Sage Jupyter Readme Md At Main Bradencarlson Sage Jupyter Github

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This project was developed for Math 4220 and Math 4230 at Southern Utah University, to provide students studying Abstract Algebra an approachable interface to SageMath, to help them understand introductory topics in the course. The goal of this project is to help students everywhere - although it is primarily aimed at students of Abstract Algebra - to learn the syntax of SageMath, so as to provide them with... Please note that the layout of all of the files and sites closely follow the layout of the Abstract Algebra course videos given by Dr. Andrew Misseldine which can be found here. We assume that the student has no prior knowledge of the Python programming language, and has not used SageMath before. Therefore, the introduction documents may not be suitable for all users.

If a student has prior experience with the Python programming language, they should jump right into the project. At any time during the use of this project, if you encounter an error in the preloaded code, or there are other issues that you find, or even if you have an idea on... There was an error while loading. Please reload this page. There was an error while loading. Please reload this page.

Explanation of how to use this project with SageMathCell is unclear and needs to be rewritten. Here we go over a brief inroduction to SageMath, and its syntax, to provide us with the tools that we need to study some Abstract Algebra. Let's take a look at the following cell. We can easily define variables, perform various operations on them, and have them printed out to the screen. Also note the optional use of f-strings. This is a feture inherited from Python, when a string is preceeded by an f, then any variable that appears in backets will have it's value printed, rather than the variable name.

We can also combine variables to form other variables in SageMath. This will be very useful as we explore more complicated examples throughout this series. We will also need to know a little about types of data. There are many different types of data that we can define, and we have already seen a few! consider the following cell. We see that not only do x and y have different values, but they are of different types.

One is an integer, the other a string. Sage will tell us if something is wrong with our code, let's see an example. Providing users and developers consistency across repos is a valuable time saver and improves user productivity. On a larger scope, having the Jupyter name appear prominently in a repo’s README.md file improves the project’s name awareness. Please include a link to the documentation in the repo’s description. One common way that individuals find documentation is to look for and click on the doc badge that commonly is found right after the title.

Another benefit is an easy visual indication if the docs are not rendering properly. A Resources section at the end of the README.md gives useful links and information to users about the individual project and the larger Project Jupyter organization. Make sure to include any links to the individual project’s demo notebooks, if available. We can easily identify messages from $\mathbb{Z}_2^{k}$ with a polynomial in $\mathbb{Z}_2[x]$ with the following map \[ (a_0,a_1,\dots,a_{k-1})\rightarrow a_0+a_1x+\cdots +a_{k-1}x^{k-1} \] If we then fix some nonconstant polynomial $g(x)\in\mathbb{Z}_2[x]$ of degree $n-k$, we can... We will make use of Polynomial Rings in SageMath to implement this here. Consider the following example, taken from Judson's Abstract Algebra: Theory and Applications.

Here is another example, complete with creating a message and encodeding it. Here we will expound on the polynomial codes that we explored in the previous document. BCH codes are very similar, although we are a little more careful with the choice of the generating polynomial. Let $d=2r+1$. Then if \[ g(x)=\text{lcm}\{m_1(x),m_2(x),\dots,m_{2r}(x)\} \] where $m_i(x)$ is the minimal polynomial of $\omega^i$ where $\omega $ is the primitive $n^{th}$ root of unity over $\mathbb{Z}_2$, then with this choice of $g$, we have that... If we recall the previous results from the Linear codes that were discussed earlier, we have that this code can detect $2r$ errors, and correct $r$ errors.

Here is an example of defining a BCH code, and encoding a message using the corresponding matrix. Similarly to what we did with Linear Codes, we define a BurstChannel that we can transmit our messages through, which will randomly flip bits in the message. This class will also have a higher probability of burst errors, that is, if the previous bit has been flipped, then the probability that the next bit will be flipped is higher. In this cell we also define encode and decode functions, so that we may use lists for our messages, rather than matrices. Run the next cell to define this class, then proceed to the examples. SageMath files (via Jupyter Notebooks) that give an introduction to using SageMath to explore selected topics from Abstract Algebra.

Originally created as a project for Math 4220 at Southern Utah University, this Project will guide the user through installing SageMath and Jupyter Notebooks. Then we will introduce basic computations in SageMath. SageMath provides a rich environment for visualizing and experimenting with groups, rings, fields, as well as a few selected applications. The goal of this Project is to help students everywhere, although it is primarily aimed at students of Abstract Algebra, to learn the syntax of SageMath, so as to provide them with a helpful... While doing this, the Project will also guide the user through a few important and very interesting applications of the theory that is being studied; such as the Ceasar Cipher, the RSA Encryption system,... This Project may be used with no local installation of SageMath or Jupyter Notebooks.

If no access to a local installation is available, please visit our Project's website to see all the examples in this project. Alternatively, all code used in this Project may be executed on the Sage Cell webpage. To do this, please visit the Python folder, and copy the code that needs to be run. This code should then be pasted into the cell at the webpage above and can then be executed. In Addition to SageCell, which gives a feel for what it would be like to run this code from a terminal, CoCalc is an online alternative to Jupyter Notebooks that is compatible with all... This will allow the user to view the documents used in this Project just as they were designed to be seen in Jupyter Notebooks.

To use this resource, download the code that needs to be run, (either the python code or the original .ipynb files, note that the latter will give prettier output), create an account with CoCalc,... CoCalc is a free service, but there is a disclaimer that should be noted.

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