let's say you want to compute a power series for those $x$ such that $x \sin(x) + \cos(x) = 0$ (as indeed I do). This can only happen when $\sin(x) \approx 0$, so we want to look near $n \pi$. Here we can cheat a little bit and use the fact that $\sin$ and $\cos$ are periodic to get a good series expansion for this. If we write $q = n \pi$, we get Now we have $$ s = 1 + q \epsilon + \frac{1}{2} \epsilon^{2} -\frac{1}{6} q \epsilon^{3} -\frac{1}{8} \epsilon^{4} + \frac{1}{120} q \epsilon^{5} + \ldots $$ Since we want to know that $x \sin(x) + \cos(x) = 0$, we should set $s = 0$ and solve for $\epsilon$ (which will depend on $n$). Then our roots will be exactly $q + \epsilon$, that is, $n \pi + \epsilon$. We can do this using lagrange inversion, where if $s^{-1}$ is the inverse of $s$ we'll have $\epsilon = s^{-1}(0)$ and our problem will be solved. Unfortunately, there's no way (as far as I know) to do lagrange inversion on a symbolic series (and in my experience symbolic power series are probably best avoided anyways. It seems like other people share this belief too). I'm happy to do this trick of working over some other field, but I'm getting an error: Is there a way I can force sage to see that If not, is there another (better) way to handle series reversion with variable coefficients? Thanks in advance! ^_^ |
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2021-08-07 02:14:30 +0200 | commented question | polynomial multiplication is unexpectedly slow As an aside, I wasn't able to get this particular implementation working efficiently, but I found an algorithm to more e |
2021-07-22 03:46:09 +0200 | commented question | polynomial multiplication is unexpectedly slow @mwageringel, @nbruin, @rburing |
2021-07-22 03:45:46 +0200 | commented question | polynomial multiplication is unexpectedly slow Thank you all for your ideas! I've modified my code to use the S.flattening_morphism().codomain(), and this has helped s |
2021-07-17 22:45:40 +0200 | commented question | polynomial multiplication is unexpectedly slow @rburing -- that's exactly the next step. We know that the coefficients of f are symmetric polynomials in the roots a[i] |
2021-07-17 09:30:59 +0200 | edited question | polynomial multiplication is unexpectedly slow polynomial multiplication is unexpectedly slow Hello! I'm writing some code to solve by radicals a polynomial with solv |
2021-07-17 09:29:29 +0200 | asked a question | polynomial multiplication is unexpectedly slow polynomial multiplication is unexpectedly slow Hello! I'm writing some code to solve by radicals a polynomial with solv |
2021-06-23 08:16:18 +0200 | edited question | Change Valuation to do Series Reversion Change Valuation to do Series Reversion I've run into the problem of doing series reversion with symbolic power series a |
2021-06-23 08:12:21 +0200 | edited question | Change Valuation to do Series Reversion Change Valuation to do Series Reversion I've run into the problem of doing series reversion with symbolic power series a |
2021-06-23 08:10:02 +0200 | asked a question | Change Valuation to do Series Reversion Change Valuation to do Series Reversion I've run into the problem of doing series reversion with symbolic power series a |
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2021-06-04 20:10:25 +0200 | edited question | Regular Languages in Sage? Regular Languages in Sage? I see there's a package for automata, but is there a way to work directly with regular langua |
2021-06-04 20:10:05 +0200 | edited question | Regular Languages in Sage? Regular Languages in Sage? I see there's a package for automata, but is there a way to work directly with regular langua |
2021-06-04 20:09:04 +0200 | edited question | Regular Languages in Sage? Regular Languages in Sage? I see there's a package for automata, but is there a way to work directly with regular langua |
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2021-06-04 20:08:54 +0200 | asked a question | Regular Languages in Sage? Regular Languages in Sage? I see there's a package for automata, but is there a way to work directly with regular langua |
2021-02-24 09:13:11 +0200 | commented answer | Can sage draw simplicial complexes? Thanks for the answer! I'll have to look into writing my own, then... If it's decently robust, maybe I'll look into submitting a pull request (or however sage handles code submission... I'll look into it once I actually have code in hand :P ) |
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2021-02-23 00:07:22 +0200 | asked a question | Can sage draw simplicial complexes? I understand it's asking a lot to draw complexes in dimensions $>3$, but for (fairly simple) 2 dimensional complexes, it seems reasonable that some plotting algorithm should exist. Even looking at, say, Since the things I'm trying to draw are fairly simple, I would be wiling to plot the $1$-skeleton (which sage can do) and then fill in the $2$-cells myself, but I'm not even sure how to go about doing that. Obviously if there is a pre-existing method or library for this, that would be the best possible solution. Thanks in advance! ^{1}: I don't have the karma to post links, but I'm referencing doc.sagemath.org/html/en/reference/homology/sage/homology/simplicial_complex.html |