Prime Numbers

Appendix
BOOK PSEUDOCODE
All algorithms in this book are written in a particular pseudocode form
describable, perhaps, as a “fusion of English and C languages.” The
motivations for our particular pseudocode design have been summarized in
the Preface, where we have indicated our hope that this “mix” will enable all
readers to understand, and programmers to code, the algorithms. Also in the
Preface we indicated a network source for Mathematica implementations of
the book algorithms.
That having been said, the purpose of this Appendix is to provide not
a rigorous compendium of instruction definitions, for that would require
something like an entire treatise on syntactical rules as would be expected
to appear in an off-the-shelf C reference. Instead, we give below some explicit
examples of how certain pseudocode statements are to be interpreted.
English, and comments
For the more complicated mathematical manipulations within pseudocode,
we elect for English description. Our basic technical motivation for allowing
“English” pseudocode at certain junctures is evident in the following example.
A statement in the C language
if((n== floor(n)) && (j == floor(sqrt(j))*floor(sqrt(j)))) ...,
which really means “if n is an integer and j is a square,” we might have cast
in this book as
if(n, √ j ∈ Z) ...
That is, we have endeavored to put “chalkboard mathematics” within
conditionals. We have also adopted a particular indentation paradigm. If we
had allowed (which we have not) such English as:
For all pseudoprimes in S, apply equation (X); Apply equation (Y);
then, to the aspiring programmer, it might be ambiguous whether equation
(Y) were to be applied for all pseudoprimes, or just once, after the loop on
equation (X). So the way we wish such English to appear, assuming the case
that equation (Y) is indeed applied only once after looping, is like so:
For all pseudoprimes in S, apply equation (X);
Apply equation (Y);