\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch1}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull1}{ZeroDimensionalSolvePackageXmpPageEmpty1}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull1}{\hidepaste}
\tab{5}\spadcommand{R := Integer\bound{R }}
\indentrel{3}\begin{verbatim}
   (1)  Integer
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty1}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty1}{ZeroDimensionalSolvePackageXmpPagePatch1}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty1}{\showpaste}
\tab{5}\spadcommand{R := Integer\bound{R }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch2}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull2}{ZeroDimensionalSolvePackageXmpPageEmpty2}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull2}{\hidepaste}
\tab{5}\spadcommand{ls : List Symbol := [x,y,z,t]\bound{ls }}
\indentrel{3}\begin{verbatim}
   (2)  [x, y, z, t]
                                     Type: List(Symbol)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty2}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty2}{ZeroDimensionalSolvePackageXmpPagePatch2}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty2}{\showpaste}
\tab{5}\spadcommand{ls : List Symbol := [x,y,z,t]\bound{ls }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch3}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull3}{ZeroDimensionalSolvePackageXmpPageEmpty3}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull3}{\hidepaste}
\tab{5}\spadcommand{ls2 : List Symbol := [x,y,z,t,new()$Symbol]\bound{ls2 }}
\indentrel{3}\begin{verbatim}
   (3)  [x, y, z, t, %A]
                                     Type: List(Symbol)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty3}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty3}{ZeroDimensionalSolvePackageXmpPagePatch3}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty3}{\showpaste}
\tab{5}\spadcommand{ls2 : List Symbol := [x,y,z,t,new()$Symbol]\bound{ls2 }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch4}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull4}{ZeroDimensionalSolvePackageXmpPageEmpty4}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull4}{\hidepaste}
\tab{5}\spadcommand{pack := ZDSOLVE(R,ls,ls2)\free{ls }\free{ls2 }\free{R }\bound{pack }}
\indentrel{3}\begin{verbatim}
   (4)
   ZeroDimensionalSolvePackage
      Integer
  ,
      [x, y, z, t]
  ,
      [x, y, z, t, %A]
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty4}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty4}{ZeroDimensionalSolvePackageXmpPagePatch4}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty4}{\showpaste}
\tab{5}\spadcommand{pack := ZDSOLVE(R,ls,ls2)\free{ls }\free{ls2 }\free{R }\bound{pack }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch5}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull5}{ZeroDimensionalSolvePackageXmpPageEmpty5}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull5}{\hidepaste}
\tab{5}\spadcommand{p1 := x^2*y*z + x*y^2*z + x*y*z^2 + x*y*z + x*y + x*z + y*z\bound{p1 }}
\indentrel{3}\begin{verbatim}
             2       2     2
   (5)  x y z  + (x y  + (x  + x + 1)y + x)z + x y
                              Type: Polynomial(Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty5}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty5}{ZeroDimensionalSolvePackageXmpPagePatch5}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty5}{\showpaste}
\tab{5}\spadcommand{p1 := x^2*y*z + x*y^2*z + x*y*z^2 + x*y*z + x*y + x*z + y*z\bound{p1 }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch6}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull6}{ZeroDimensionalSolvePackageXmpPageEmpty6}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull6}{\hidepaste}
\tab{5}\spadcommand{p2 := x^2*y^2*z + x*y^2*z^2 + x^2*y*z + x*y*z + y*z + x + z\bound{p2 }}
\indentrel{3}\begin{verbatim}
           2 2     2 2     2
   (6)  x y z  + (x y  + (x  + x + 1)y + 1)z + x
                              Type: Polynomial(Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty6}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty6}{ZeroDimensionalSolvePackageXmpPagePatch6}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty6}{\showpaste}
\tab{5}\spadcommand{p2 := x^2*y^2*z + x*y^2*z^2 + x^2*y*z + x*y*z + y*z + x + z\bound{p2 }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch7}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull7}{ZeroDimensionalSolvePackageXmpPageEmpty7}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull7}{\hidepaste}
\tab{5}\spadcommand{p3 := x^2*y^2*z^2 + x^2*y^2*z + x*y^2*z + x*y*z + x*z + z + 1\bound{p3 }}
\indentrel{3}\begin{verbatim}
         2 2 2      2      2
   (7)  x y z  + ((x  + x)y  + x y + x + 1)z + 1
                              Type: Polynomial(Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty7}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty7}{ZeroDimensionalSolvePackageXmpPagePatch7}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty7}{\showpaste}
\tab{5}\spadcommand{p3 := x^2*y^2*z^2 + x^2*y^2*z + x*y^2*z + x*y*z + x*z + z + 1\bound{p3 }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch8}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull8}{ZeroDimensionalSolvePackageXmpPageEmpty8}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull8}{\hidepaste}
\tab{5}\spadcommand{lp := [p1, p2, p3]\free{p1 }\free{p2 }\free{p3 }\bound{lp }}
\indentrel{3}\begin{verbatim}
   (8)
         2       2     2
   [x y z  + (x y  + (x  + x + 1)y + x)z + x y,
       2 2     2 2     2
    x y z  + (x y  + (x  + x + 1)y + 1)z + x,
     2 2 2      2      2
    x y z  + ((x  + x)y  + x y + x + 1)z + 1]
                        Type: List(Polynomial(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty8}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty8}{ZeroDimensionalSolvePackageXmpPagePatch8}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty8}{\showpaste}
\tab{5}\spadcommand{lp := [p1, p2, p3]\free{p1 }\free{p2 }\free{p3 }\bound{lp }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch9}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull9}{ZeroDimensionalSolvePackageXmpPageEmpty9}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull9}{\hidepaste}
\tab{5}\spadcommand{triangSolve(lp)$pack\free{lp }\free{pack }}
\indentrel{3}\begin{verbatim}
   (9)
   [
     {
          20      19       18       17        16       15
         z   - 6 z   - 41 z   + 71 z   + 106 z   + 92 z
       + 
              14        13        12        11        10
         197 z   + 145 z   + 257 z   + 278 z   + 201 z
       + 
              9        8        7        6       5
         278 z  + 257 z  + 145 z  + 197 z  + 92 z
       + 
              4       3       2
         106 z  + 71 z  - 41 z  - 6 z + 1
       ,

