polexpr (10dec18)

git-svn-id: svn://tug.org/texlive/trunk@49378 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 68 insertions, 67 deletions

diff --git a/Master/texmf-dist/tex/latex/polexpr/polexpr.sty b/Master/texmf-dist/tex/latex/polexpr/polexpr.sty
index 601446cf671..9bc286115d8 100644
--- a/Master/texmf-dist/tex/latex/polexpr/polexpr.sty
+++ b/Master/texmf-dist/tex/latex/polexpr/polexpr.sty
@@ -1,7 +1,7 @@
 % author: Jean-François Burnol
 % License: LPPL 1.3c (author-maintained)
 \ProvidesPackage{polexpr}%
-  [2018/12/08 v0.7 Polynomial expressions with rational coefficients (JFB)]%
+  [2018/12/09 v0.7.2 Polynomial expressions with rational coefficients (JFB)]%
 \RequirePackage{xintexpr}[2018/06/17]% xint 1.3c for \ifxintglobaldefs boolean
 \edef\POL@restorecatcodes
     {\catcode`\noexpand\_ \the\catcode`\_ %
@@ -914,12 +914,13 @@
         {\let\POL@findrat@E\POL@findrat@Dexp} % aussi ok pour 1[0]
         {\edef\POL@findrat@E{\the\numexpr\xintLen{\POL@findrat@Dint}%
                                                  +\POL@findrat@Dexp}}%
+% ATTENTION QUE LA CONVENTION DE SIGNE POUR \POL@findrat@E EST OPPOSÉE À CELLE
+% POUR LE CODE PLUS ANCIEN FAISANT "REFINE"
      \POL@initarray\POL@IfMultIsKnown\xint_secondoftwo
      \let\POL@findrat@nbofirrroots\POL@isolz@NbOfRoots
      % find all rational roots, and their multiplicities,
      % factor them out in passing from original (Sturm root) polynomial
      \ifnum\POL@findrat@E<7
-         \PolEnsureIntervalLength{\POL@sturmname}{1}{-\POL@findrat@E}%
          \def\POL@findrat@index{1}%
          \POL@findrat@loop@secondpass@direct
      \else
@@ -928,7 +929,6 @@
          \POL@findrat@loop@firstpass
      % and now we do the final pass finding them all
          \def\POL@findrat@index{1}%
-         \PolEnsureIntervalLength{\POL@sturmname}{1}{-\POL@findrat@E}%
          \POL@findrat@loop@secondpass
      \fi
      % declare the new polynomials
@@ -947,7 +947,7 @@
     {}%
     \ifnum\xintiloopindex<\POL@isolz@NbOfRoots\space
     \repeat }%
-  \begingroup\globaldefs1
+  \begingroup\globaldefs\@ne
   % attention de ne surtout pas faire un \expandafter ici, car en cas d'un
   % seul item, \xintAssignArray l'unbraces...
   \xintAssignArray\POL@temp\to#1%
@@ -956,36 +956,20 @@
 \def\POL@findrat@loop@firstpass{%
   \PolSturmIfZeroExactlyKnown{\POL@sturmname}{\POL@findrat@index}%
      \POL@findrat@loop@decimal% get its multiplicity
-     \POL@findrat@loop@a
+     \POL@findrat@loop@aa     % refine interval and check
   \edef\POL@findrat@index{\the\numexpr\POL@findrat@index+\@ne}%
   \ifnum\POL@findrat@index>\POL@isolz@NbOfRoots
   \else
     \expandafter\POL@findrat@loop@firstpass
   \fi
 }%
-\def\POL@findrat@loop@secondpass{%
+\def\POL@findrat@loop@aa{%
+  % we do a first pass to identify roots with denominators < 1000
+  \PolEnsureIntervalLength{\POL@sturmname}{\POL@findrat@index}{-6}%
+  % attention that perhaps now the root is known!
   \PolSturmIfZeroExactlyKnown{\POL@sturmname}{\POL@findrat@index}%
-     {}% nothing more to be done, already stored
-     \POL@findrat@loop@b
-  \edef\POL@findrat@index{\the\numexpr\POL@findrat@index+\@ne}%
-  \ifnum\POL@findrat@index>\POL@isolz@NbOfRoots
-  \else
-     \PolEnsureIntervalLength
-         {\POL@sturmname}{\POL@findrat@index}{-\POL@findrat@E}% dynamic
-     \expandafter\POL@findrat@loop@secondpass
-  \fi
-}%
-\def\POL@findrat@loop@secondpass@direct{%
-  \PolSturmIfZeroExactlyKnown{\POL@sturmname}{\POL@findrat@index}%
-     \POL@findrat@loop@decimal
-     \POL@findrat@loop@b
-  \edef\POL@findrat@index{\the\numexpr\POL@findrat@index+\@ne}%
-  \ifnum\POL@findrat@index>\POL@isolz@NbOfRoots
-  \else
-     \PolEnsureIntervalLength
-         {\POL@sturmname}{\POL@findrat@index}{-\POL@findrat@E}% dynamic
-     \expandafter\POL@findrat@loop@secondpass@direct
-  \fi
+      \POL@findrat@loop@decimal
+      \POL@findrat@loop@a
 }%
 \def\POL@findrat@loop@decimal{% we have an already found decimal root
   % we do not go via @storeit, as it is already stored
@@ -1002,6 +986,7 @@
   \edef\POLuserpol@_findrat@oneterm{1.\noexpand\empty
         {\xintiiOpp\POL@findrat@xN/1[0]}{\POL@findrat@xD/1[0]}}%
   \POL@divide{\POL@sturmname\POL@sqfnorr}{_findrat@oneterm}% the one without mult.
