# Some included EULER files

We explain shortly some of the included EULER files. More help is contained in the help text of the loaded functions. You can load these files with the load command, e.g.

        >load demo

and either the files will start a show immediately or will display all defined functions.

- demo
- apple
- bezier
- games
- hondt
- interest
- sound

## demo

You probably know this one. Just load it. There is also an autodemo, which is designed to show the capabilities of Euler without any user interaction.

## apple

This is a nice plot of the Mandelbrot apple set and its potential. Just load the file.

## bezier

This file computes some Bezier curves and survaces. Some demo functions are available.

beziertest lets you click at points to define (x,y) values and computes and shows the bezier curve to these points. It is based on the function bezier(p,t), which evaluates the Bezier curve through the columns of the matrix p in t. bezier3dtest displays a Bezier curve in 3D-space.

nurbstest shows some quadratic nurbs with increasing weight in the middle point. It is bases on nurbs(p,b,t), which works like bezier(p,t), but needs a weight vector b.

beziersurftest shows a bezier surface with its determining grid of points. beziersurf(x,y,z) computes the surface. x,y,z are the coordinates of the grid points (kxl-matrices). It returns three values {xb,yb,zb}, which are the coordinates of the (n+1)^2 surface points.

c1test is another demo.

## games

This computes the optimal strategy for some simple games. Read the help for a description of the games (gambling,scissors,poker).

game(A) computes the optimal strategy for a game with matrix A.

## hondt

Computes seat distributions for votes.

hondt(v,n) and best(v,n) take the votes for the parties and the numer of seats as parameters and compute a vector of seats for the parties.

## interest

Computes the interest rate of an investment.

The general purpose functions are rate(x) or rate2(x,n). Both compute the interest rate of a payment vector x, with positive or negative entries. The first function assumes times 0,...,n and the latter times n[1],....,n[m].

investment computes the interest rate of an investment with a start installment, several payments (positive) and a final installment. See the help for more information.

## sound

With this file, you can load or save mono WAV files in 8 or 16 bit.

v=loadwave(filename) loads a WAV file into a vector v. It does also return the sampling rate r and will save this to the global variable defaultrate.

savewave(filename,v) will save the sound with the defaultrate and 8 bits. You may specify the rate and bits as extra parameters.

analyze(v) does a spectrum decomposition of the sound. the full parameter list is analyze(v,fmin,fmax,rate,points). fmin and fmax are the minimal and maximal frequencies of interest, rate is the sampling rate and points are the number of points to be used (should be a power of 2).

mapsound(v) does an analysis for the sound at certain time increments. It will procude a nice density plot of the frequencies. the full parameter list is mapsound(v,dt,fmin,fmax,simpl,rate), where dt is the time increment in seconds, simp is a simplification factor (take 1), and rate is the sampling rate

playwave(filename) plays the wave in that file on some systems.