                       19             18              17
             14745844 z   + 50357474 z   - 130948857 z
           + 
                          16              15
             - 185261586 z   - 180077775 z
           + 
                          14              13
             - 338007307 z   - 275379623 z
           + 
                          12              11
             - 453190404 z   - 474597456 z
           + 
                          10              9              8
             - 366147695 z   - 481433567 z  - 430613166 z
           + 
                          7              6              5
             - 261878358 z  - 326073537 z  - 163008796 z
           + 
                          4              3             2
             - 177213227 z  - 104356755 z  + 65241699 z
           + 
             9237732 z - 1567348
        *
           y
       + 
                  19            18             17
         1917314 z   + 6508991 z   - 16973165 z
       + 
                     16             15             14
         - 24000259 z   - 23349192 z   - 43786426 z
       + 
                     13             12             11
         - 35696474 z   - 58724172 z   - 61480792 z
       + 
                     10             9             8
         - 47452440 z   - 62378085 z  - 55776527 z
       + 
                     7             6             5
         - 33940618 z  - 42233406 z  - 21122875 z
       + 
                     4             3            2
         - 22958177 z  - 13504569 z  + 8448317 z
       + 
         1195888 z - 202934
       ,

               3        2       3    2                2
             (z  - 2 z)y  + (- z  - z  - 2 z - 1)y - z
           + 
             - z + 1
        *
           x
       + 
          2
         z  - 1
       }
     ]
            Type: List(RegularChain(Integer,[x,y,z,t]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty9}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty9}{ZeroDimensionalSolvePackageXmpPagePatch9}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty9}{\showpaste}
\tab{5}\spadcommand{triangSolve(lp)$pack\free{lp }\free{pack }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch10}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull10}{ZeroDimensionalSolvePackageXmpPageEmpty10}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull10}{\hidepaste}
\tab{5}\spadcommand{univariateSolve(lp)$pack\free{lp }\free{pack }}
\indentrel{3}\begin{verbatim}
   (10)
   [
     [
         complexRoots
       = 
            12       11       10      9      8       7
           ?   - 12 ?   + 24 ?   + 4 ?  - 9 ?  + 27 ?
         + 
               6       5      4      3       2
         - 21 ?  + 27 ?  - 9 ?  + 4 ?  + 24 ?  - 12 ? + 1
       ,

         coordinates
       = 
         [
                         11         10          9
             63 x + 62 %A   - 721 %A   + 1220 %A
           + 
                   8         7          6         5
             705 %A  - 285 %A  + 1512 %A  - 735 %A
           + 
                    4        3         2
             1401 %A  - 21 %A  + 215 %A  + 1577 %A - 142
           ,

