polexpr (9apr18)

git-svn-id: svn://tug.org/texlive/trunk@47412 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 159 insertions, 78 deletions

diff --git a/Master/texmf-dist/tex/latex/polexpr/polexpr.sty b/Master/texmf-dist/tex/latex/polexpr/polexpr.sty
index 7e132905392..02d3ecdec76 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}%
-  [2018/03/03 v0.4.2 Polynomial expressions with rational coefficients (JFB)]%
+  [2018/04/08 v0.5 Polynomial expressions with rational coefficients (JFB)]%
 \RequirePackage{xintexpr}[2018/03/01]% xint 1.3
 \edef\POL@restorecatcodes
     {\catcode`\noexpand\_ \the\catcode`\_ \catcode0 \the\catcode0\relax}%
@@ -24,7 +24,7 @@
                              \else\expandafter\xint_secondoftwo
                           \fi}%
 \def\POL@split#1.#2;#3#4% separates degree and list of coefficients
-% The \empty token is to avoid brace removal issues for degree 0 polynomials
+% The \expandafter chain removes the \empty token
    {\def#3{#1}\expandafter\def\expandafter#4\expandafter{#2}}%
 %
 \def\POL@resultfromarray #1{% ATTENTION, **MUST** be executed with
@@ -64,8 +64,8 @@
      \let\xintPow\POL@pow
      \let\xintOpp\POL@opp
      \def\xintSub ##1##2{\xintAdd{##1}{\xintOpp{##2}}}%
-     % \xintAdd to get \POL@result defined even if numerical only expression
-     % I could also test \ifPOL@pol, but well, this is very small overhead
+     % \xintAdd{0} to get \POL@result defined even if numerical only expression
+     % I could also test \ifPOL@pol, but this is anyhow small overhead
      \xintAdd{0}%
        {\csname XINT_expr_userfunc___pol\endcsname
         {\global\POL@poltrue\def\POL@result{1.\empty{0/1[0]}{1/1[0]}}}}%
@@ -209,32 +209,45 @@
 }%
 
 
-\newcommand\PolGet{}
+\newcommand\PolGet{}%
 \def\PolGet#1#2\fromarray#3{%
     \begingroup % closed in \POL@getfromarray
     \POL@getfromarray{#1}{#3}%
     \POL@newpol{#1}%
 }%
 \def\POL@getfromarray#1#2{%
-        \count@=#2{0} %<- intentional space,
-        %  must be > 0, else could create infinite loop
+        \count@=#2{0} %<- intentional space
+  \ifnum\count@=\z@
+     \def\POL@result{-1.\empty{0/1[0]}}% 0.5 fix for empty array
+  \else
+        \xintloop
+          \edef\POL@tmp{#2{\count@}}%
+          \edef\POL@tmp{\xintRaw{\POL@tmp}}%
+% sadly xinttools (current 1.3a) arrays have no setters for individual items... 
