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Archiv der Kategorie Euler

Modulo Arithmetic with Euler Math Toolbox

Recently, I came across the problem to compute expressions in the modulo arithmetic with integer numbers. Here is an example: We like to compute expressions modulo 31. Since 31 is prime the numbers 0 to 30 with addition and multiplication … Weiterlesen

29. März 2016 von mga010
Kategorien: English, Euler | Schreibe einen Kommentar

Euler Math Toolbox and Matlab

Recently, this site got more traffic than usual. So I thought I welcome all of you in the new year (which is already three weeks old now). And I provide some new content for you to read. For me, the … Weiterlesen

25. Januar 2016 von mga010
Kategorien: English, Euler | 2 Kommentare

Pure Symbolic Functions in Maxima and EMT

I like to demonstrate a few tricks with Maxima and EMT. Assume you want to generate the Vandermonde matrix, and check the identity \(\det \begin{pmatrix} 1 & x_0 & \ldots & x_0^n \\ \vdots & \vdots &  & \vdots \\ … Weiterlesen

12. Dezember 2015 von mga010
Kategorien: English, Euler | Schreibe einen Kommentar

December Problem

I found the following problem on the page of the wonderful Science Blogs. It is in German. Let me translate it. Bernd writes two different numbers between 1 and 1000 on two cards of paper. Anna selects one, and after … Weiterlesen

07. Dezember 2015 von mga010
Kategorien: English, Euler | Schreibe einen Kommentar

Linear Optimization with Maxima and EMT

Maxima and EMT do of course have implementations of the Simplex algorithm. The algorithm in Maxima seems to work differently for floating point numbers and for fractions. Here is an example in fractions. We solve a problem in standard form. … Weiterlesen

21. Oktober 2015 von mga010
Kategorien: English, Euler | Schreibe einen Kommentar

Povray in Euler Math Toolbox

EMT can do a lot of 3D plots, but it is not an OpenGL application. This means that it has restrictions concerning hidden surfaces and intersecting objects. But if you install Povray you can do a lot more. Note that … Weiterlesen

17. Oktober 2015 von mga010
Kategorien: English, Euler | Schreibe einen Kommentar

Random Dices

This is just an answer to a question that came up in a discussion. Can you simulate 2 dice throws and display the frequencies in EMT? Actually, this is quite simple. We demonstrate it with 20 repetitions first. The trick … Weiterlesen

05. Oktober 2015 von mga010
Kategorien: English, Euler | Schreibe einen Kommentar

You define a vector valued function of two variables in EMT as follows. >function f([x,y]) := [x^2+y^2-10,x*y-1] >broyden(„f“,[1,2]) [0.317837, 3.14626] Then f can be used in the form f(x,y) or f(v) with a 1×2 vector v. The Broyden algorithm needs … Weiterlesen

30. September 2015 von mga010
Kategorien: English, Euler | Schreibe einen Kommentar

Visualizing the Newton Method in EMT

In a post by squareCircleZ I found a visualization of the Newton method with JavaScript. This looks like a modern and sleek way of providing demos to students. I have some doubts about the depth of the insights gained by this … Weiterlesen

25. August 2015 von mga010
Kategorien: English, Euler | 3 Kommentare

Functions for Maxima in EMT

Assume we want a function that evaluates a number to n digits using Maxima’s big float numbers. You can write a purely symbolic function for this. >function N(x,n) &&= block(fpprec:n, bfloat(x)) block(fpprec : n, bfloat(x)) >&N(pi,100) 3.141592653589793238462643383279502884197169399375105820974944\ 592307816406286208998628034825342117068b0 The value … Weiterlesen

20. August 2015 von mga010
Kategorien: English, Euler | Schreibe einen Kommentar

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