![]() ![]() This problem encompasses a lot of the challenges I have with CAS software, that is, utilize mathematical functions (in this case, we only use matrix multiplication and transpose), yet at the same time express a nontrivial control flow. Finally, multiply the matrices modulo 5 and check if it equals the identity matrix, and output.Figure out how to do control flow, either by looping over a list (procedural) or with a map and filter (functional).Figure out how to convert a list into a 2×2 matrix form that the system can perform matrix operations on.We will probably do this with a cartesian product or list comprehension. Enumerate all lists of length 4 of values between 0 to 4, that is, ,…,].We can break this problem into several steps: Let the field be (so all operations are taken modulo 5). This problem came up as a part of a recent linear algebra assignment. So I came up with a trial - I had a short (but nontrivial) problem representative of the type of problem I’d be looking at, and I would try to solve it in all 3 languages, to determine which one was easiest to work with. Here’s my setup (all running on Windows 7): I began to experiment with several systems, but after a few days I still couldn’t decide which one was the winner. To start off, there are many different competing computer algebra systems, all incompatible with each other, and it’s far from clear which one is best for my needs. I have no experience with symbolic computing, so it wasn’t clear to me where to begin. So I looked to learn a CAS (computer algebra system), so in the future I won’t have to hack together buggy code for common math operations. But I found this solution to be unsatisfactory: my Haskell programs worked with integers and floating numbers and I couldn’t easily generalize it to work with symbolic expressions. Usually I implemented an ad-hoc solution using Haskell, either using a simple library or rolling my own implementation if the library didn’t have it. The tutorial is by MCC Py Tutorials and it is a great launching point into the world of Mathematics-based software and technical computing.I’ve never been very good at doing manual computations, and whenever I need to do a tedious computation for an assignment, I like to automate it by writing a computer program. there is a great tutorial that will get you started with SageMath which assumes you have no coding experience (so it is a great way to learn some python at the same time). You can download SageMath HERE and tinker with the console, or if you prefer to just use it in a web browser and make use of visuals, you can Visit and just as easily get started! Whichever you prefer. Not only is SageMath free and versatile, but it also comes in two flavours: Downloadable console and web browser application. It is quite common to find these programs utilized in some upper level University Mathematics classes and are often taught alongside the python coding language as part of one’s Mathematics/Physics/Computer-Science Degree.Īs it turns out, During my physics Degree I will eventually be learning computational Methods using Python, and even sooner than that, I will be using either Maple or Mathematica to accompany my multivariable calculus classes so of course I considered getting a head start and learning a bit on my own The problem is that both Mathematica and Maple can be pricey (as some of you may have already noticed), and it is times like these that we need open-source alternatives: Enter SageMath! Image Source: Ĭreated by William Stein, a Mathematician from the University of Washington in 2005, SageMath (Previously SAGE: an abbreviation for “System for Algebra and Geometry Experimentation”) was created as an Open-source alternative to Maple, Mathematica, MATLAB and Magma, and from what I have observed so far, it has much of the same functionality as it’s paid predecessors along with the unique advantage of having been programmed in the powerful and simple language of Python (is it any wonder why I seemed to be biased in learning Python?). Many of you may be familiar with programs such as Maple & Mathematica, which are considered to be CAS: “Computer Algebra Systems” with features covering many aspects of mathematics, such as Algebra, Calculus, Number Theory, Number Analysis, Statistics and Combinatorics.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |