Crandi

Examples Sagemath Ipynb Github

Leo Migdal
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examples sagemath ipynb github

This repository contains a collection of SageMath notebooks used to validate key steps in large-scale calculation involving partition generating functions and their analogues. These computations arise from combinatorial and generating function-related research in partition theory. The codebase supports the verification of both final results and intermediate stages within a complex chain of reasoning in partition theory, particularly related to generating functions. The scripts encapsulate various aspects of these calculations. Please note: This collection of sagemath notebooks is largely undocumented, reflecting their origin as internal research tools developed primarily for personal validation rather than public distribution. I apologize for the limited documentation and understand this may make exploration challenging.

A provided tutorial notebook is intended as a more accessible starting point and the best entry for understanding the workflow and methodology. Running the tutorial notebook The easiest way to get started is to open and run The 5-core partitions.ipynb with SageMath kernel, which walks through example calculations and explains the workflow. This notebook provides context and commentary that helps make sense of the rest of the scripts. Exploring the other scripts The rest of the code files can be executed within SageMath to reproduce checks and intermediate steps. Due to limited documentation, familiarity with the theory of partitions and generating functions is assumed. In this lab, we will use SageMath to determine the convergence or divergence of a sequence of numbers and of infinite series.

Consider the sequence {cos⁡(nπ)arctan⁡(n)}n=1∞\{\cos(n\pi)\arctan(n)\}_{n=1}^\infty{cos(nπ)arctan(n)}n=1∞​. We start by determining the first 10 terms of this sequence. We can do this in SageMath by letting an=cos⁡(nπ)arctan⁡(n)a_n = \cos(n\pi)\arctan(n)an​=cos(nπ)arctan(n) and then using a for\textbf{for}for loop and the range\textbf{range}range command. We can get a better idea of what these numbers are by using the round\textbf{round}round command. Note that the terms of the sequence do not appear to approach a specific number. We can better tell what is happening by plotting the first 100 or so terms of the sequence.

We can plot a point in SageMath by using the point\textbf{point}point command along with the show\textbf{show}show command. To plot multiple points on the same plot, we will store the points in a list and then show the list. SageMath does not allow us to plug the list directly into the show\textbf{show}show command. Instead, we must input the sum of the elements in the list. From the graph, we see that the odd terms are approaching a specific value, namely −π2-\frac{\pi}{2}−2π​, and the even terms are approaching a specfic value, namely π2.\frac{\pi}{2}.2π​. However, since these values are different, the sequence diverges.

In Math with Sagemath you will find a collection of basic math problems solved using SageMath. I divided the blog in sections. Each section will start with the explanation on how to solve the problems by hand and what SageMath functions we can use. You will also find links to examples solved using SageMath. To better understand how to solve the examples with SageMath, I recommend downloading the corresponding Jupyter notebooks, or launch the binder (see below) so that you can execute them online. The content will be added as posts and I will post randomly on different topics… So be patient if there is a topic missing!

If you want to test the examples without having to download all the software, you can use my container that I set up on Binder. You will be able to run the SageMath notebooks online. Instantly share code, notes, and snippets. The notebooks are in the Jupyter format (ipynb). They can be read directly in the browser by just clicking on their names in the list below. The notebooks are opened in read-only mode, but you can access to an interactive version by clicking on Execute on Binder in the top right menu.

To download a notebook and run it on your computer, click on [ipynb] (or on the download button in the notebook top right menu). See also the tutorial notebook (Japanese version is here), the tutorial videos, the plot tutorial (plots of coordinate charts, manifold points, vector fields and curves), the tutorial on pseudo-Riemannian manifolds (metric, Levi-Civita connection, curvature,... Other examples regarding black hole spacetimes are posted here. Examples regarding black branes in 5-dimensional spacetimes: black branes in Lifshitz-like spacetimes and Vaidya-Lifshitz solution Here are some instructions on how to view and use a .ipynb-File containing SageMath computations. In order to run the Notebook, you need to access an installation of SageMath somehow.

