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2019-08-14 11:15:47 -0600 | asked a question | How to expand the result of derivative()? I ran:
and the result was:
I personally would prefer |

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2019-07-24 09:21:35 -0600 | commented answer | Complex numerical integration: how can it be performed in SageMath? This specific integral isn't symbolically integratable at all; I originally meant to write the bounds as -infinity to infinity, in that case the solution is the Airy $2\pi Ai(z)$ function. Complex integrals that are analytically integratable (e.g. $\int_{0}^{2\pi} e^{ix} dx$) can be analytically (or symbolically) solved in SageMath, but not numerically solved. |

2019-07-24 08:52:17 -0600 | commented answer | Complex numerical integration: how can it be performed in SageMath? Well, it's a roundabout way of solving it, but sure it's satisfactory. Although, if anyone has a more direct way of numerical integration with complex numbers I'll be happy to accept such an answer. |

2019-07-24 08:48:24 -0600 | commented answer | How to solve Sturm-Liouville problems in SageMath? If you look at my question the conditions are: $y(0)=y(\infty)=0$ (granted, I added that like 30 mins before you published this answer, so maybe you missed it). I didn't really expect desolve to work on this, otherwise my DuckDuckGo search probably would have detected a mention of its use for this purpose (SLEs are a different kettle of fish to usual ODEs in terms of how they are solved, so I would have expected a special mention of them, if desolve could solve them). Nonetheless, I gave it a go, here's the code I used and I placed the error in a comment: https://gist.github.com/fusion809/b3e.... |

2019-07-24 07:53:06 -0600 | asked a question | Complex numerical integration: how can it be performed in SageMath?
Likewise: returns: . If I add a |

2019-07-24 05:32:11 -0600 | commented answer | How to solve Sturm-Liouville problems in SageMath? Incorrect, because it does not take the boundary conditions into account, nor does it take into account that lambda is an eigenvalue, not just any old parameter. The solution only satisfies the boundary conditions when lambda is a zero of the Airy Ai(x) function. |

2019-07-24 05:01:37 -0600 | commented question | How to solve Sturm-Liouville problems in SageMath? Thanks, shall do. |

2019-07-24 00:17:12 -0600 | asked a question | How to solve Sturm-Liouville problems in SageMath? I've conducted DuckDuckGo searches for "Sturm-Liouville sagemath" and received no usable results, and as a result I am here to ask, how can one solve Sturm-Liouville problems with SageMath? I know how to do so numerically with Julia, GNU Octave and Scilab, using matrices, but is there any way to solve at least some of them analytically in SageMath (e.g. $\frac{d^2 y}{dx^2}-xy = \lambda y$ has solutions $y_n=C\cdot \textit{Ai}(x+\lambda_n)$, where $\lambda_n $ are the zeros of the Airy $\textit{Ai}(x)$ function, if $y(0)=y(\infty)=0$)? Failing this, is there a way to numerically solve them in SageMath (without resorting to its interfaces with the languages I just mentioned)? If it helps, here's the code I use in GNU Octave to solve the aforementioned SLE: . It uses a Chebyshev spectral method on the extrema grid, and then analyses the results. |

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2019-04-14 11:25:52 -0600 | marked best answer | How do I plot a 3D Lorenz attractor with x, y and z labels? I have been attempting to perform a 3D wireframe plot of the solution to the Lorenz equations, which is stored in the variables X, Y and Z. This is what I am presently using (unsuccessfully I might add): How do I get this plot to work? I'm guessing you'll probably be able to guess that X, Y and Z are ndarrays, produced from this SageMath script: |

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2017-08-16 21:34:18 -0600 | commented question | How to calculate the double factorial in SageMath? Ya I'm well aware convergence is an issue. This method with N (number of terms) = 10,000 is only accurate to 6 decimal places. I know a far more convergent method of estimating $\sqrt{2}$ is Newton's method. Just wanted to give this a try. |

2017-08-16 20:44:38 -0600 | marked best answer | How to calculate the double factorial in SageMath? I would like to implement the square root of 2 power series: $ \sqrt{2} = -\sum \limits_{n=0}^{\infty}{\frac{(-1)^n (2n-3)!!}{2^n \times n!}} $ (which I obtained from the Maclaurin series of $\sqrt{1+x}$ with $x=1$) in SageMath but I cannot seem to find the double factorial function in the SageMath docs. Is there one? I suppose if a double factorial function is not available I could use this method of finding the double factorial that I found on Wolfram MathWorld: $\Gamma(n+\frac{1}{2}) = \frac{(2n-1)!!}{2^n}\sqrt{\pi}$ |

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