Ilya Zakharevich on Thu, 17 Oct 2002 12:09:34 -0700

 [PATCH CVS] Docs nitpicks

--- ./doc/usersch4.tex-pre	Tue Oct 15 17:33:48 2002
+++ ./doc/usersch4.tex	Thu Oct 17 11:32:32 2002
@@ -1191,7 +1191,8 @@ considering the hierarchical structure o
polynomial in variable of \emph{lesser} priority (see \secref{se:priority})
than the modulus variable is valid, since it can be considered as the
constant term of a polynomial of degree 0 in the correct variable. On the
-other hand a variable of \emph{greater} priority would not be acceptable.
+other hand a variable of \emph{greater} priority would not be acceptable;
+see \secref{se:priority} for the problems which may arise.

\subsec{Type \typ{POL} (polynomial):}\kbdsidx{t_POL}\sidx{polynomial} this
type has a second codeword which is analogous to the one for integers. It
@@ -1340,7 +1341,8 @@ polynomials yourself (and not just let P
usually less efficient). For instance, it does not make sense to have a
variable number occur in the components of a polynomial whose main variable
has a higher number (lower priority), even though there's nothing PARI can do
-to prevent you from doing it.
+to prevent you from doing it; see \secref{se:priority} for a discussion
+of possible problems in a similar situation.

\subsec{Creating variables}
A basic difficulty is to create'' a variable. As we have seen in
--- ./doc/usersch2.tex-pre	Tue Oct 15 17:33:46 2002
+++ ./doc/usersch2.tex	Thu Oct 17 11:28:26 2002
@@ -864,7 +864,11 @@ priority (which have been introduced lat
operations (typically between a polynomial and a polmod). For example, PARI
will not recognize that \kbd{Mod(y, y\pow2 + 1)} is the same as \kbd{Mod(x,
x\pow2 + 1)}. Hopefully, this problem will pass away when type element of a
-number field'' is eventually introduced. See \secref{se:priority} for a
+number field'' is eventually introduced. \footnote{*}{On the other hand, one can argue that
+there is no reason to consider these quantities equal.  E.g., one can be the
+opposite of another.  Compare with numerous discussions on whether the
+algebraic closure of $\Q$ is canonically defined'', or one needs to consider
+a groupoid of algebraic closures.} See \secref{se:priority} for a
definition of priority'' and a discussion of (PARI's idea of) multivariate
polynomial arithmetic.