From stanly  Sat Jan  8 11:19:21 1983
To: fateman
Subject: comments on primer
Status: R

		comments by Stanly Steinberg on 
		MACSYMA Primer for VAX/UNIX
		by Richard Fateman

	The primer is excellent.  I found chapter 1 much like what I
do when I give demos or workshops on vaxima.  For people who want
to use vaxima on applied math problems, I include a lot of stuff
on calculus before I start on programming. However, for programmers
wanting to learn about symbol manipulation I would proceed as in the
primer.  The demos in my directory show how I introduce material for
physics and applied math types.  I found Chapter 2 especially interesting,
helpful and, in fact, I learned a few new things.

	Some suggestions.  On page 1-1 , near the bottom how about
		equivalent --> mathematically equivalent

	How about describing how to quit() right after how to start?

	The Rules 1.22 section is really good!

	Section 2.1 first line.
	f1 and f2 --> f1 and f2, defined below,

	I prefer the following program to compute n! to one containing
an explicit loop.

f(n) := block([temp],
	temp:1,
	while n > 1 do (
		temp:n*temp,
		n:n-1,
		endwhile),
	temp)$

	The note in 2.4 on using an arbitrary number of parameters
is very helpful.  This is not in the old manual??

	I would like to see the array convention removed from any 
future symbol manipulators.  This could be replaced by some
explicit convention for saving calculations!

	Serious Business (2.7) is excellent.

	In Section 2.9, I would have avoided the lambda notation
(save this for much later) and would have included a call of the form:
		p[n](x)

I find the use of functional notation much more natural for Newton's 
method.  Thus I have a preference for a program of the following form:

newton(f,x,x0,eps) := block([xnew,xtemp,numer],
	/*

	This is a program for estimating the zero of a function of a
	single variable.

	f     is the name of a function of one variable
	x     is the variable in which the zero is to be found
	x0    is an initial guess for the zero
	xnew  is used to store the estimates of the zero
	xtemp is used to avoid a diff-subst confusion
	eps   is the tolerance within which the zero is to be found
	numer is a flag

	*/
	
	numer:true,
	xnew:x0,
	fprime(x) := subst(x,xtemp,diff(f(xtemp),xtemp)),
	while abs(f(xnew)) > eps do (
		xnew:xnew-f(xnew)/fprime(xnew)),
	return(xnew))$

The use of the xtemp varible in the definition of fprime is, I believe,
natural from the mathematical point of view.

I don't remember this as always being true but, in fact, this program
is broken! Thus if 
f(x) := (x-1)*(x-2) 
then all works.  However, the call newton(sin,x,5,10^-5) will find
a zero of the previously defined f! Try the program:
test(f,x) := display(f(x))
?Que pasa?

	On page 1-28, I don't understand the purpose of the declare 
construction of complex numbers.

	Section (Chapter) 3 page 1-29.  This stuff is really important
for my programs and cannot be over emphasized.