                         11         10          9
             63 y - 75 %A   + 890 %A   - 1682 %A
           + 
                     8         7          6          5
             - 516 %A  + 588 %A  - 1953 %A  + 1323 %A
           + 
                    4         3         2
           - 1815 %A  + 426 %A  - 243 %A  - 1801 %A + 679
           ,
          z - %A]
       ]
     ,

                      6    5    4    3    2
     [complexRoots = ?  + ?  + ?  + ?  + ?  + ? + 1,
                           5        3
      coordinates = [x - %A , y - %A , z - %A]]
     ,

                      2
     [complexRoots = ?  + 5 ? + 1,
      coordinates = [x - 1, y - 1, z - %A]]
     ]
Type: List(Record(complexRoots: SparseUnivariatePolynomial(Integer),coordinates: List(Polynomial(Integer))))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty10}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty10}{ZeroDimensionalSolvePackageXmpPagePatch10}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty10}{\showpaste}
\tab{5}\spadcommand{univariateSolve(lp)$pack\free{lp }\free{pack }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch11}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull11}{ZeroDimensionalSolvePackageXmpPageEmpty11}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull11}{\hidepaste}
\tab{5}\spadcommand{lr := realSolve(lp)$pack;\free{lp }\free{pack }\bound{lr }}
\indentrel{3}\begin{verbatim}
       Type: List(List(RealClosure(Fraction(Integer))))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty11}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty11}{ZeroDimensionalSolvePackageXmpPagePatch11}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty11}{\showpaste}
\tab{5}\spadcommand{lr := realSolve(lp)$pack;\free{lp }\free{pack }\bound{lr }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch12}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull12}{ZeroDimensionalSolvePackageXmpPageEmpty12}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull12}{\hidepaste}
\tab{5}\spadcommand{\# lr\free{lr }}
\indentrel{3}\begin{verbatim}
   (12)  8
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty12}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty12}{ZeroDimensionalSolvePackageXmpPagePatch12}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty12}{\showpaste}
\tab{5}\spadcommand{\# lr\free{lr }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch13}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull13}{ZeroDimensionalSolvePackageXmpPageEmpty13}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull13}{\hidepaste}
\tab{5}\spadcommand{[[approximate(r,1/1000000) for r in point] for point in lr];\free{lr }}
\indentrel{3}\begin{verbatim}
                    Type: List(List(Fraction(Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty13}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty13}{ZeroDimensionalSolvePackageXmpPagePatch13}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty13}{\showpaste}
\tab{5}\spadcommand{[[approximate(r,1/1000000) for r in point] for point in lr];\free{lr }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch14}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull14}{ZeroDimensionalSolvePackageXmpPageEmpty14}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull14}{\hidepaste}
\tab{5}\spadcommand{lpr := positiveSolve(lp)$pack\free{lp }\free{pack }\bound{lpr }}
\indentrel{3}\begin{verbatim}
   (14)  []
       Type: List(List(RealClosure(Fraction(Integer))))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty14}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty14}{ZeroDimensionalSolvePackageXmpPagePatch14}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty14}{\showpaste}
\tab{5}\spadcommand{lpr := positiveSolve(lp)$pack\free{lp }\free{pack }\bound{lpr }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch15}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull15}{ZeroDimensionalSolvePackageXmpPageEmpty15}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull15}{\hidepaste}
\tab{5}\spadcommand{f0 := x^3 + y + z + t- 1\bound{f0 }}
\indentrel{3}\begin{verbatim}
                  3
   (15)  z + y + x  + t - 1
                              Type: Polynomial(Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty15}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty15}{ZeroDimensionalSolvePackageXmpPagePatch15}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty15}{\showpaste}
\tab{5}\spadcommand{f0 := x^3 + y + z + t- 1\bound{f0 }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch16}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull16}{ZeroDimensionalSolvePackageXmpPageEmpty16}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull16}{\hidepaste}
\tab{5}\spadcommand{f1 := x + y^3 + z + t -1\bound{f1 }}
\indentrel{3}\begin{verbatim}
              3
   (16)  z + y  + x + t - 1
                              Type: Polynomial(Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty16}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty16}{ZeroDimensionalSolvePackageXmpPagePatch16}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty16}{\showpaste}
\tab{5}\spadcommand{f1 := x + y^3 + z + t -1\bound{f1 }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch17}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull17}{ZeroDimensionalSolvePackageXmpPageEmpty17}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull17}{\hidepaste}
\tab{5}\spadcommand{f2 := x + y + z^3 + t-1\bound{f2 }}
\indentrel{3}\begin{verbatim}
          3
   (17)  z  + y + x + t - 1
                              Type: Polynomial(Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty17}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty17}{ZeroDimensionalSolvePackageXmpPagePatch17}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty17}{\showpaste}
\tab{5}\spadcommand{f2 := x + y + z^3 + t-1\bound{f2 }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch18}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull18}{ZeroDimensionalSolvePackageXmpPageEmpty18}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull18}{\hidepaste}
\tab{5}\spadcommand{f3 := x + y + z + t^3 -1\bound{f3 }}
\indentrel{3}\begin{verbatim}
                      3
   (18)  z + y + x + t  - 1
                              Type: Polynomial(Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty18}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty18}{ZeroDimensionalSolvePackageXmpPagePatch18}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty18}{\showpaste}
\tab{5}\spadcommand{f3 := x + y + z + t^3 -1\bound{f3 }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch19}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull19}{ZeroDimensionalSolvePackageXmpPageEmpty19}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull19}{\hidepaste}
\tab{5}\spadcommand{lf := [f0, f1, f2, f3]\free{f0 }\free{f1 }\free{f2 }\free{f3 }\bound{lf }}
\indentrel{3}\begin{verbatim}
   (19)
             3               3
   [z + y + x  + t - 1, z + y  + x + t - 1,
     3                               3
    z  + y + x + t - 1, z + y + x + t  - 1]
                        Type: List(Polynomial(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty19}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty19}{ZeroDimensionalSolvePackageXmpPagePatch19}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty19}{\showpaste}
\tab{5}\spadcommand{lf := [f0, f1, f2, f3]\free{f0 }\free{f1 }\free{f2 }\free{f3 }\bound{lf }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch20}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull20}{ZeroDimensionalSolvePackageXmpPageEmpty20}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull20}{\hidepaste}
\tab{5}\spadcommand{lts := triangSolve(lf)$pack\free{lf }\free{pack }\bound{lts }}
\indentrel{3}\begin{verbatim}
   (20)
   [
       2           3        3
     {t  + t + 1, z  - z - t  + t,

