polexpr (18jan18)

git-svn-id: svn://tug.org/texlive/trunk@46377 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 165 insertions, 37 deletions

diff --git a/Master/texmf-dist/tex/latex/polexpr/polexpr.sty b/Master/texmf-dist/tex/latex/polexpr/polexpr.sty
index 9f2bd0c0ea5..752efa3fa77 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}%
-  [2018/01/14 v0.2 Polynomial expressions with rational coefficients (JFB)]%
+  [2018/01/18 v0.3.1 Polynomial expressions with rational coefficients (JFB)]%
 \RequirePackage{xintexpr}[2016/03/19]% xint 1.2g (or 1.2c 2015/11/16 at least)
 \edef\POL@restorecatcodes
     {\catcode`\noexpand\_ \the\catcode`\_ \catcode0 \the\catcode0\relax}%
@@ -76,12 +76,16 @@
 %%
 \def\POL@newpol#1{%
    \expandafter\POL@ifZero\csname POLuserpol@#1\endcsname
-      {\@namedef{XINT_expr_userfunc_#1}##1,{0/1[0]}}%
+      {\@namedef{XINT_expr_userfunc_#1}##1,{0/1[0]}%
+       \@namedef{XINT_flexpr_userfunc_#1}##1,{0[0]}}%
       {\POL@newpolhorner{#1}}%
    \unless\ifcsname XINT_expr_userfuncNE:#1\endcsname\POL@addtoextras{#1}\fi
    \expandafter\XINT_expr_defuserfunc
      \csname XINT_expr_func_#1\expandafter\endcsname
      \csname XINT_expr_userfunc_#1\endcsname
+   \expandafter\XINT_expr_defuserfunc
+     \csname XINT_flexpr_func_#1\expandafter\endcsname
+     \csname XINT_flexpr_userfunc_#1\endcsname
    \ifxintverbose\POL@info{#1}\fi
 }%
 \def\POL@info #1{%
@@ -90,7 +94,11 @@
          associated to \string\XINT_expr_userfunc_#1\space
          whose meaning uses Horner scheme:
          \expandafter\meaning
-         \csname XINT_expr_userfunc_#1\endcsname}%
+         \csname XINT_expr_userfunc_#1\endcsname^^J%
+         \@spaces And \string\XINT_flexpr_userfunc_#1\space for
+         the \string\xintfloatexpr\space parser has meaning
+         \expandafter\meaning
+         \csname XINT_flexpr_userfunc_#1\endcsname}%
 }%
 %
 \def\POL@newpolhorner#1{%
@@ -102,17 +110,37 @@
    \edef\POL@var@coeffs{\xintRevWithBraces{\POL@var@coeffs}}%
    \begingroup
       \expandafter\POL@newpol@horner\POL@var@coeffs\relax
+   \expandafter
+   \endgroup
+   \expandafter\def\csname XINT_expr_userfunc_#1\expandafter\endcsname
+      \expandafter##\expandafter1\expandafter,\expandafter{\POL@tmp{##1}}%
+   \begingroup
+      \expandafter\POL@newpol@floathorner\POL@var@coeffs\relax
+   \expandafter
    \endgroup
-   \expandafter\let\csname XINT_expr_userfunc_#1\endcsname\POL@tmp
+   \expandafter\def\csname XINT_flexpr_userfunc_#1\expandafter\endcsname
+      \expandafter##\expandafter1\expandafter,\expandafter{\POL@tmp{##1}}%
 }%
 \def\POL@newpol@horner#1{\let\xintAdd\relax\let\xintMul\relax
-                  \gdef\POL@tmp##1,{#1}\POL@newpol@horner@loop.}%
+                  \def\POL@tmp##1{#1}\POL@newpol@horner@loop.}%
 \def\POL@newpol@horner@loop.#1{%
   \if\relax#1\expandafter\xint_gob_til_dot\fi
-  \xdef\POL@tmp##1,{\xintiiifZero{#1}{\@firstofone}{\xintAdd{#1}}%
-                    {\xintMul{##1}{\POL@tmp##1,}}}%
+  \edef\POL@tmp##1{\xintiiifZero{#1}
+                    {\@firstofone}{\xintAdd{#1}}%
+                    {\xintMul{##1}{\POL@tmp{##1}}}}%
   \POL@newpol@horner@loop.%
 }%
+\def\POL@newpol@floathorner#1{\let\XINTinFloatAdd\relax\let\XINTinFloatMul\relax
+                  \def\xintAdd{\XINTinFloatAdd}\def\xintMul{\XINTinFloatMul}%
+                  \edef\POL@tmp##1{\XINTinFloatdigits{#1}}%
+                  \POL@newpol@floathorner@loop.}%
+\def\POL@newpol@floathorner@loop.#1{%
+  \if\relax#1\expandafter\xint_gob_til_dot\fi
+  \edef\POL@tmp##1{\xintiiifZero{#1}
+                    {\@firstofone}{\xintAdd{\XINTinFloatdigits{#1}}}%
+                    {\xintMul{##1}{\POL@tmp{##1}}}}%
+  \POL@newpol@floathorner@loop.%
+}%
 %% Customizes xintexpr.sty's \XINT_NewExpr (\POL@addtoextras{name})
 \begingroup
 \catcode`~ 12
@@ -150,15 +178,24 @@
 \def\POL@redefinemacros{\POL@original_redefinemacros\POL@redefineextras}%
 \let\POL@redefineextras\@empty
 %
-\newcommand\PolLet[2]{%
+\newcommand\PolLet[2]{\if=\noexpand#2\expandafter\xint_firstoftwo
+                      \else\expandafter\xint_secondoftwo\fi
+                      \POL@@let\POL@let {#1}{#2}}%
+\def\POL@@let#1#2#3{\POL@let{#1}{#3}}%
+\def\POL@let#1#2{%
     \expandafter\let\csname POLuserpol@#1\expandafter\endcsname
                     \csname POLuserpol@#2\endcsname
     \unless\ifcsname XINT_expr_userfuncNE:#1\endcsname\POL@addtoextras{#1}\fi
     \expandafter\let\csname XINT_expr_userfunc_#1\expandafter\endcsname
                     \csname XINT_expr_userfunc_#2\endcsname
+    \expandafter\let\csname XINT_flexpr_userfunc_#1\expandafter\endcsname
+                    \csname XINT_flexpr_userfunc_#2\endcsname
     \expandafter\XINT_expr_defuserfunc
        \csname XINT_expr_func_#1\expandafter\endcsname
        \csname XINT_expr_userfunc_#1\endcsname
+    \expandafter\XINT_expr_defuserfunc
+       \csname XINT_flexpr_func_#1\expandafter\endcsname
+       \csname XINT_flexpr_userfunc_#1\endcsname
     \ifxintverbose\POL@info{#1}\fi
 }%
 