+  %\expandafter\POL@split\POL@R;\POL@degR\POL@polR
   \POL@findrat@loop@updatequotients
   \POL@findrat@loop@getmultiplicity
 }%
@@ -1018,10 +1003,7 @@
 \def\POL@findrat@getE #1/1[#2]{#2}% /1 as it should be there.
 % so an error will arise if not but cf \POL@refine@getE where I did not put it
 \def\POL@findrat@loop@a{%
-  % we do a first pass to identify roots with denominators < 1000
-  \PolEnsureIntervalLength{\POL@sturmname}{\POL@findrat@index}{-6}%
   % attention that the width may have been already smaller than 10^{-6}
-  % also attention that one of the bound may be zero
   \POL@get@IsoLeft@rawin
   \POL@get@IsoRight@rawin
   \edef\POL@findrat@localW
@@ -1046,28 +1028,20 @@
   \fi
 }%
 \def\POL@findrat@gcdloop{%
-  % we must be careful with sign (attention one of the bounds may be zero)
-  \let\POL@findrat@IfNeg\xint_secondoftwo
+  % we must be careful with sign
+  % but we are certain no extremity is a root
+  \let\POL@findrat@ifnegative\xint_secondoftwo
   \xintiiifSgn\POL@IsoLeft@Int
     \POL@findrat@gcdloop@n
-    \POL@findrat@gcdloop@zero
+    \POL@error@thisisimpossible
     \POL@findrat@gcdloop@p
 }%
 \def\POL@findrat@gcdloop@n{%
-  \let\POL@findrat@IfNeg\xint_firstoftwo
+  \let\POL@findrat@ifnegative\xint_firstoftwo
   \let\POL@temp\POL@IsoRight@Int
   \edef\POL@IsoRight@Int{\xintiiOpp{\POL@IsoLeft@Int}}%
   \edef\POL@IsoLeft@Int{\xintiiOpp{\POL@temp}}%
-  \xintiiifSgn\POL@IsoLeft@Int
-     \POL@error % impossible branch
-     \POL@findrat@gcdloop@zero
-     \POL@findrat@gcdloop@p
-}%
-\def\POL@findrat@gcdloop@zero{%
-  % the continued fraction would be the one of 1/2, so only 1/2 to test...
-  \edef\POL@findrat@x
-      {1/2\romannumeral\xintreplicate{\POL@findrat@localW}{0}[0]}%
-  \POL@findrat@gcdloop@testit
+  \POL@findrat@gcdloop@p
 }%
 \def\POL@findrat@gcdloop@p{%
   \edef\POL@findrat@gcdloop@Ap{\xintDec{\xintDouble\POL@IsoRight@Int}}%
@@ -1140,7 +1114,7 @@
 }%
 \def\POL@findrat@gcdloop@testit{%
   % zero should never occur here
-  \POL@findrat@IfNeg{\edef\POL@findrat@x{-\POL@findrat@x}}{}%
+  \POL@findrat@ifnegative{\edef\POL@findrat@x{-\POL@findrat@x}}{}%
   \POL@xintfrac@getNDE\POL@findrat@x\POL@findrat@xN\POL@findrat@xD\POL@_
   \edef\POLuserpol@_findrat@oneterm{1.\noexpand\empty
       {\xintiiOpp{\POL@findrat@xN}/1[0]}{\POL@findrat@xD/1[0]}}%
@@ -1151,10 +1125,36 @@
     \POL@findrat@loop@updatequotients
     \POL@findrat@loop@getmultiplicity % will continue updating the mult. one
     \def\POL@findrat@gcdloop@done{1}%
-  \else
   \fi
 }%            
 % This is second phase
+\def\POL@findrat@loop@secondpass{%
+  \PolSturmIfZeroExactlyKnown{\POL@sturmname}{\POL@findrat@index}%
+     {}% nothing more to be done, already stored
+     \POL@findrat@loop@bb % refine interval and check
+  \edef\POL@findrat@index{\the\numexpr\POL@findrat@index+\@ne}%
+  \ifnum\POL@findrat@index>\POL@isolz@NbOfRoots
+  \else
+     \expandafter\POL@findrat@loop@secondpass
+  \fi
+}%
+\def\POL@findrat@loop@secondpass@direct{%
+  \PolSturmIfZeroExactlyKnown{\POL@sturmname}{\POL@findrat@index}%
+     \POL@findrat@loop@decimal
+     \POL@findrat@loop@bb
+  \edef\POL@findrat@index{\the\numexpr\POL@findrat@index+\@ne}%
+  \ifnum\POL@findrat@index>\POL@isolz@NbOfRoots
+  \else
+     \expandafter\POL@findrat@loop@secondpass@direct
+  \fi
+}%
+\def\POL@findrat@loop@bb{%
+  \PolEnsureIntervalLength{\POL@sturmname}{\POL@findrat@index}{-\POL@findrat@E}%
+  % ATTENTION THAT PERHAPS NOW THE ROOT IS KNOWN!
