The text looks really great. I lament the fact that like so many other introductory texts it includes exercises with no answers. This makes it just about useless for an independent student.

I don't understand why people do this? Is it just too much work/don't have time to actually work through the exercises/don't want an answer key to leak out so lazy professors can't set exam questions directly from the textbook/I'm just really stupid and no one else has this requirement?

I haven't read much of this book, but in general, with textbooks like this, if you cannot do the exercises and _know_ that you got them right, you didn't understand the mathematics that the text tries to learn you.

If you cannot do the exercises, and read a proof written by the authors that couldn't teach you the mathematics instead, why would that help you learn the mathematics?

Having said that, in some cases it might help to get a hint. What hint to give depends heavily on the student. Give too much, and the hole point of the exercise goes away. Perhaps the best one one can give is to read Polya's "How to solve it"

> I don't understand why people do this?

I have the answers to all exercises, worked out, including proofs, in my Free text Linear Algebra. Took me a year. (Also, as you say, I am sometimes told by potential adopters thta they cannot use the book because it has the answers. That argument is fast losing its impact, though, as it has become clear even to middle aged professors that for any major commercial text any undergraduate can get the full answers off the net in minutes.)

I'll raise you the work to arrive at the solutions, as well. At least, in my school answers were a small, nearly insignificant portion of the credit for a problem - no work meant almost no credit, which is critical for engineers. (That way if you make a mistake you can debug it!)

I'd imagine all of it has to be available in order to even post the exercises, but editing/formatting the work and solutions almost certainly is quite a lot of work.

Edit: In retrospect, in this context the work is the answer, so my distinction may be irrelevant. (I'll leave the comment as a hearty agreement with the parent though - solutions often help solidify ideas for me, and are great references later when applying the ideas in the real world!)

If the problems have answers, they cannot be assigned as homework, which decreases the book's usefulness as a textbook. Maybe you view this as a case of "lazy professor" but you may consider that professors have other things to do too.

The book is available in hardcover too, which means it probably gets used as a university textbook. In this case, getting the answers usually requires being a lecturer...

Writing out full solution of all the exercise might be another textbooks. Math textbooks even left proof of theorems as an exercise to the reader.

For a computational introduction to algebraic number theory, you can take a look at William Steins' book on the subject: http://wstein.org/books/ant/ant.pdf. It deals with more advanced topics but has concrete examples in Sage.

Shoup's NTL library is also a great resource.

A link for those who may be interested: http://shoup.net/ntl/