Programming with Mathematica An Introduction

Abstract

Solutions to the exercises in Programming with Mathematica: An Introduction are given here. The exercises to every section are listed first, followed by the solutions. Solutions are provided both as a PDF file and in notebook form at www.cambridge.org/wellin.

Figures (31)

Using graphs you can accomplish the same thing. A bit of thought should convince you that adding the matrix to its transpose and then totaling all the 1s in each row will give the correct count.

And here is a rule to transform each circle into a scoped list that includes Thick and RandomColor. Note the need for the delayed rule (:>).

9|:= Graphics[circles /. Circle[x__] +» {Thick, RandomColor[], Circle[x]}]

In[{14]:= SierpinskiTriangle[8, ImageSize > Small]

The idea in these two examples is to convert a string to a list of characters, operate on that list using

Select those data elements whose distance to the mean is less than one standard deviation.

The case for directed graphs is similar. Here then is a function that returns the adjacency list for a given vertex u in graph gr.

StemPlot::badarg : The first argument to StemPlot must be a list of numbers.

TABLE 7.1. Eulerian number triangle Because of the triple recursion, you will find it necessary to use a dynamic programming implemen tation to compute any Eulerian numbers of even modest size. Hint: Although the above formulas will compute it, you can add the following rule to simplify some of the computation:

NIST describes the data in lew.dat as originating “from an underlying single-cycle sinusoidal model.’

Finally, here is a histogram displaying the distribution of sentence lengths.

Then find those values of r for which the x and y coordinates are identical. Here then are those values of r that are positive.

This implementation contains one Polygon per hexagon.

Use those indices as the positions in pts through which we wish to pass a line. Note the need to close up the polygon, connecting the last point with the first.

The output above suffers from the fact that the display jumps around a lot as Mathematica tries to figure out a sensible plot range for each frame. Instead, we should fix the plot range for all frames to avoid this jumpiness. This is done in the definitions for xran and yran inthe Initializatior below.

And here is the dynamic version.

Here is the dynamic interface using EventHand1er to choose a new set of random points with each mouse click.

A suggested addition would be to add a control to change the number of points that are used. But be careful: traveling salesman type problems are notoriously hard; in fact they are known to be NP-

12.3 Parallel processing Increase the resolution of the graphic by running the computation in parallel.