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.