+  \PolSturmIfZeroExactlyKnown{\POL@sturmname}{\POL@findrat@index}%
+      \POL@findrat@loop@decimal
+      \POL@findrat@loop@b
+}%
 \def\POL@findrat@loop@b{%
   \edef\POL@findrat@Lscaled{\xintMul{\POL@findrat@D}%
        {\POL@xintexprGetVar{\POL@sturmname L_\POL@findrat@index}}}%
@@ -1206,11 +1206,13 @@
   \let\csname POL_ZeroIsKnown\POL@sturmname\POL@findrat@index\endcsname
         \xint_stop_atfirstoftwo
   \begingroup\xintglobaldefstrue
-  \xintdefvar
-    \POL@sturmname L_\POL@findrat@index,%
-    \POL@sturmname R_\POL@findrat@index,%
-    \POL@sturmname Z_\POL@findrat@index _isknown
-    := qfrac(\POL@findrat@x),qfrac(\POL@findrat@x),1;%
+    % skip some overhead of \xintdefvar...
+    \XINT_expr_defvar_one{\POL@sturmname L_\POL@findrat@index}%
+       {\csname .=\POL@findrat@x\endcsname}%
+    \XINT_expr_defvar_one{\POL@sturmname R_\POL@findrat@index}%
+       {\csname .=\POL@findrat@x\endcsname}%
+    \XINT_expr_defvar_one{\POL@sturmname Z_\POL@findrat@index _isknown}%
+       {\csname .=1\endcsname}%
   \endgroup
 }%
 \def\POL@findrat@loop@updatequotients{%
@@ -1320,8 +1322,9 @@
   % added at 0.7
   \let\x\POL@isolz@NbOfRoots
     \xintloop
-      \xintdefvar \POL@sturmname M_\x
-                  := \csname POL_ZeroMult\POL@sturmname\x\endcsname ;%
+    % skip some overhead of \xintdefvar...
+      \XINT_expr_defvar_one{\POL@sturmname M_\x}%
+         {\csname .=\csname POL_ZeroMult\POL@sturmname\x\endcsname\endcsname}%
     \edef\x{\the\numexpr\x-\@ne}%
     \ifnum\x>\z@
     \repeat
@@ -1694,11 +1697,11 @@
   \repeat
 }%
 \def\POL@isolz@check{% \POL@IsoRightSign must be ready for use here
-% \ifxintverbose
-%   \xintMessage{polexpr}{Info}%
-%   {\the\numexpr\POL@IsoLeftSV-\POL@IsoRightSV\relax\space roots
-%    in (\POL@IsoLeft@raw,\POL@IsoRight@raw] (E = \POL@isolz@E)}%
-% \fi
+\ifxintverbose
+  \xintMessage{polexpr}{Info}%
+  {\the\numexpr\POL@IsoLeftSV-\POL@IsoRightSV\relax\space roots
+   in (\POL@IsoLeft@raw,\POL@IsoRight@raw] (E = \POL@isolz@E)}%
+\fi
     \ifcase\numexpr\POL@IsoLeftSV-\POL@IsoRightSV\relax
     % no root in ]left, right]
       \global\POL@isolz@nextwillneedrefinefalse
@@ -1896,18 +1899,16 @@
           \xint_stop_atfirstoftwo
     \fi
     \begingroup\xintglobaldefstrue
-    \xintdefvar
-      \POL@sturmname L_\POL@isolz@IntervalIndex,%
-      \POL@sturmname R_\POL@isolz@IntervalIndex,%
+    % skip some overhead of \xintdefvar...
+      \XINT_expr_defvar_one{\POL@sturmname L_\POL@isolz@IntervalIndex}%
+         {\csname .=\POL@IsoLeft@rawout\endcsname}%
+      \XINT_expr_defvar_one{\POL@sturmname R_\POL@isolz@IntervalIndex}%
+         {\csname .=\POL@IsoRight@rawout\endcsname}%
       % added at 0.7
-      \POL@sturmname Z_\POL@isolz@IntervalIndex _isknown
-        := qfrac(\POL@IsoLeft@rawout),%
-           qfrac(\POL@IsoRight@rawout),%
-           \ifnum\POL@IsoRightSign=\z@ 1\else 0\fi;%
+      \XINT_expr_defvar_one{\POL@sturmname Z_\POL@isolz@IntervalIndex _isknown}%
+         {\csname .=\ifnum\POL@IsoRightSign=\z@ 1\else 0\fi\endcsname}%
     \endgroup
 }%
-
-
 %% \PolRefineInterval
 \def\POL@xintexprGetVar#1{\expandafter\expandafter\expandafter
     \XINT_expr_unlock\csname XINT_expr_var_#1\endcsname}%