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RSS Feed for Wolfram Community showing any discussions in tag Algebra sorted by activeExploring the potential of the Wolfram Language in symbolic cryptography
https://community.wolfram.com/groups/-/m/t/2104590
In these [slides][1], I develop a computational essay concerning the implementation of a part of the [spi-calculus][2] in the Wolfram language.
[1]: https://www.wolframcloud.com/obj/jose.manuel.rodriguez.caballero/Published/TCSTalk%28October30_2020%29.nb
[2]: https://www.sciencedirect.com/science/article/pii/S0890540198927407José Manuel Rodríguez Caballero2020-10-30T03:11:47Z[WSG20] New Linear Algebra Daily Study Group begins Monday, October 12
https://community.wolfram.com/groups/-/m/t/2091247
A new study group devoted to linear algebra begins Monday! A list of daily topics can be found on our [Daily Study Groups page][1]. This group will be led by Wolfram certified instructor [@Luke Titus][at0] and will meet daily, Monday to Friday, over the next three weeks. Luke will share the excellent short lesson videos created by [@Devendra Kapadia][at1] for the Wolfram U course [Introduction to Linear Algebra][2]. Study group sessions include time for exercises, discussion and Q&A. Certifications are available. Sign up: [https://wolfr.am/Q9qbTXu3][3]
[at0]: https://community.wolfram.com/web/luket
[at1]: https://community.wolfram.com/web/dkapadia
[1]: https://www.wolfram.com/wolfram-u/special-event/study-groups/
[2]: https://www.wolfram.com/wolfram-u/introduction-to-linear-algebra/
[3]: https://wolfr.am/Q9qbTXu3Jamie Peterson2020-10-08T17:22:30ZPlot Question using Show[] function with different domain ranges
https://community.wolfram.com/groups/-/m/t/2102789
My goal is to display the inverse trigonometric function of ArcCos and Cos through a specific x range of 0 to Pi for Cos and -1 to 1 for the ArcCos since those domain ranges will pass the horizontal line test as being one-to-one and thus inverses within that domain.
I do not have any problem plotting Cos and ArcCos individually as shown below in the following two plots - see attached.
However when I try to combine the two plots using the Show[] function, as displayed in the last plot, the results are far from desirable.
I have tried a bunch of different configurations and various options, but so far nothing has seemed to correct the problem so I decided to reach out to the community for help. Undoubtedly it is something that I am not doing correctly and I would appreciate someone in the community showing me the correct way of handling this sort of situation.
Thanks,
Mitch SandlinMitchell Sandlin2020-10-27T18:02:16ZSolving equation system with quadratic terms
https://community.wolfram.com/groups/-/m/t/2100880
Hello,
I am trying to solve a system of equations
eqn = Table[(x[i] - a[i])*Sum[x[k], {k, 1, n}] + b[i]*x[i] == 0, {i, 1, n}]
in a fast way for the x[i] (coefficients a[i] and b[i] are known).
I found that for n = 2, 3, 4, 5, 6 Mathematica can eliminate n-1 equations by
eqn1 = Eliminate[eqn, Table[x[i], {i, 1, n - 1}]]
and obtain a single equation, e.g. for x[n], in the form
c[0] + c[1] x + c[2] x^2 + ... + c[n+1] x^(n+1) == 0
with coefficients c[i].
It seems that there is some pattern in how these coefficients look, e.g. for c[1] and c[n+1] I found
c[1] == a[n]^(n - 1)*Product[b[i], {i, 1, n}]*(1 - Sum[a[i]/b[i], {i, 1, n}])
c[n+1] == Product[b[n] - b[i], {i, 1, n - 1}]
Are there similar (simple) rules for the other c[i]? That would allow to reduce solving the equation system to solving a single polynomial equation.
Thanks for your input,
MaxMaximilian Ulbrich2020-10-24T08:41:57ZNo solution for solving equation in W|A?
https://community.wolfram.com/groups/-/m/t/2101121
Wolfram|Alpha gives me no solution exists, but I could solve the problem: (x+2*(x-1)^0.5)^0.5-(x-2*(x-1)^0.5)^0.5=3
https://www.wolframalpha.com/input/?i=%28x%2B2*%28x-1%29%5E0.5%29%5E0.5-%28x-2*%28x-1%29%5E0.5%29%5E0.5%3D3R R2020-10-24T13:26:57ZNo progress in Jordan decomposition of a symbolic matrix
https://community.wolfram.com/groups/-/m/t/2100017
Hello and thanks for reading my first post in this amazing community.
I'm an econometrics student and for the purpose of my master thesis from the area of stability in economic modelling I'm performing an Jacobian decomposition of a 5x5 symbolic matrix.
The matrix includes quite large expressions that include 15 variables and the file has about 1.4 MB. The decomposition performed with the command `JacobDecomposition[mat]` is making no progress.
Is there any way to perform the decomposition in accepting time? It has taken about a day and a half, in comparison to the operations like matrix multiplication that are done in a couple of seconds.
I attached the file with code, I hope this will work.Svit Valenčič2020-10-22T15:51:50ZFinding the root of a messy function
https://community.wolfram.com/groups/-/m/t/2101021
I got a complicated function as shown in the figure and I am trying to find the root of it. However, I have tried using the FindRoot/Solve/NSolve function, they are not giving me the correct answer/not able to converge within 100 iteration. Is there any other way to approach the problem?
P.S : There are some procedural lines inside the function. Does it affect anything?spidey jj2020-10-24T10:24:04ZA step-by-step walkthrough of the k-means algorithm
https://community.wolfram.com/groups/-/m/t/2099792
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/laneym/Published/k-means-algorithm.nbLaney Moy2020-10-22T17:28:29Z