+          \expandafter\let\csname POL@tmparray\the\count@\endcsname\POL@tmp
+        \if0\xintiiSgn{\POL@tmp}%
+            \advance\count@\m@ne
+        \repeat
+% dans le cas particulier d'un array avec que des éléments nuls, \count@ est
+% ici devenu 0 et la boucle s'est arrêtée car #2{0} était au moins 1. De plus
+% \POL@tmparray1 est bien 0/1[0] donc ok pour polynôme nul dans \POL@result
+        \count\tw@\count@
         \xintloop
+% on mouline tous les coeffs via \xintRaw
+        \ifnum\count@>\@ne
+          \advance\count@\m@ne
           \edef\POL@tmp{#2{\count@}}%
-          \xintiiifZero{\POL@tmp}%
-            {\iftrue}%
-            {\iffalse}%
-        \advance\count@\m@ne
+          \edef\POL@tmp{\xintRaw{\POL@tmp}}%
+          \expandafter\let\csname POL@tmparray\the\count@\endcsname\POL@tmp
         \repeat
-% should I use \xintRaw ? but if #2 expands only in an \edef, problem
-% (but it is not very probable the #2 macro does not already give completely
-% expanded contents), I would need to proceed in two steps. Or the \xintRaw
-% could get injected at level of \POL@newpol
-        \def\POL@tmp##1.{{#2{##1}}}%
+        \count@\count\tw@          
+        \def\POL@tmp##1.{{\csname POL@tmparray##1\endcsname}}%
         \edef\POL@result{\the\numexpr\count@-\@ne.\noexpand\empty
                          \xintiloop[1+1]%
                          \expandafter\POL@tmp\xintiloopindex.%
                          \ifnum\xintiloopindex<\count@
                          \repeat}%
+  \fi
     \expandafter
     \endgroup
     \expandafter
@@ -325,14 +338,14 @@
 }%
 \def\POL@mapcoeffs#1#2{%
     \begingroup
-       \def\POL@map@macro{#1}%
+       \def\POL@mapcoeffs@macro{#1}%
        \expandafter\expandafter\expandafter\POL@split
-         \csname POLuserpol@#2\endcsname;\POL@var@deg\POL@var@coeffs
+         \csname POLuserpol@#2\endcsname;\POL@mapcoeffs@deg\POL@mapcoeffs@coeffs
 % attention à ne pas faire un \expandafter ici, car brace removal si 1 item
-       \xintAssignArray\POL@var@coeffs\to\POL@arrayA
+       \xintAssignArray\POL@mapcoeffs@coeffs\to\POL@arrayA
        \def\index{0}%
        \count@\z@
-       \expandafter\POL@map@loop\expandafter.\POL@var@coeffs\relax
+       \expandafter\POL@map@loop\expandafter.\POL@mapcoeffs@coeffs\relax
        \xintloop
 % this abuses that \POL@arrayA0 is never 0.
        \xintiiifZero{\csname POL@arrayA\the\count@\endcsname}%
@@ -349,7 +362,7 @@
 }%
 \def\POL@map@loop.#1{\if\relax#1\expandafter\xint_gob_til_dot\fi
     \advance\count@\@ne
-    \edef\POL@map@coeff{\POL@map@macro{#1}}%
+    \edef\POL@map@coeff{\POL@mapcoeffs@macro{#1}}%
     \expandafter
     \let\csname POL@arrayA\the\count@\endcsname\POL@map@coeff
     \edef\index{\the\numexpr\index+\@ne}%
@@ -620,28 +633,61 @@
    \fi
 }%
 
+%% IContent and \PolMakePrimitive (0.5)
+\def\POL@aux@mgcd@loop#1#2{%
+    \if\relax#2\expandafter\POL@aux@mgcd@exit\fi
+    \expandafter
+    \POL@aux@mgcd@loop\romannumeral0\POL@aux@gcd#1.#2.%
+}%
+\def\POL@aux@mgcd@exit
+    \expandafter
+    \POL@aux@mgcd@loop\romannumeral0\POL@aux@gcd#1.\relax.{\xintiiabs{#1}}%
+\def\POL@aux@gcd#1.#2.{%
+    \if0\xintiiSgn{#1}\expandafter\POL@aux@gcd@exit\fi
+    \expandafter\POL@aux@gcd\romannumeral0\xintmod {#2}{#1}.#1.}%
+\def\POL@aux@gcd@exit
+    \expandafter\POL@aux@gcd\romannumeral0\xintmod #1#2.#3.{{#1}}%
+
+\def\POL@icontent #1{\romannumeral0\expandafter
+    \POL@aux@mgcd@loop\romannumeral`^^@#1\relax}%