                   3      2
         (3 z + 3 t  - 3)y
       + 
             2       3            6      3
         (3 z  + (6 t  - 6)z + 3 t  - 6 t  + 3)y
       + 
             3      2       6      3          9      6
         (3 t  - 3)z  + (3 t  - 6 t  + 3)z + t  - 3 t
       + 
            3
         5 t  - 3 t
       ,
      x + y + z}
     ,

       16      13      10      7       4       2
     {t   - 6 t   + 9 t   + 4 t  + 15 t  - 54 t  + 27,

                      15             14              13
             4907232 t   + 40893984 t   - 115013088 t
           + 
                       12             11              10
             22805712 t   + 36330336 t   + 162959040 t
           + 
                          9              8              7
             - 159859440 t  - 156802608 t  + 117168768 t
           + 
                        6              5              4
             126282384 t  - 129351600 t  + 306646992 t
           + 
                        3               2
             475302816 t  - 1006837776 t  - 237269088 t
           + 
             480716208
        *
           z
       + 
             54        51         48       46          45
         48 t   - 912 t   + 8232 t   - 72 t   - 46848 t
       + 
               43           42         40           39
         1152 t   + 186324 t   - 3780 t   - 543144 t
       + 
                 38          37            36          35
         - 3168 t   - 21384 t   + 1175251 t   + 41184 t
       + 
                 34            33           32
         278003 t   - 1843242 t   - 301815 t
       + 
                    31            30            29
         - 1440726 t   + 1912012 t   + 1442826 t
       + 
                  28           27            26
         4696262 t   - 922481 t   - 4816188 t
       + 
                     25           24             23
         - 10583524 t   - 208751 t   + 11472138 t
       + 
                   22           21             20
         16762859 t   - 857663 t   - 19328175 t
       + 
                     19            18             17
         - 18270421 t   + 4914903 t   + 22483044 t
       + 
                   16            15             14
         12926517 t   - 8605511 t   - 17455518 t
       + 
                    13            12            11
         - 5014597 t   + 8108814 t   + 8465535 t
       + 
                 10            9            8           7
         190542 t   - 4305624 t  - 2226123 t  + 661905 t
       + 
                  6           5           4           3
         1169775 t  + 226260 t  - 209952 t  - 141183 t
       + 
         27216 t
       ,

