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

[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]

[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.