In case of questions, I’m happy to help — just contact me any way you prefer. In order to install SageMath locally, please follow the instructions in the SageMath installation guide. For particularly quick access, consider installing SageMath via binaries (directly available for most operating systems), see the SageMath download page. As soon as you have a running version of SageMath, you can start a local notebook server with the command Then, a tab in your browser should open where you can navigate and selevt the ipynb-file in order to view its content and to run the computations in the file. The methods learned in Chapter 4 of the text for finding extreme values have practical applications in many areas of life.

In this lab, we will use SageMath to help with solving several optimization problems. The following strategy for solving optimization problems is outlined on Page 264 of the text. Read and understand the problem. What is the unknown? What are the given quantities and conditions? Draw a picture.

In most problems it is useful to draw a picture and identify the given and required quantities in the picture. Introduce variables. Asign a symbol for the quantity, let us call it QQQ, that is to be maximized or minimized. Also, select symbols for other unknown quantities. Use suggestive notation whenever possible: AAA for area, hhh for height, rrr for radius, etc. There was an error while loading.

Please reload this page. In your Calculus course, you will encounter many types of functions. The most beneficial way of understanding how a function behaves is to study its graph. In this lab, we will learn how to use SageMath to create graphs of various functions. SageMath has many built in functions, commands, and constants such as tan⁡(x),expand(… ),π,\tan(x), \textbf{expand}(\dots), \pi,tan(x),expand(…),π, etc. One way to learn more about these is to read the SageMath documentation.

The easiest way to do this in the notebook is to use the ?\textbf{?}? command. This command opens up a new window at the bottom of the screen filled with useful information and examples on how to use the function or command. Use SageMath to bring up the documentation for the plot\textbf{plot}plot command and look through all of the available options you have to customize your graph of a function. We will use this information to plot cos⁡(x)\cos(x)cos(x) as an orange dashed line in the viewing window [−2π,2π]×[−1,1][-2\pi, 2\pi] \times [-1,1][−2π,2π]×[−1,1]. Plot the function f(x)=x−2+1f(x) = \sqrt{x-2} + 1f(x)=x−2​+1 as a green dotted line with the xxx-range being 2≤x≤112 \leq x \leq 112≤x≤11.

SageMath is an open-source mathematical software, similar to Wolfram Mathematica. SageMath has an interface to GAP by default. For Mac OSX, a simple way is to download a binary release (e.g. SageMath-10.2_arm64.dmg). For Linux, it is complicated to install the latest version. Since the package managers can install only SageMath v9, one needs to build it from source code in GitHub.

See the instructions at Reinstall Ubuntu. Type sage in Terminal. If you want to launch jupyter notebook, type Create an ipynb file, and choose SageMath kernel.

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This repository contains a collection of SageMath notebooks used to validate key steps in large-scale calculation involving partition generating functions and their analogues. These computations arise from combinatorial and generating function-related research in partition theory. The codebase supports the verification of both final results and intermediate stages within a complex chain of reasoni...

A Provided Tutorial Notebook Is Intended As A More Accessible

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Consider The Sequence {cos⁡(nπ)arctan⁡(n)}n=1∞\{\cos(n\pi)\arctan(n)\}_{n=1}^\infty{cos(nπ)arctan(n)}n=1∞​. We Start By Determining The First

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We can plot a point in SageMath by using the point\textbf{point}point command along with the show\textbf{show}show command. To plot multiple points on the same plot, we will store the points in a list and then show the list. SageMath does not allow us to plug the list directly into the show\textbf{show}show command. Instead, we must input the sum of the elements in the list. From the graph, we see...

In Math With Sagemath You Will Find A Collection Of

In Math with Sagemath you will find a collection of basic math problems solved using SageMath. I divided the blog in sections. Each section will start with the explanation on how to solve the problems by hand and what SageMath functions we can use. You will also find links to examples solved using SageMath. To better understand how to solve the examples with SageMath, I recommend downloading the c...