                   3      2
         (3 z + 3 t  - 3)y
       + 
             2       3            6      3
         (3 z  + (6 t  - 6)z + 3 t  - 6 t  + 3)y
       + 
             3      2       6      3          9      6
         (3 t  - 3)z  + (3 t  - 6 t  + 3)z + t  - 3 t
       + 
            3
         5 t  - 3 t
       ,
                   3
      x + y + z + t  - 1}
     ,
                2                          2
    {t, z - 1, y  - 1, x + y}, {t - 1, z, y  - 1, x + y},
             2
    {t - 1, z  - 1, z y + 1, x},

       16      13      10      7       4       2
     {t   - 6 t   + 9 t   + 4 t  + 15 t  - 54 t  + 27,

                      29             28              27
             4907232 t   + 40893984 t   - 115013088 t
           + 
                        26              25              24
             - 1730448 t   - 168139584 t   + 738024480 t
           + 
                          23              22
             - 195372288 t   + 315849456 t
           + 
                           21              20
             - 2567279232 t   + 937147968 t
           + 
                         19               18
             1026357696 t   + 4780488240 t
           + 
                           17               16
             - 2893767696 t   - 5617160352 t
           + 
                           15               14
             - 3427651728 t   + 5001100848 t
           + 
                         13               12
             8720098416 t   + 2331732960 t
           + 
                          11                10
             - 499046544 t   - 16243306272 t
           + 
                           9               8
             - 9748123200 t  + 3927244320 t
           + 
                          7                6
             25257280896 t  + 10348032096 t
           + 
                            5                4
             - 17128672128 t  - 14755488768 t
           + 
                        3                2
             544086720 t  + 10848188736 t  + 1423614528 t
           + 
             - 2884297248
        *
           z
       + 
               68         65          62        60
         - 48 t   + 1152 t   - 13560 t   + 360 t
       + 
                 59         57           56          54
         103656 t   - 7560 t   - 572820 t   + 71316 t
       + 
                  53         52           51            50
         2414556 t   + 2736 t   - 402876 t   - 7985131 t
       + 
                  49            48             47
         - 49248 t   + 1431133 t   + 20977409 t
       + 
                 46            45             44
         521487 t   - 2697635 t   - 43763654 t
       + 
                    43            42             41
         - 3756573 t   - 2093410 t   + 71546495 t
       + 
                   40             39             38
         19699032 t   + 35025028 t   - 89623786 t
       + 
                     37              36             35
         - 77798760 t   - 138654191 t   + 87596128 t
       + 
                    34              33             32
         235642497 t   + 349607642 t   - 93299834 t
       + 
                      31              30              29
         - 551563167 t   - 630995176 t   + 186818962 t
       + 
                    28              27              26
         995427468 t   + 828416204 t   - 393919231 t
       + 
                       25               24              23
         - 1076617485 t   - 1609479791 t   + 595738126 t
       + 
                     22               21               20
         1198787136 t   + 4342832069 t   - 2075938757 t
       + 
                       19               18
         - 4390835799 t   - 4822843033 t
       + 
                     17               16               15
         6932747678 t   + 6172196808 t   + 1141517740 t
       + 
                       14               13
         - 4981677585 t   - 9819815280 t
       + 
                       12              11
         - 7404299976 t   - 157295760 t
       + 
                      10                9                8
         29124027630 t   + 14856038208 t  - 16184101410 t
       + 
                        7               6                5
         - 26935440354 t  - 3574164258 t  + 10271338974 t
       + 
                      4               3               2
         11191425264 t  + 6869861262 t  - 9780477840 t
       + 
         - 3586674168 t + 2884297248
       ,

