CTAN sync 202002020302

1 files changed, 321 insertions, 103 deletions

diff --git a/macros/latex/contrib/polexpr/polexpr.sty b/macros/latex/contrib/polexpr/polexpr.sty
index e9509d8942..30fef28914 100644
--- a/macros/latex/contrib/polexpr/polexpr.sty
+++ b/macros/latex/contrib/polexpr/polexpr.sty
@@ -1,33 +1,178 @@
 % author: Jean-François Burnol
 % License: LPPL 1.3c (author-maintained)
 \ProvidesPackage{polexpr}%
-  [2019/02/12 v0.7.4 Polynomial expressions with rational coefficients (JFB)]%
-\RequirePackage{xintexpr}[2018/06/17]% xint 1.3c for \ifxintglobaldefs boolean
-\edef\POL@restorecatcodes
+  [2020/01/31 v0.7.5 Polynomial expressions with rational coefficients (JFB)]%
+\RequirePackage{xintexpr}[2020/01/31]% xint 1.4
+\edef\POL@restorecatcodes % TODO: think better about what is reasonable here
     {\catcode`\noexpand\_ \the\catcode`\_ %
      \catcode`\noexpand\! \the\catcode`\! %
      \catcode`\noexpand\* \the\catcode`\* %
+     \catcode`\noexpand\~ \the\catcode`\~ %
+     \catcode`\noexpand\: \the\catcode`\: %
      \catcode0 \the\catcode0\relax}%
 \catcode`\_ 11 \catcode0 12 \catcode`\* 12
 \long\def\xint_stop_atfirstoftwo  #1#2{ #1}% not yet in xint 1.3c
 \long\def\xint_stop_atsecondoftwo #1#2{ #2}%
 
-%% PATCH xintexpr TO AUTHORIZE ' IN NAMES (0.5.1)
-\catcode`\! 11
+%% 0.7.5 VERY SERIOUS TROUBLES TO GET polexpr TO WORK WITH xintexpr 1.4
+
+%% I hesitated about incorporating it directly into xint 1.4
+%% Don't do this at home, only xint gurus are allowed.
+\let\POL@originalXINT_expr_redefinemacros\XINT_expr_redefinemacros
+\def\XINT_expr_redefinemacros
+{%
+    \POL@originalXINT_expr_redefinemacros
+    \POL@activateNEhook
+}%
+%% Using \def's and not \let's to get better readable trace
+%% in case I need to debug but this never happens
+\def\POL@activateNEhook@xint % done in a group
+{%
+    \def\POL@NEhook@polfunc{\POL@NE@polfunc}%
+}%
+\def\POL@activateNEhook@pol
+{%
+    \def\POL@NEhook@polfunc{\POL@NP@polfunc}%
+}%
+\def\POL@activateNEhook{\POL@activateNEhook@xint}%
+%
+%
+\catcode`~ 12
+\catcode`! 11
+\catcode`: 11
+% We drop consideration of \XINT_global matters
+% because we have other more urgent and arduous problems
+\def\POL@defpolfunc #1#2%
+{%
+  \expandafter\POL@defpolfunc_a
+  \csname XINT_#2_func_#1\expandafter\endcsname
+  \csname XINT_#2_polfunc_#1\endcsname {#1}{#2}%
+}%
+\def\POL@defpolfunc_a #1#2#3#4%
+{%
+  \protected % xintexpr 1.4 does things such as \expandafter\xintAdd\expanded 
+  \expandafter\def\expandafter#2\expandafter##\expandafter1\expandafter
+  {%
+      #2{##1}%
+  }%
+  \def#1##1##2##3%
+  {%
+  % put it directly at the correct level of bracing
+  % don't worry for now about minimizing how many times ##3 is grabbed 
+     \expandafter##1\expandafter##2\expandafter{\expandafter
+     {\romannumeral`^^@\POL@NEhook@polfunc{XINT_#4_polfunc_#3}#2{##3}}}%
+  }%
+}%
+%
+\def\POL@polfunc@go #1#2#3{#2#3}% brace stripping intentional
+\def\POL@NEhook@polfunc{\POL@polfunc@go}% default for pure numerics
+%
+% Hook for expansion in \poldef
+\def\POL@NP@polfunc #1{%
+\def\POL@NP@polfunc ##1##2##3%
+{%
+    \if0\expandafter\XINT:NE:hastilde\detokenize{##3}~!\relax
+        \expandafter\XINT:NE:hashash\detokenize{##3}#1!\relax 0%
+      \expandafter\POL@polfunc@go
+    \else
+      \expandafter\POL:NP:polfunc:p
+    \fi {##1}{##2}{##3}%
+}}\expandafter\POL@NP@polfunc\string#%
+\def\POL:NP:polfunc:p #1#2#3%
+{%
+    ~romannumeral~POL:usepolfunc:pol{#1}{#3}%
+}%
+\def\POL:usepolfunc:pol #1%#2%
+{%
+% Here we are in the core of \poldef and we really
+% need to get rid of some \expanded tokens so
+% we accept being exposed to \expanded but arrange to
+% remain invariant. Then we will try to speed up