+
+\newcommand\PolIContent[1]{\romannumeral0\expandafter
+    \POL@aux@mgcd@loop\romannumeral`^^@\PolToList{#1}\relax}%
+
+
+\def\POL@makeprim@macro#1%
+   {\xintREZ{\xintNum{\xintDiv{#1}{\POL@makeprim@icontent}}}}%
+\newcommand\PolMakePrimitive[1]{%
+    \edef\POL@makeprim@icontent{\PolIContent{#1}}%
+    \PolMapCoeffs\POL@makeprim@macro{#1}%
+}%
+
 
 %% Sturm Algorithm (polexpr 0.4)
+%% 0.5 uses primitive polynomials for faster evaluations afterwards
 \newcommand\PolToSturm{%
     \@ifstar{\POL@sturm@normalizefalse}{\POL@sturm@normalizetrue}%
     \POL@ToSturm
 }%
-\newcommand\POL@ToSturm[2]{%
+\def\POL@aux@toint#1{\xintREZ{\xintNum{#1}}}%
+\def\POL@ToSturm#1#2{%
   \edef\POL@sturmname{#2}%
   \POL@let{\POL@sturmname _0}{#1}%
-  \POL@mapcoeffs{\xintPIrr}{\POL@sturmname _0}%
+  \PolMakePrimitive{\POL@sturmname _0}%
   \POL@Diff@@one{\POL@sturmname _0}{\POL@sturmname _1}%
+  % re-utiliser \POL@varcoeffs directement?
+  \PolMakePrimitive{\POL@sturmname _1}%
   \POL@count\@ne
   \xintloop
     \POL@divide{\POL@sturmname _\the\numexpr\POL@count-\@ne}%
                {\POL@sturmname _\the\POL@count}%
     \expandafter\POL@split\POL@R;\POL@degR\POL@polR
   \unless\ifnum\POL@degR=\m@ne
-    % suis-je sûr format raw certain?
-    \edef\POL@polR{\xintApply{\POL@dooppandirr}{\POL@polR}}%
     \advance\POL@count\@ne
-    \expandafter\edef\csname POLuserpol@\POL@sturmname _\the\POL@count\endcsname
-       {\POL@degR.\noexpand\empty\POL@polR}%
+    \expandafter\let
+    \csname POLuserpol@\POL@sturmname _\the\POL@count\endcsname\POL@R
+    \edef\POL@makeprim@icontent{-\POL@icontent\POL@polR}%
+    \POL@mapcoeffs\POL@makeprim@macro{\POL@sturmname _\the\POL@count}%
   \repeat
   \edef\POL@sturm@N{\the\POL@count}%
   \ifPOL@sturm@normalize
@@ -650,12 +696,10 @@
        \advance\POL@count\m@ne
        \POL@divide{\POL@sturmname _\the\POL@count}%
                   {\POL@sturmname _\POL@sturm@N}%
-       \expandafter\POL@split\POL@Q;\POL@degQ\POL@polQ
-       \edef\POL@polQ % suis-je sûr format raw certain?
-          {\xintApply{\expandafter\XINT_pirr_start\xint_firstofone}{\POL@polQ}}%
-       \edef\POL@Q{\POL@degQ.\noexpand\empty\POL@polQ}%
-       \expandafter\edef\csname POLuserpol@\POL@sturmname _\the\POL@count\endcsname
-          {\POL@degQ.\noexpand\empty\POL@polQ}%
+       \expandafter\let
+       \csname POLuserpol@\POL@sturmname _\the\POL@count\endcsname\POL@Q
+       % quotient actually belongs to Z[X]
+       \POL@mapcoeffs{\POL@aux@toint}{\POL@sturmname _\the\POL@count}%    
      \ifnum\POL@count>\z@
      \repeat
      \@namedef{POLuserpol@\POL@sturmname _\POL@sturm@N}{0.\empty{1/1[0]}}%
@@ -667,9 +711,10 @@
   \unless\ifnum\POL@sturm@N=\POL@count
     \advance\POL@count\@ne
   \repeat
-  \expandafter\let\csname PolSturmChainLength_\POL@sturmname \endcsname\POL@sturm@N
+  \expandafter\let
+  \csname PolSturmChainLength_\POL@sturmname \endcsname\POL@sturm@N
 }%
-\def\POL@dooppandirr#1{\xintiiOpp{\XINT_pirr_start#1}}%
+
 \newcommand\PolSturmChainLength[1]
     {\romannumeral`^^@\csname PolSturmChainLength_#1\endcsname}%
 \newcommand\PolSetToSturmChainSignChangesAt[4][\global]{%
@@ -681,8 +726,8 @@
 }%
 \def\POL@sturmchain@getSV@at#1{% ATTENTION USES \POL@count
   \def\POL@sturmchain@SV{0}%
-  \edef\POL@isolz@lastsign{\xintiiSgn{\PolEval{\POL@sturmname _0}\At{#1}}}%
-  \let\POL@IsoRightSign\POL@isolz@lastsign % needed only for SturmIsolate etc...
+  \edef\POL@sturmchain@sign{\xintiiSgn{\PolEval{\POL@sturmname _0}\At{#1}}}%
+  \let\POL@isolz@lastsign\POL@sturmchain@sign
   \POL@count \z@
   \ifnum\POL@isolz@lastsign=\z@
     \edef\POL@isolz@lastsign
@@ -717,17 +762,63 @@
 }%
 
 
-\newcommand\PolSturmIsolateZeros[1]{%
-  % #1 name of Sturm chain (already pre-computed from a given polynomial)
-  \edef\POL@sturmname{#1}%
-  \edef\POL@sturmlength{\PolSturmChainLength{#1}}%
+\newcommand\PolSturmIsolateZeros[2][\empty]{%
+  % #1 optional E such that roots are searched in -10^E < x < 10^E
+  % both -10^E and +10^E must not be roots!
+  % #2 name of Sturm chain (already pre-computed from a given polynomial)
+  \edef\POL@sturmname{#2}%
+  \edef\POL@sturmlength{\PolSturmChainLength{#2}}%
+  \ifx\empty#1\relax
+    \POL@isolz@getsignchanges@plusinf
+    \POL@isolz@getsignchanges@minusinf
+  \else
+    \edef\POL@isolz@E{\the\numexpr\xint_zapspaces #1 \xint_gobble_i\relax}%
+    \POL@sturmchain@getSV@at{1[\POL@isolz@E]}%
+    \let\POL@isolz@plusinf@SV  \POL@sturmchain@SV
+    \let\POL@isolz@plusinf@sign\POL@sturmchain@sign
+    \POL@sturmchain@getSV@at{-1[\POL@isolz@E]}%
+    \let\POL@isolz@minusinf@SV  \POL@sturmchain@SV
+    \let\POL@isolz@minusinf@sign\POL@sturmchain@sign
+    \ifnum\POL@isolz@plusinf@sign=\z@
+        \PackageError{polexpr}%
+{The polynomial #2 vanishes at set upper bound 10^\POL@isolz@E}%
+{Compile again with a bigger exponent in source. (X to abort).}%
+    \fi
+    \ifnum\POL@isolz@minusinf@sign=\z@
+        \PackageError{polexpr}%
+{The polynomial #2 vanishes at set lower bound -10^\POL@isolz@E}%
+{Compile again with a bigger exponent in source. (X to abort).}%
+    \fi
+  \fi
+  \edef\POL@isolz@NbOfRoots
+      {\the\numexpr\POL@isolz@minusinf@SV-\POL@isolz@plusinf@SV}%
+  \ifnum\POL@isolz@NbOfRoots=\z@
+     \begingroup\globaldefs\@ne
+     \expandafter\xintAssignArray\expandafter\to\csname POL_ZeroInt#2L\endcsname
+     \expandafter\xintAssignArray\expandafter\to\csname POL_ZeroInt#2R\endcsname
+     \endgroup
+  \else
+     \begingroup\globaldefs\@ne
+     \expandafter\POL@isolz@initarray\csname POL_ZeroInt#2L\endcsname
+     \expandafter\POL@isolz@initarray\csname POL_ZeroInt#2R\endcsname
+     \endgroup
+     \ifx\empty#1\relax\expandafter\POL@isolz@getaprioribound\fi
+     \expandafter\POL@isolz@main
+  \fi
+}%
+\def\POL@isolz@initarray#1{%
+  \expandafter\xintAssignArray
+    \romannumeral\xintreplicate{\POL@isolz@NbOfRoots}{{0}}\to#1%
+}%
+\def\POL@isolz@getsignchanges@plusinf{%
   % Count number of sign changes at plus infinity in Sturm sequence
   \def\POL@isolz@plusinf@SV{0}%
-  \edef\POL@isolz@lastsign{\xintiiSgn{\PolLeadingCoeff{#1_0}}}%
+  \edef\POL@isolz@lastsign{\xintiiSgn{\PolLeadingCoeff{\POL@sturmname _0}}}%
   \let\POL@isolz@plusinf@sign\POL@isolz@lastsign
   \POL@count\@ne
   \xintloop
-    \edef\POL@isolz@newsign{\xintiiSgn{\PolLeadingCoeff{#1_\the\POL@count}}}%
+    \edef\POL@isolz@newsign
+        {\xintiiSgn{\PolLeadingCoeff{\POL@sturmname _\the\POL@count}}}%
     \unless\ifnum\POL@isolz@newsign=\POL@isolz@lastsign
        \edef\POL@isolz@plusinf@SV{\the\numexpr\POL@isolz@plusinf@SV+\@ne}%
     \fi
@@ -735,17 +826,20 @@
   \ifnum\POL@sturmlength>\POL@count
     \advance\POL@count\@ne
   \repeat
+}%
+\def\POL@isolz@getsignchanges@minusinf{%
   % Count number of sign changes at minus infinity in Sturm sequence
   \def\POL@isolz@minusinf@SV{0}%
-  \edef\POL@isolz@lastsign{\xintiiSgn{\PolLeadingCoeff{#1_0}}}%
-  \ifodd\PolDegree{#1_0}
+  \edef\POL@isolz@lastsign{\xintiiSgn{\PolLeadingCoeff{\POL@sturmname _0}}}%
+  \ifodd\PolDegree{\POL@sturmname _0}
       \edef\POL@isolz@lastsign{\xintiiOpp{\POL@isolz@lastsign}}%
   \fi
   \let\POL@isolz@minusinf@sign\POL@isolz@lastsign
   \POL@count\@ne
   \xintloop
-    \edef\POL@isolz@newsign{\xintiiSgn{\PolLeadingCoeff{#1_\the\POL@count}}}%
-    \ifodd\PolDegree{#1_\the\POL@count}
+    \edef\POL@isolz@newsign
+      {\xintiiSgn{\PolLeadingCoeff{\POL@sturmname _\the\POL@count}}}%
+    \ifodd\PolDegree{\POL@sturmname _\the\POL@count}
       \edef\POL@isolz@newsign{\xintiiOpp{\POL@isolz@newsign}}%
     \fi
     \unless\ifnum\POL@isolz@newsign=\POL@isolz@lastsign
@@ -755,24 +849,6 @@
   \ifnum\POL@sturmlength>\POL@count
     \advance\POL@count\@ne
   \repeat
-  \edef\POL@isolz@NbOfRoots
-      {\the\numexpr\POL@isolz@minusinf@SV-\POL@isolz@plusinf@SV}%
-  \ifnum\POL@isolz@NbOfRoots=\z@
-     \begingroup\globaldefs\@ne
-     \expandafter\xintAssignArray\expandafter\to\csname POL_ZeroInt#1L\endcsname
-     \expandafter\xintAssignArray\expandafter\to\csname POL_ZeroInt#1R\endcsname
-     \endgroup
-  \else
-     \begingroup\globaldefs\@ne
-     \expandafter\POL@isolz@initarray\csname POL_ZeroInt#1L\endcsname
-     \expandafter\POL@isolz@initarray\csname POL_ZeroInt#1R\endcsname
-     \endgroup
-     \expandafter\POL@isolz@getaprioribound
-  \fi
-}%
-\def\POL@isolz@initarray#1{%
-  \expandafter\xintAssignArray
-    \romannumeral\xintreplicate{\POL@isolz@NbOfRoots}{{0}}\to#1%
 }%
 % utility macro for a priori bound on root decimal exponent, via Float Rounding
 \def\POL@isolz@updateE #1e#2;%
@@ -800,7 +876,6 @@
   % \ifxintverbose\xintMessage{polexpr}{Info}%
   %   {Roots a priori bounded in absolute value by 10 to the \POL@isolz@E.}%
   % \fi
-  \POL@isolz@main
 }%
 \def\POL@IsoRight@raw{\POL@IsoRight@Int/1[\POL@isolz@E]}%
 \def\POL@IsoLeft@raw {\POL@IsoLeft@Int/1[\POL@isolz@E]}%
@@ -817,8 +892,9 @@
   \global\POL@isolz@nextwillneedrefinefalse
   \def\POL@IsoRight@Int{0}%
   \POL@sturmchain@getSV@at\POL@IsoRight@raw
-  \let\POL@IsoRightSV\POL@sturmchain@SV
-  \let\POL@IsoAtZeroSV\POL@IsoRightSV
+  \let\POL@IsoRightSV  \POL@sturmchain@SV
+  \let\POL@IsoRightSign\POL@sturmchain@sign
+  \let\POL@IsoAtZeroSV  \POL@IsoRightSV
   \let\POL@IsoAtZeroSign\POL@IsoRightSign
   \ifnum\POL@IsoAtZeroSign=\z@
     \xdef\POL@isolz@IntervalIndex
@@ -830,7 +906,7 @@
       {\xintiiOpp{\xintiiSgn{\PolEval{\POL@sturmname _1}\At{0/1[0]}}}}%
   \fi
   \def\POL@IsoLeft@Int{-1}% -10^E isn't a root!
-  \let\POL@IsoLeftSV\POL@isolz@minusinf@SV
+  \let\POL@IsoLeftSV  \POL@isolz@minusinf@SV
   \let\POL@IsoLeftSign\POL@isolz@minusinf@sign
   \edef\POL@isolz@NbOfNegRoots{\the\numexpr\POL@IsoLeftSV-\POL@IsoRightSV}%
   \gdef\POL@isolz@IntervalIndex{0}%
@@ -842,7 +918,8 @@
       \xintloop
         \edef\POL@isolz@E{\the\numexpr\POL@isolz@E-\@ne}%
         \POL@sturmchain@getSV@at\POL@IsoRight@raw
-        \let\POL@IsoRightSV\POL@sturmchain@SV
+        \let\POL@IsoRightSV  \POL@sturmchain@SV
+        \let\POL@IsoRightSign\POL@sturmchain@sign
       % would an \ifx test be quicker? (to be checked)
       \ifnum\POL@IsoRightSV=\POL@IsoLeftSV\space
         % no roots in-between, sign and SV kept
@@ -854,7 +931,8 @@
         \edef\POL@IsoRight@Int{\the\numexpr\POL@IsoLeft@Int+\@ne}%
 % we could arguably do a more efficient dichotomy here
         \POL@sturmchain@getSV@at\POL@IsoRight@raw
-        \let\POL@IsoRightSV\POL@sturmchain@SV
+        \let\POL@IsoRightSV  \POL@sturmchain@SV
+        \let\POL@IsoRightSign\POL@sturmchain@sign
         \POL@isolz@check
       \ifnum\POL@isolz@IntervalIndex=\POL@isolz@NbOfNegRoots\space
         \expandafter\xintbreakloop
@@ -883,7 +961,7 @@
   \fi
   \endgroup
   \def\POL@IsoLeft@Int{0}%
-  \let\POL@IsoLeftSV\POL@IsoAtZeroSV
+  \let\POL@IsoLeftSV  \POL@IsoAtZeroSV
   \let\POL@IsoLeftSign\POL@IsoAtZeroSign
   \ifnum\POL@IsoLeftSign=\z@
     \xdef\POL@isolz@IntervalIndex{\the\numexpr\POL@isolz@IntervalIndex+\@ne}%
@@ -891,8 +969,8 @@
   \else
     \global\POL@isolz@nextwillneedrefinefalse
   \fi
-  \let\POL@@IsoRightSV=\POL@isolz@plusinf@SV
-  \let\POL@@IsoRightSign=\POL@isolz@plusinf@sign % 10^E not a root!
+  \let\POL@@IsoRightSV  \POL@isolz@plusinf@SV
+  \let\POL@@IsoRightSign\POL@isolz@plusinf@sign % 10^E not a root!
   \edef\POL@isolz@NbOfPosRoots
     {\the\numexpr\POL@IsoLeftSV-\POL@@IsoRightSV}% attention @@
   \ifnum\POL@isolz@NbOfPosRoots>\z@
@@ -900,7 +978,8 @@
       \xintloop
         \edef\POL@isolz@E{\the\numexpr\POL@isolz@E-\@ne}%
         \POL@sturmchain@getSV@at\POL@IsoRight@raw
-        \let\POL@IsoRightSV\POL@sturmchain@SV
+        \let\POL@IsoRightSV  \POL@sturmchain@SV
+        \let\POL@IsoRightSign\POL@sturmchain@sign
       \ifnum\POL@IsoRightSV=\POL@@IsoRightSV\space
         \let\POL@@IsoRightSign\POL@IsoRightSign % root here possible!
       \repeat
@@ -914,7 +993,8 @@
 % we could arguably do a more efficient dichotomy here
         \edef\POL@IsoRight@Int{\the\numexpr\POL@IsoLeft@Int+\@ne}%
         \POL@sturmchain@getSV@at\POL@IsoRight@raw
-        \let\POL@IsoRightSV\POL@sturmchain@SV
+        \let\POL@IsoRightSV  \POL@sturmchain@SV
+        \let\POL@IsoRightSign\POL@sturmchain@sign
         \POL@isolz@check
         \let\POL@IsoLeft@Int\POL@IsoRight@Int
         \let\POL@IsoLeftSign\POL@IsoRightSign
@@ -925,7 +1005,7 @@
       \ifnum\POL@IsoLeft@Int < \xint_c_ix
       \repeat
       \ifnum\POL@isolz@IntervalIndex<\POL@isolz@NbOfRoots\space
-      % get now the last, right most, root (or roots)
+      % get now the last, rightmost, root (or roots)
         \def\POL@IsoRight@Int{10}%
         \let\POL@IsoRightSign\POL@@IsoRightSign
         \let\POL@IsoRightSV\POL@@IsoRightSV
@@ -976,7 +1056,8 @@
   \xintiloop[1+1]
     \edef\POL@IsoRight@Int{\xintInc{\POL@IsoLeft@Int}}%
     \POL@sturmchain@getSV@at\POL@IsoRight@raw
-    \let\POL@IsoRightSV\POL@sturmchain@SV
+    \let\POL@IsoRightSV  \POL@sturmchain@SV
+    \let\POL@IsoRightSign\POL@sturmchain@sign
     \POL@isolz@check
     \let\POL@IsoLeft@Int\POL@IsoRight@Int
     \let\POL@IsoLeftSV\POL@IsoRightSV