@@ -230,12 +267,12 @@
 
 
 \newif\ifpoltypesetall
-\newcommand\PolTypesetPlus[1]{\xintiiifSgn{#1}{}{+}{+}}%
+\newcommand\PolTypesetCmdPrefix[1]{\xintiiifSgn{#1}{}{+}{+}}%
 \newcommand\PolTypesetCmd[1]{\xintifOne{\xintiiAbs{#1}}%
                                {\ifnum\PolIndex=\z@\xintiiSgn{#1}\else
                                 \xintiiifSgn{#1}{-}{}{}\fi}%
                                {\xintSignedFrac{#1}}}%
-\newcommand\PolTypesetMonomial{%
+\newcommand\PolTypesetMonomialCmd{%
   \ifcase\PolIndex\space
   %
   \or\PolVar
@@ -262,12 +299,12 @@
         \fi
         \def\PolVar{#1}%
         \ifnum\POL@var@deg<\z@
-            \PolTypesetCmd{0/1[0]}%
+            \PolTypesetCmd{0/1[0]}\PolTypesetMonomialCmd
         \else
          \ifnum\POL@var@deg=\z@
-           \expandafter\PolTypesetCmd\POL@var@coeffs
+           \expandafter\PolTypesetCmd\POL@var@coeffs\PolTypesetMonomialCmd
          \else
-           \def\POL@ts@plus##1{\let\POL@ts@plus\PolTypesetPlus}%
+           \def\POL@ts@prefix##1{\let\POL@ts@prefix\PolTypesetCmdPrefix}%
            \expandafter\POL@ts@loop
               \romannumeral-`0\POL@ts@reverse{\POL@var@coeffs}\relax
          \fi
@@ -282,12 +319,12 @@
   \if\relax#1\expandafter\xint_gob_til_dot\fi
   \xintiiifZero{#1}%
       {}%
-      {\POL@ts@plus{#1}\PolTypesetCmd{#1}\PolTypesetMonomial}%
+      {\POL@ts@prefix{#1}\PolTypesetCmd{#1}\PolTypesetMonomialCmd}%
   \edef\PolIndex{\the\numexpr\PolIndex+\POL@@ne@or@m@ne}\POL@ts@check.%
 }%
 \def\POL@ts@nocheck.#1{%
   \if\relax#1\expandafter\xint_gob_til_dot\fi
-  \POL@ts@plus{#1}\PolTypesetCmd{#1}\PolTypesetMonomial
+  \POL@ts@prefix{#1}\PolTypesetCmd{#1}\PolTypesetMonomialCmd
   \edef\PolIndex{\the\numexpr\PolIndex+\POL@@ne@or@m@ne}\POL@ts@nocheck.%
 }%
 
@@ -495,7 +532,7 @@
    \else\xint_afterfi{\POL@Iterate\POL@Diff@one}%
    \fi
 }%
-\def\POL@Diff@no #1#2{\PolLet{#2}{#1}}%
+\def\POL@Diff@no #1#2{\POL@let{#2}{#1}}%
 \def\POL@Diff@one #1#2{%
    \expandafter\expandafter\expandafter\POL@split
       \csname POLuserpol@#1\endcsname;\POL@var@deg\POL@var@coeffs
@@ -920,11 +957,17 @@
 
 %% EXPANDABLE MACROS
 \newcommand\PolEval{}%
-\def\PolEval#1#2\At#3{%
+\def\PolEval#1#2\At#3{\romannumeral`^^@\xinttheexpr #1(#3)\relax}%
+%
+\newcommand\PolEvalReduced{}%
+\def\PolEvalReduced#1#2\At#3{%
     \romannumeral0\xintpraw % only serves to not print denominator if = 1
-    {\xintIrr{\csname XINT_expr_userfunc_#1\endcsname {#3},}[0]}%
+    {\xintIrr{\romannumeral`^^@\xintthebareeval#1(#3)\relax}[0]}%
 }%
 %
+\newcommand\PolFloatEval{}%
+\def\PolFloatEval#1#2\At#3{\romannumeral`^^@\xintthefloatexpr #1(#3)\relax}%
+%
 \newcommand\PolNthCoeff[2]{\romannumeral`^^@%
     \expandafter\POL@nthcoeff
     \romannumeral0\xintnthelt{\ifnum\numexpr#2<\z@#2\else(#2)+1\fi}%
@@ -949,34 +992,119 @@
 
 \newif\ifpoltoexprall
 \newcommand\PolToExprCmd[1]{\xintPRaw{\xintRawWithZeros{#1}}}%
-\newcommand\PolToExprCmdWithSep[1]{\xintiiifSgn{#1}{}{+}{+}\PolToExprCmd{#1}}%
-\newcommand\PolToExpr[1]{\expandafter\expandafter\expandafter
-                      \POL@toexpr\csname POLuserpol@#1\endcsname\relax}%
-%
-\def\POL@toexpr#1.\empty{%
-    \ifnum#1<\z@
-       \PolToExprCmd{0/1[0]}\expandafter\@gobbletwo
+\newcommand\PolToFloatExprCmd[1]{\xintFloat{#1}}%
+\let\PolToExprTermPrefix\PolTypesetCmdPrefix
+\newcommand\PolToExprOneTerm[2]{%
+    \ifnum#2=\z@
+      \PolToExprCmd{#1}%
+    \else
+      \xintifOne{\xintiiAbs{#1}}
+        {\xintiiifSgn{#1}{-}{}{}}% + from \PolToExprTermPrefix
+        {\PolToExprCmd{#1}\PolToExprTimes}%
+    \fi
+    \ifcase\xintiiAbs{#2} %<-- space here mandatory
+         \or\PolToExprVar
+       \else\PolToExprVar^\xintiiAbs{#2}%
+    \fi
+}%
+\newcommand\PolToExprOneTermStyleB[2]{%
+    \ifnum#2=\z@
+      \xintNumerator{#1}%
     \else
-       \expandafter\POL@toexpr@a
-    \fi}%
+      \xintifOne{\xintiiAbs{\xintNumerator{#1}}}
+        {\xintiiifSgn{#1}{-}{}{}}% + from \PolToExprTermPrefix
+        {\xintNumerator{#1}\PolToExprTimes}%
+    \fi
+    \ifcase\xintiiAbs{#2} %<-- space here mandatory
+         \or\PolToExprVar
+       \else\PolToExprVar^\xintiiAbs{#2}%
+    \fi
+    \xintiiifOne{\xintDenominator{#1}}{}{/\xintDenominator{#1}}%
+}%
+\newcommand\PolToFloatExprOneTerm[2]{%
+    \ifnum#2=\z@
+      \PolToFloatExprCmd{#1}%
+    \else
+      \PolToFloatExprCmd{#1}\PolToExprTimes
+    \fi
+    \ifcase\xintiiAbs{#2} %<-- space here mandatory
+         \or\PolToExprVar
+       \else\PolToExprVar^\xintiiAbs{#2}%
+    \fi
+}%
+\newcommand\PolToExprTimes{*}%
+\newcommand\PolToExprVar{x}%
+\newcommand\PolToExpr[1]{%
+    \if*\noexpand#1\expandafter\xint_firstoftwo\else
+    \expandafter\xint_secondoftwo\fi
+    \PolToExprAscending\PolToExprDescending{#1}}%
+\newcommand\PolToFloatExpr[1]{%
+    \if*\noexpand#1\expandafter\xint_firstoftwo\else
+    \expandafter\xint_secondoftwo\fi
+    \PolToFloatExprAscending\PolToFloatExprDescending{#1}}%
+\newcommand\PolToExprAscending[2]{%
+   \expandafter\POL@toexpr\csname POLuserpol@#2\endcsname
+   \PolToExprOneTerm\POL@toexprA}%
+\newcommand\PolToFloatExprAscending[2]{%
+   \expandafter\POL@toexpr\csname POLuserpol@#2\endcsname
+   \PolToFloatExprOneTerm\POL@toexprA}%
+\newcommand\PolToExprDescending[1]{%
+   \expandafter\POL@toexpr\csname POLuserpol@#1\endcsname
+   \PolToExprOneTerm\POL@toexprD}%
+\newcommand\PolToFloatExprDescending[1]{%
+   \expandafter\POL@toexpr\csname POLuserpol@#1\endcsname
+   \PolToFloatExprOneTerm\POL@toexprD}%
 %
-\def\POL@toexpr@a #1{\ifpoltoexprall\expandafter\POL@toexprall@b
-                         \else\expandafter\POL@toexpr@b
-                  \fi{#1}{}\PolToExprCmd0.}%
+\def\POL@toexpr#1#2#3{\expandafter\POL@toexpr@
+                      \expandafter#3\expandafter#2#1\relax}%
+\def\POL@toexpr@#1#2#3.{%
+    \ifnum#3<\z@
+       #2{0/1[0]}{0}\expandafter\xint_gobble_v
+    \else
+       \expandafter#1%
+    \fi {#3}#2}%
 %
+\def\POL@toexprA #1#2\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
+    \expandafter\POL@toexprD@a\expandafter#2%
+    \the\numexpr #1\expandafter.\romannumeral0\xintrevwithbraces{#3}\relax
+}%
+\def\POL@toexprD@a #1#2.#3{%
+    \ifpoltoexprall\expandafter\POL@toexprall@b
+              \else\expandafter\POL@toexpr@b
+    \fi{#3}#1{-#2}\the\numexpr\@ne+-#2.%
+}%
 \def\POL@toexpr@b #1#2#3{%
     \xintiiifZero{#1}%
-      {\expandafter\POL@toexpr@loop\expandafter#3}%
-      {#3{#1}#2\expandafter\POL@toexpr@loop\expandafter\PolToExprCmdWithSep}%
-    \expandafter\POL@toexpr@b\the\numexpr\@ne+%
+      {\expandafter\POL@toexpr@loop\expandafter\POL@toexpr@b}%
+      {#2{#1}{#3}%
+      \expandafter\POL@toexpr@loop\expandafter\POL@toexpr@c}%
+   \expandafter#2%
+}%
+\def\POL@toexpr@c #1#2#3{%
+    \xintiiifZero{#1}%
+      {}%
+      {\PolToExprTermPrefix{#1}#2{#1}{#3}}%
+    \expandafter\POL@toexpr@loop\expandafter\POL@toexpr@c
+    \expandafter#2%
 }%
 \def\POL@toexprall@b #1#2#3{%
-    #3{#1}#2%
-    \expandafter\POL@toexpr@loop\expandafter\PolToExprCmdWithSep
-    \expandafter\POL@toexprall@b\the\numexpr\@ne+%
+    #2{#1}{#3}%
+    \expandafter\POL@toexpr@loop\expandafter\POL@toexprall@c
+    \expandafter#2%
+}%
+\def\POL@toexprall@c #1#2#3{%
+    \PolToExprTermPrefix{#1}#2{#1}{#3}%
+    \expandafter\POL@toexpr@loop\expandafter\POL@toexprall@c
+    \expandafter#2%
 }%
 \def\POL@toexpr@loop#1#2#3.#4{%
-  \if\relax#4\expandafter\xint_gob_til_dot\fi #2{#4}{*x^#3}#1#3.%
+  \if\relax#4\expandafter\xint_gob_til_dot\fi
+  #1{#4}#2{#3}\the\numexpr\@ne+#3.%
 }%