+% polynomial composition (at this time the \#1
+% is a nested Horner type macro) by «pre-expanding»
+% the argument, but this means using the \POL@get
+% methods inside an \hbox
+%
+% \POL@applypolfunc will be defined \protected
+%
+    \expandafter\xint_c_\expandafter\POL@applypolfunc
+% This will be \protected
+    \csname#1\endcsname
+%    #2% brace stripping is deliberate
+}%
+%
+% Hook for expansion in \xintexpr
+\def\POL@NE@polfunc #1{%
+\def\POL@NE@polfunc ##1##2##3%
+{%
+    \if0\expandafter\XINT:NE:hastilde\detokenize{##3}~!\relax
+        \expandafter\XINT:NE:hashash\detokenize{##3}#1!\relax 0%
+      \expandafter\POL@polfunc@go
+    \else
+      \expandafter\POL:NE:polfunc:p
+    \fi {##1}{##2}{##3}%
+}}\expandafter\POL@NE@polfunc\string#%
+\def\POL:NE:polfunc:p #1#2#3%
+{%
+    ~romannumeral~POL:usepolfunc:xint{#1}{#3}%
+}%
+\def\POL:usepolfunc:xint #1%
+{%
+% This is done to overcome \protected and is useful
+% in case the polynomial function ends up nested
+% in some non-polynomial user declared function
+% as the latter (and other things) tries to pre-expand
+% its arguments (as they may be used multiple time)
+% using \expanded, but \#1 is protected.
+% And this works recursively. We are inside braces.
+% However we have a very big problem with constant
+% polynomial functions. We have to handle them
+% in a special way.
+    -`0\csname#1\expandafter\endcsname\expanded
+}%
+\catcode`~ 13
+\catcode`: 12
+
+
+%% Start defining some \protected ones here
+\protected\def\POL@empty{}%
+\newif\ifPOL@pol
+\protected\def\POL@polglobaltrue {\global\let\ifPOL@pol\iftrue}%
+\protected\def\POL@polglobalfalse{\global\let\ifPOL@pol\iffalse}%
+
+
+%% Patch xintexpr to authorize ' in names (0.5.1)
+%% Adapted 0.7.5 to follow-up on xintexpr 1.4 internal changes
+%% (much simpler than previous stuff...)
+%% This allows ' as a character in a polynomial name (not initial one)
 \def\POL@XINT_expr_scanfunc_b #1%
 {%
-  \ifx !#1\xint_dothis{(_}\fi
-  \ifcat \relax#1\xint_dothis{(_}\fi
-  \if (#1\xint_dothis{\xint_firstoftwo{(`}}\fi
-  \if '#1\xint_dothis \XINT_expr_scanfunc_a \fi
-  \if @#1\xint_dothis \XINT_expr_scanfunc_a \fi
-  \if _#1\xint_dothis \XINT_expr_scanfunc_a \fi
-  \ifnum \xint_c_ix<1\string#1 \xint_dothis \XINT_expr_scanfunc_a \fi
-  \ifcat a#1\xint_dothis \XINT_expr_scanfunc_a \fi
-  \xint_orthat {(_}%
-    #1%
+  \ifcat \relax#1\xint_dothis{\iffalse{\fi}(_#1}\fi
+  \if (#1\xint_dothis{\iffalse{\fi}(`}\fi
+  \if 1\ifcat a#10\fi
+       \ifnum\xint_c_ix<1\string#1 0\fi
+       \if @#10\fi
+       \if _#10\fi
+       \if '#10\fi
+      1%
+      \xint_dothis{\iffalse{\fi}(_#1}\fi
+  \xint_orthat {#1\XINT_expr_scanfunc_a}%
 }%
 
+
+%% Activate polexp's modified xintexpr (only during definitions
+%% of polynomials)
+\def\POL@hackxintexpr {%
+    \let\POL@originalXINT_expr_scanfunc_b\XINT_expr_scanfunc_b
+    \let\XINT_expr_scanfunc_b\POL@XINT_expr_scanfunc_b
+    \def\POL@activateNEhook{\POL@activateNEhook@pol}%
+}%
+\def\POL@restorexintexpr {%
+    \let\XINT_expr_scanfunc_b\POL@originalXINT_expr_scanfunc_b
+    \def\POL@activateNEhook{\POL@activateNEhook@xint}%
+}%
+
+
 %% AUXILIARIES
 \catcode`! 3
 %% added at 0.7
@@ -46,7 +191,6 @@
 \polexprsetup{norr=_norr, sqfnorr=_sqf_norr}
 
 \newcount\POL@count
-\newif\ifPOL@pol
 \newif\ifxintveryverbose
 \newif\ifpoltypesetall
 \newif\ifPOL@tosturm@makefirstprimitive
@@ -54,7 +198,7 @@
 \newif\ifPOL@isolz@nextwillneedrefine
 \newif\ifpoltoexprall
 %% the main exchange structure (stored in macros \POLuserpol@<name>)
-%% is: degree.\empty{coeff0}{coeff1}....{coeffN}
+%% is: degree.\POL@empty{coeff0}{coeff1}....{coeffN}
 %% (degree=N except zero polynomial recognized from degree set to -1
 %%  but it has always the {0/1[0]} coeff0.)
 \def\POL@ifZero#1{\expandafter\POL@ifZero@aux#1;}%
@@ -67,13 +211,17 @@
 %
 \def\POL@resultfromarray #1{% ATTENTION, **MUST** be executed with
 % \count@ set to 1 + degree (\count@ = 0 for zero polynomial)
-    \edef\POL@result{\ifnum\count@>\z@
-      \the\numexpr\count@-\@ne.\noexpand\empty
+% Attention to the \protected here at 0.7.5
+% They are many all over the place
+    \protected\edef\POL@result{\ifnum\count@>\z@
+      \the\numexpr\count@-\@ne.\POL@empty
       \xintiloop [1+1]%
       \expandafter\POL@braceit\csname POL@array#1\xintiloopindex\endcsname
       \ifnum\xintiloopindex<\count@
       \repeat
-      \else-1.\noexpand\empty{0/1[0]}\fi}%
+% Attention to this \protected\POL@empty
+% They are many all over the place
+      \else-1.\POL@empty{0/1[0]}\fi}%
 }%
 \def\POL@braceit#1{{#1}}% needed as \xintiloopindex can not "see" through braces
 
@@ -85,12 +233,11 @@
    \POL@restoresemicolon
    \edef\POL@tmp{\ifxintverbose1\else0\fi}%
    \unless\ifxintveryverbose\xintverbosefalse\fi
-   \let\POL@originalXINT_expr_scanfunc_b\XINT_expr_scanfunc_b
-   \let\XINT_expr_scanfunc_b\POL@XINT_expr_scanfunc_b
+   \POL@hackxintexpr
    \xintdeffunc __pol(#2):=0+(#4);% force conversion to raw if a constant
+   \POL@restorexintexpr
    \if1\POL@tmp\xintverbosetrue\fi
    \edef\POL@polname{\xint_zapspaces #1 \xint_gobble_i}%
-   \let\XINT_expr_scanfunc_b\POL@originalXINT_expr_scanfunc_b
    \begingroup
      \setbox0\hbox{%
      \let\xintScalarAdd\xintAdd
@@ -107,48 +254,79 @@
      \def\xintSub ##1##2{\xintAdd{##1}{\xintOpp{##2}}}%
      % \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]}}}}%
+% Attention that xintexpr 1.4 has braces all over the place
+     \expandafter\xintAdd\expandafter{\expandafter0\expandafter}%
+       \romannumeral0\csname XINT_expr_userfunc___pol\endcsname
+        {\POL@polglobaltrue\protected\def\POL@result{1.\POL@empty{0/1[0]}{1/1[0]}}}%
      \expandafter}\expandafter
    \endgroup\expandafter
    \def\csname POLuserpol@\POL@polname\expandafter\endcsname
         \expandafter{\POL@result}%
    \expandafter\POL@newpol\expandafter{\POL@polname}%
 }%
-%%
+%
+
+
 \def\POL@newpol#1{%
-   \expandafter\POL@ifZero\csname POLuserpol@#1\endcsname
-      {\@namedef{XINT_expr_userfunc_#1}##1{0/1[0]}}%
-      {\POL@newpolhorner{#1}}%
-   \expandafter\XINT_expr_defuserfunc
-     \csname XINT_expr_func_#1\endcsname{#1}{expr}%
+%% We must handle specially constant polynomials because they must
+%% be made to work expandably in \poldef of other polynomials due
+%% to complicated matters having to do with the \POL@ifpol conditional
+   \ifnum\PolDegree{#1}<\@ne
+      % non-zero constant
+      % I am defining this one only for the Info message, no time now
+      \expandafter\edef\csname XINT_expr_polfunc_#1\endcsname
+          ##1{\PolNthCoeff{#1}{0}}%
+      % No hooks here!
+      \expandafter\edef\csname XINT_expr_func_#1\endcsname ##1##2##3%
+          {##1##2{{\PolNthCoeff{#1}{0}}}}%
+   \else
+      % polynomial of degree at least 1. This means that mechanism
+      % to get \POL@result will get activated and we must be very careful
+      % to never \edef when the Horner macro will be converted to
+      % a polynomial
+      \POL@newpolhorner{#1}%
+      \POL@defpolfunc{#1}{expr}%
+   \fi
    \expandafter\let\csname XINT_flexpr_func_#1\endcsname\@undefined
    \ifxintverbose\POL@info{#1}\fi
 }%
 \def\POL@newfloatpol#1{%
-   \expandafter\POL@ifZero\csname POLuserpol@#1\endcsname
-      {\@namedef{XINT_flexpr_userfunc_#1}##1{0[0]}}%
-      {\POL@newfloatpolhorner{#1}}%
-   \expandafter\XINT_expr_defuserfunc
-     \csname XINT_flexpr_func_#1\endcsname{#1}{flexpr}%
+%% We must handle specially constant polynomials because they must
+%% be made to work expandably in \poldef of other polynomials due
+%% to complicated matters having to do with the \POL@ifpol conditional
+   \ifnum\PolDegree{#1}<\@ne
+      % non-zero constant
+      % I am defining this one only for the Info message, no time now
+      \expandafter\edef\csname XINT_flexpr_polfunc_#1\endcsname
+          ##1{\PolNthCoeff{#1}{0}}%
+      % No hooks here!
+      \expandafter\edef\csname XINT_flexpr_func_#1\endcsname ##1##2##3%
+          {##1##2{{\PolNthCoeff{#1}{0}}}}%
+   \else
+      % polynomial of degree at least 1. This means that mechanism
+      % to get \POL@result will get activated and we must be very careful
+      % to never \edef when the Horner macro will be converted to
+      % a polynomial
+      \POL@newfloatpolhorner{#1}%
+      \POL@defpolfunc{#1}{flexpr}%
+   \fi
    \ifxintverbose\POL@floatinfo{#1}\fi
 }%
 \def\POL@info #1{%
    \xintMessage {polexpr}{Info}%
         {Function #1 for the \string\xintexpr\space parser is
-         associated to \string\XINT_expr_userfunc_#1\space
+         associated to \string\XINT_expr_polfunc_#1\space
          whose meaning uses Horner scheme:
          \expandafter\meaning
-         \csname XINT_expr_userfunc_#1\endcsname}%
+         \csname XINT_expr_polfunc_#1\endcsname}%
 }%
 \def\POL@floatinfo #1{%
    \xintMessage {polexpr}{Info}%
         {Function #1 for the \string\xintfloatexpr\space parser is
-         associated to \string\XINT_flexpr_userfunc_#1\space
+         associated to \string\XINT_flexpr_polfunc_#1\space
          whose meaning uses Horner scheme:
          \expandafter\meaning
-         \csname XINT_flexpr_userfunc_#1\endcsname}%
+         \csname XINT_flexpr_polfunc_#1\endcsname}%
 }%
 %
 \def\POL@newpolhorner#1{%
@@ -162,7 +340,7 @@
       \expandafter\POL@newpol@horner\POL@var@coeffs\relax
    \expandafter
    \endgroup
-   \expandafter\def\csname XINT_expr_userfunc_#1\expandafter\endcsname
+   \expandafter\def\csname XINT_expr_polfunc_#1\expandafter\endcsname
       \expandafter##\expandafter1\expandafter{\POL@tmp{##1}}%
 }%
 \def\POL@newfloatpolhorner#1{%
@@ -176,7 +354,7 @@
       \expandafter\POL@newpol@floathorner\POL@var@coeffs\relax
    \expandafter
    \endgroup
-   \expandafter\def\csname XINT_flexpr_userfunc_#1\expandafter\endcsname
+   \expandafter\def\csname XINT_flexpr_polfunc_#1\expandafter\endcsname
       \expandafter##\expandafter1\expandafter{\POL@tmp{##1}}%
 }%
 \def\POL@newpol@horner#1{\let\xintAdd\relax\let\xintMul\relax
@@ -211,10 +389,9 @@
 \def\POL@let#1#2{%
     \expandafter\let\csname POLuserpol@#1\expandafter\endcsname
                     \csname POLuserpol@#2\endcsname
-    \expandafter\let\csname XINT_expr_userfunc_#1\expandafter\endcsname
-                    \csname XINT_expr_userfunc_#2\endcsname
-    \expandafter\XINT_expr_defuserfunc
-       \csname XINT_expr_func_#1\endcsname{#1}{expr}%
+    \expandafter\let\csname XINT_expr_polfunc_#1\expandafter\endcsname
+                    \csname XINT_expr_polfunc_#2\endcsname
+    \POL@defpolfunc{#1}{expr}%
     \ifxintverbose\POL@info{#1}\fi
 }%
 \newcommand\PolGlobalLet[2]{\begingroup
@@ -259,7 +436,7 @@
 \def\POL@getfromarray#1#2{%
         \count@=#2{0} %<- intentional space
   \ifnum\count@=\z@
-     \def\POL@result{-1.\empty{0/1[0]}}% 0.5 fix for empty array
+     \protected\def\POL@result{-1.\POL@empty{0/1[0]}}% 0.5 fix for empty array
   \else
         \xintloop
           \edef\POL@tmp{#2{\count@}}%
@@ -283,7 +460,7 @@
         \repeat
         \count@\count\tw@          
         \def\POL@tmp##1.{{\csname POL@tmparray##1\endcsname}}%
-        \edef\POL@result{\the\numexpr\count@-\@ne.\noexpand\empty
+        \protected\edef\POL@result{\the\numexpr\count@-\@ne.\POL@empty
                          \xintiloop[1+1]%
                          \expandafter\POL@tmp\xintiloopindex.%
                          \ifnum\xintiloopindex<\count@
@@ -480,7 +657,7 @@
         {\ifnum\POL@degB<\z@
           \expandafter\xint_firstoftwo\else\expandafter\xint_secondoftwo
         \fi
-          {\def\POL@result{-1.\empty{0/1[0]}}}%
+          {\protected\def\POL@result{-1.\POL@empty{0/1[0]}}}%
           {\xintAssignArray\POL@polB\to\POL@arrayB
            \POL@normalize{B}%
            \POL@gcd@exit BA}}%
@@ -606,11 +783,11 @@
    \expandafter\expandafter\expandafter\POL@split
       \csname POLuserpol@#1\endcsname;\POL@var@deg\POL@var@coeffs
    \ifnum\POL@var@deg<\@ne
-      \@namedef{POLuserpol@#2}{-1.\empty{0/1[0]}}%
+      \@namedef{POLuserpol@#2}{-1.\POL@empty{0/1[0]}}%
    \else
      \edef\POL@var@coeffs{\expandafter\POL@diff\POL@var@coeffs\relax}%
      \expandafter\edef\csname POLuserpol@#2\endcsname
-        {\the\numexpr\POL@var@deg-\@ne.\noexpand\empty\POL@var@coeffs}%
+        {\the\numexpr\POL@var@deg-\@ne.\POL@empty\POL@var@coeffs}%
    \fi
 }%
 % lazy way but allows to share with AntiDiff
@@ -666,11 +843,11 @@
    \expandafter\expandafter\expandafter\POL@split
       \csname POLuserpol@#1\endcsname;\POL@var@deg\POL@var@coeffs
    \ifnum\POL@var@deg<\z@
-      \@namedef{POLuserpol@#2}{-1.\empty{0/1[0]}}%
+      \@namedef{POLuserpol@#2}{-1.\POL@empty{0/1[0]}}%
    \else
      \edef\POL@var@coeffs{\expandafter\POL@antidiff\POL@var@coeffs\relax}%
      \expandafter\edef\csname POLuserpol@#2\endcsname
-         {\the\numexpr\POL@var@deg+\@ne.\noexpand\empty{0/1[0]}\POL@var@coeffs}%
+         {\the\numexpr\POL@var@deg+\@ne.\POL@empty{0/1[0]}\POL@var@coeffs}%
    \fi
 }%
 
@@ -737,7 +914,7 @@
      \POL@count\z@
      % if I applied the same as for positive degree, I should make it -1
      % if constant is negative. I also don't worry if polynomial is zero.
-     \@namedef{POLuserpol@\POL@sturmname _0}{0.\empty{1/1[0]}}%
+     \@namedef{POLuserpol@\POL@sturmname _0}{0.\POL@empty{1/1[0]}}%
   \else
      \ifPOL@tosturm@makefirstprimitive\POL@makeprimitive{\POL@sturmname _0_}\fi
      \POL@tosturm@dosturm
@@ -793,7 +970,7 @@
       \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]}}%
+    \@namedef{POLuserpol@\POL@sturmname _\POL@sturm@N}{0.\POL@empty{1/1[0]}}%
   \else % they are already normalized
     \advance\POL@count\@ne % attention to include last one also
     \xintloop
@@ -984,7 +1161,7 @@
     \POL@findrat@xN\POL@findrat@xD\POl@_
   % we can't move this to updatequotients because other branch will
   % need to do the division first anyhow
-  \edef\POLuserpol@_findrat@oneterm{1.\noexpand\empty
+  \edef\POLuserpol@_findrat@oneterm{1.\POL@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
@@ -1118,7 +1295,7 @@
   % zero should never occur here
   \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
+  \edef\POLuserpol@_findrat@oneterm{1.\POL@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
@@ -1185,7 +1362,7 @@
   % safer to do the edef as \POL@findrat@x used later in storeit
   \edef\POL@findrat@x{\xintIrr{\xintDiv\POL@findrat@Num\POL@findrat@D}[0]}%
   \POL@xintfrac@getNDE\POL@findrat@x\POL@findrat@xN\POL@findrat@xD\POL@_
-  \edef\POLuserpol@_findrat@oneterm{1.\noexpand\empty
+  \edef\POLuserpol@_findrat@oneterm{1.\POL@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
@@ -1210,11 +1387,11 @@
   \begingroup\xintglobaldefstrue
     % skip some overhead of \xintdefvar...
     \XINT_expr_defvar_one{\POL@sturmname L_\POL@findrat@index}%
-       {\csname .=\POL@findrat@x\endcsname}%
+       {\POL@findrat@x}%
     \XINT_expr_defvar_one{\POL@sturmname R_\POL@findrat@index}%
-       {\csname .=\POL@findrat@x\endcsname}%
+       {\POL@findrat@x}%
     \XINT_expr_defvar_one{\POL@sturmname Z_\POL@findrat@index _isknown}%
-       {\csname .=1\endcsname}%
+       {1}%
   \endgroup
 }%
 \def\POL@findrat@loop@updatequotients{%
@@ -1326,7 +1503,7 @@
     \xintloop
     % skip some overhead of \xintdefvar...
       \XINT_expr_defvar_one{\POL@sturmname M_\x}%
-         {\csname .=\csname POL_ZM\POL@sturmname*\x\endcsname\endcsname}%
+         {\csname POL_ZM\POL@sturmname*\x\endcsname}%
     \edef\x{\the\numexpr\x-\@ne}%
     \ifnum\x>\z@
     \repeat
@@ -1901,17 +2078,16 @@
     \begingroup\xintglobaldefstrue
     % skip some overhead of \xintdefvar...
       \XINT_expr_defvar_one{\POL@sturmname L_\POL@isolz@IntervalIndex}%
-         {\csname .=\POL@IsoLeft@rawout\endcsname}%
+         {\POL@IsoLeft@rawout}%
       \XINT_expr_defvar_one{\POL@sturmname R_\POL@isolz@IntervalIndex}%
-         {\csname .=\POL@IsoRight@rawout\endcsname}%
+         {\POL@IsoRight@rawout}%
       % added at 0.7
       \XINT_expr_defvar_one{\POL@sturmname Z_\POL@isolz@IntervalIndex _isknown}%
-         {\csname .=\ifnum\POL@IsoRightSign=\z@ 1\else 0\fi\endcsname}%
+         {\ifnum\POL@IsoRightSign=\z@ 1\else 0\fi}%
     \endgroup
 }%
 %% \PolRefineInterval
-\def\POL@xintexprGetVar#1{\expandafter\expandafter\expandafter
-    \XINT_expr_unlock\csname XINT_expr_var_#1\endcsname}%
+\def\POL@xintexprGetVar#1{\csname XINT_expr_varvalue_#1\endcsname}%
 % attention, also used by \POL@findrat@loop@a
 \def\POL@get@IsoLeft@rawin{%
     \edef\POL@IsoLeft@rawin
@@ -2277,28 +2453,70 @@
 %% The idea is to execute it with another meaning given to \xintAdd etc..,
 %% so that it operates on "polynomials". This is a mixture of expandable
 %% and non-expandable techniques.
+%%
+%% And it was complicated to let it work with xintexpr 1.4
+%%
 \def\POL@get#1#2#3{%
-    \global\POL@polfalse
+    \relax %!! part de la tambouille pour fonctionner en xint 1.4
+    \POL@polglobalfalse
     \begingroup
-        \def\POL@result{#3}%
+        \protected\def\POL@result{#3}%
         #3%
         \expandafter
     \endgroup
     \expandafter\def\expandafter#1\expandafter{\POL@result}%
     \unless\ifPOL@pol
         % avoid expanding more than twice #3
+        % #3 must be purely numerical or at least compatible with \edef
+        % this is why at 0.7.5 I had to handle especially constant
+        % polynomial functions to remove any protection from them
+        % (because the protection triggers the COMPOSITION when
+        %  the polynomial is found as argument of another one and
+        %  this is not expandable) 
         \edef#1{#3}%
         \xintiiifZero{#1}%
-            {\def#1{-1.\empty{0/1[0]}}}%
-            {\edef#1{0.\noexpand\empty{#1}}}%
+            {\def#1{-1.\POL@empty{0/1[0]}}}%
+            {\edef#1{0.\POL@empty{#1}}}%
     \fi
     #2%
 }%
+
+%% COMPOSITION
+%% This did not exist before 0.7.5 and is part of its adaptation to xint 1.4
+%% We thus took up this opportunity to speed up substantially composition.
+%% Very serious difficulties with constant polynomials. Had to handle them
+%% especially.
+%% OK, that was really tough, but advantage now is that composition
+%% at 0.7.5 should be more efficient than before. However when polynomials
+%% become big via composition, coefficients also are big and the time
+%% taken by arithmetic dominates.  No time to test really, though, relieved
+%% I can release xint 1.4 at last.  My basic polexpr test suite passes,
+%% but it goes back already to old releases.
+\protected\def\POL@applypolfunc#1#2%
+{%
+% This #2 may be also invoing \POL@applypolfunc...
+   \POL@get\POL@A\POL@applypolfunc@b#2#1%
+}%
+\def\POL@applypolfunc@b #1%
+{%
+% and now the have our Horner scheme nested macro
+% which hopefully will do its job with \POL@add, \POL@mul etc...
+    \POL@polglobalfalse
+    \expandafter#1\expanded
+    {{\POL@polglobaltrue\protected\def\noexpand\POL@result{\POL@A}}}%
+    \unless\ifPOL@pol
+        \odef\POL@result{#1{0}}%
+        \xintiiifZero{\POL@result}%
+            {\protected\def\POL@result{-1.\POL@empty{0/1[0]}}}%
+            {\protected\edef\POL@result{0.\POL@empty{\POL@result}}}%
+    \fi
+}%
+
 %% ADDITION
 \def\POL@add  {\POL@get\POL@A\POL@add@b}%
 \def\POL@add@b{\POL@get\POL@B\POL@add@c}%
 \def\POL@add@c{%
-    \global\POL@poltrue
+    \POL@polglobaltrue
     \POL@ifZero\POL@A
         {\let\POL@result\POL@B}%
         {\POL@ifZero\POL@B
@@ -2341,11 +2559,11 @@
 \def\POL@mul  {\POL@get\POL@A\POL@mul@b}%
 \def\POL@mul@b{\POL@get\POL@B\POL@mul@c}%
 \def\POL@mul@c{%
-    \global\POL@poltrue
+    \POL@polglobaltrue
     \POL@ifZero\POL@A
-        {\def\POL@result{-1.\empty{0/1[0]}}}%
+        {\protected\def\POL@result{-1.\POL@empty{0/1[0]}}}%
         {\POL@ifZero\POL@B
-             {\def\POL@result{-1.\empty{0/1[0]}}}%
+             {\protected\def\POL@result{-1.\POL@empty{0/1[0]}}}%
              {\POL@@mul}}%
 }%
 \def\POL@@mul{%
@@ -2436,9 +2654,9 @@
 
 %% POWERS (SCALAR EXPONENT...)
 \def\POL@pow #1#2{%
-    \global\POL@polfalse
+    \POL@polglobalfalse
     \begingroup
-        \def\POL@result{#1}%
+        \protected\def\POL@result{#1}%
         #1%
         \expandafter
     \endgroup
@@ -2446,39 +2664,39 @@
     \unless\ifPOL@pol
         \edef\POL@A{\xintScalarPow{#1}{#2}}% no error check
         \xintiiifZero{\POL@A}%
-            {\def\POL@result{-1.\empty{0/1[0]}}}%
-            {\edef\POL@result{0.\noexpand\empty{\POL@A}}}%
+            {\protected\def\POL@result{-1.\POL@empty{0/1[0]}}}%
+            {\protected\edef\POL@result{0.\POL@empty{\POL@A}}}%
     \else
       \edef\POL@B{\numexpr\xintNum{#2}\relax}% no check on exponent >= 0
       \ifcase\POL@B
-        \def\POL@result{0.\empty{1/1[0]}}%
+        \protected\def\POL@result{0.\POL@empty{1/1[0]}}%
       \or
         \let\POL@result\POL@A
       \else
         \POL@@pow@check
       \fi
     \fi
-    \global\POL@poltrue
+    \POL@polglobaltrue
 }%
 \def\POL@@pow@check {%
 % no problem here with leftover tokens!
 % should I have used that I-don't-care technique more elsewhere?
     \ifnum\@ne>\POL@A
-    % polynomial is a constant, must get rid of dot and \empty
+    % polynomial is a constant, must get rid of dot and \empty (\POL@empty)
         \edef\POL@A{\expandafter\xintScalarPow\romannumeral`^^@%
                     \expandafter\xint_gob_til_dot\POL@A{\POL@B}}%
         \xintiiifZero{\POL@A}%
-            {\def\POL@result{-1.\empty{0/1[0]}}}%
-            {\edef\POL@result{0.\noexpand\empty{\POL@A}}}%
+            {\protected\def\POL@result{-1.\POL@empty{0/1[0]}}}%
+            {\protected\edef\POL@result{0.\POL@empty{\POL@A}}}%
     \else
     \ifnum\@ne=\POL@A
     % perhaps a constant times X, check constant term
         \xintiiifZero
         {\expandafter\xint_firstoftwo\romannumeral`^^@%
          \expandafter\xint_gob_til_dot\POL@A}
-        {\edef\POL@result
+        {\protected\edef\POL@result
           {\the\POL@B.% here at least 2.
-           \noexpand\empty
+           \POL@empty
            \romannumeral\xintreplicate{\POL@B}{{0/1[0]}}%
            {\xintScalarPow
              {\expandafter\xint_secondoftwo\romannumeral`^^@%
@@ -2531,8 +2749,8 @@
        {#2}%
     \expandafter\POL@mul\expandafter
         {\expandafter\def\expandafter\POL@result\expandafter
-         {\POL@result}\global\POL@poltrue}%
-        {\def\POL@result{#1}\global\POL@poltrue}%
+         {\POL@result}\POL@polglobaltrue}%
+        {\protected\def\POL@result{#1}\POL@polglobaltrue}%
 }%
 
 %% DIVISION
@@ -2540,7 +2758,7 @@
 \def\POL@div  {\POL@get\POL@A\POL@div@b}%
 \def\POL@div@b{\POL@get\POL@B\POL@div@c}%
 \def\POL@div@c{%
-    \global\POL@poltrue
+    \POL@polglobaltrue
     \expandafter\POL@split\POL@A;\POL@degA\POL@polA
     \expandafter\POL@split\POL@B;\POL@degB\POL@polB
     \ifnum\POL@degA<\POL@degB\space
@@ -2599,9 +2817,9 @@
 
 %% MINUS SIGN AS UNARY OPERATOR
 \def\POL@opp #1{%
-    \global\POL@polfalse
+    \POL@polglobalfalse
     \begingroup
-        \def\POL@result{#1}%
+        \protected\def\POL@result{#1}%
         #1%
         \expandafter
     \endgroup
@@ -2609,13 +2827,13 @@
     \unless\ifPOL@pol
         \edef\POL@A{\xintScalarOpp{#1}}%
         \xintiiifZero{\POL@A}%
-            {\def\POL@result{-1.\empty{0/1[0]}}}%
-            {\edef\POL@result{0.\noexpand\empty{\POL@A}}}%
+            {\protected\def\POL@result{-1.\POL@empty{0/1[0]}}}%
+            {\protected\edef\POL@result{0.\POL@empty{\POL@A}}}%
     \else
-      \edef\POL@B{0.\noexpand\empty{-1/1[0]}}%
+      \edef\POL@B{0.\POL@empty{-1/1[0]}}%
       \POL@@mul
     \fi
-    \global\POL@poltrue
+    \POL@polglobaltrue
 }%
 
 
@@ -2626,9 +2844,9 @@
      \At\PolEvalAtExpr\krof {#1}{#3}%
 }%
 \newcommand\PolEvalAt[2]
-    {\xintpraw{\csname XINT_expr_userfunc_#1\endcsname{#2}}}%
+    {\xintpraw{\csname XINT_expr_polfunc_#1\endcsname{#2}}}%
 \newcommand\POL@eval[2]
-    {\csname XINT_expr_userfunc_#1\endcsname{#2}}%
+    {\csname XINT_expr_polfunc_#1\endcsname{#2}}%
 \newcommand\PolEvalAtExpr[2]{\xinttheexpr #1(#2)\relax}%
 %
 \newcommand\PolEvalReduced[3]{\romannumeral`^^@\POL@eval@fork
@@ -2637,11 +2855,11 @@
 }%
 \newcommand\PolEvalReducedAt[2]{%
     \xintpraw % in order not to print denominator if the latter equals 1
-    {\xintIrr{\csname XINT_expr_userfunc_#1\endcsname{#2}}[0]}%
+    {\xintIrr{\csname XINT_expr_polfunc_#1\endcsname{#2}}[0]}%
 }%
 \newcommand\PolEvalReducedAtExpr[2]{%
     \xintpraw
-    {\xintIrr{\romannumeral`^^@\xintthebareeval#1(#2)\relax}[0]}%
+    {\expandafter\xintIrr\romannumeral`^^@\xintthebareeval#1(#2)\relax[0]}%
 }%
 %
 \newcommand\PolFloatEval[3]{\romannumeral`^^@\POL@eval@fork
@@ -2649,7 +2867,7 @@
      \At\PolFloatEvalAtExpr\krof {#1}{#3}%
 }%
 \newcommand\PolFloatEvalAt[2]
-    {\xintpfloat{\csname XINT_flexpr_userfunc_#1\endcsname{#2}}}%
+    {\xintpfloat{\csname XINT_flexpr_polfunc_#1\endcsname{#2}}}%
 \newcommand\PolFloatEvalAtExpr[2]{\xintthefloatexpr #1(#2)\relax}%
 
 
@@ -2898,12 +3116,12 @@
        \expandafter#1%
     \fi {#3}#2}%
 %
-\def\POL@toexprA #1#2\empty#3{%
+\def\POL@toexprA #1#2\POL@empty#3{%
     \ifpoltoexprall\expandafter\POL@toexprall@b
               \else\expandafter\POL@toexpr@b
     \fi {#3}#2{0}1.%
 }%
-\def\POL@toexprD #1#2#3\relax{% #3 has \empty to prevent brace removal
+\def\POL@toexprD #1#2#3\relax{% #3 has \empty (\POL@empty) to prevent brace removal
     \expandafter\POL@toexprD@a\expandafter#2%
     \the\numexpr #1\expandafter.\romannumeral0\xintrevwithbraces{#3}\relax
 }%