                3       3      2       6       3
             3 z  + (6 t  - 6)z  + (6 t  - 12 t  + 3)z
           + 
                9      6    3
             2 t  - 6 t  + t  + 3 t
        *
           y
       + 
             3      3       6       3      2
         (3 t  - 3)z  + (6 t  - 12 t  + 6)z
       + 
             9       6       3          12      9      6
         (4 t  - 12 t  + 11 t  - 3)z + t   - 4 t  + 5 t
       + 
              3
         - 2 t
       ,
                   3
      x + y + z + t  - 1}
     ,
             2
    {t - 1, z  - 1, y, x + z},

       8    7    6      5      4      3       2
     {t  + t  + t  - 2 t  - 2 t  - 2 t  + 19 t  + 19 t - 8
       ,

                      7            6            5
             2395770 t  + 3934440 t  - 3902067 t
           + 
                         4            3             2
             - 10084164 t  - 1010448 t  + 32386932 t
           + 
             22413225 t - 10432368
        *
           z
       + 
                   7            6            5
         - 463519 t  + 3586833 t  + 9494955 t
       + 
                    4             3             2
         - 8539305 t  - 33283098 t  + 35479377 t
       + 
         46263256 t - 17419896
       ,

                4       3      3        6       3      2
             3 z  + (9 t  - 9)z  + (12 t  - 24 t  + 9)z
           + 
                     3                      6       4
             (- 152 t  + 219 t - 67)z - 41 t  + 57 t
           + 
                 3
             25 t  - 57 t + 16
        *
           y
       + 
             3      4       6       3      3
         (3 t  - 3)z  + (9 t  - 18 t  + 9)z
       + 
                 3               2
         (- 181 t  + 270 t - 89)z
       + 
                6        4       3                      7
         (- 92 t  + 135 t  + 49 t  - 135 t + 43)z + 27 t
       + 
               6       4        3
         - 27 t  - 54 t  + 396 t  - 486 t + 144
       ,
                   3
      x + y + z + t  - 1}
     ,
             3
    {t, z - t  + 1, y - 1, x - 1}, {t - 1, z, y, x},
    {t, z - 1, y, x}, {t, z, y - 1, x}, {t, z, y, x - 1}]
            Type: List(RegularChain(Integer,[x,y,z,t]))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty20}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty20}{ZeroDimensionalSolvePackageXmpPagePatch20}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty20}{\showpaste}
\tab{5}\spadcommand{lts := triangSolve(lf)$pack\free{lf }\free{pack }\bound{lts }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch21}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull21}{ZeroDimensionalSolvePackageXmpPageEmpty21}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull21}{\hidepaste}
\tab{5}\spadcommand{univariateSolve(lf)$pack\free{lf }\free{pack }}
\indentrel{3}\begin{verbatim}
   (21)
   [
     [complexRoots = ?,
      coordinates = [x - 1, y - 1, z + 1, t - %A]]
     ,

     [complexRoots = ?,
      coordinates = [x, y - 1, z, t - %A]]
     ,

     [complexRoots = ? - 1,
      coordinates = [x, y, z, t - %A]]
     ,

     [complexRoots = ?,
      coordinates = [x - 1, y, z, t - %A]]
     ,

     [complexRoots = ?,
      coordinates = [x, y, z - 1, t - %A]]
     ,

     [complexRoots = ? - 2,
      coordinates = [x - 1, y + 1, z, t - 1]]
     ,

     [complexRoots = ?,
      coordinates = [x + 1, y - 1, z, t - 1]]
     ,

     [complexRoots = ? - 1,
      coordinates = [x - 1, y + 1, z - 1, t]]
     ,

     [complexRoots = ? + 1,
      coordinates = [x + 1, y - 1, z - 1, t]]
     ,

                      6      3      2
     [complexRoots = ?  - 2 ?  + 3 ?  - 3,

         coordinates
       = 
                  3                   3
         [2 x + %A  + %A - 1, 2 y + %A  + %A - 1, z - %A,
          t - %A]
       ]
     ,

                      5      3      2
     [complexRoots = ?  + 3 ?  - 2 ?  + 3 ? - 3,

         coordinates
       = 
                                3
         [x - %A, y - %A, z + %A  + 2 %A - 1, t - %A]
       ]
     ,

                      4    3      2
     [complexRoots = ?  - ?  - 2 ?  + 3,

         coordinates
       = 
                3                 3
         [x + %A  - %A - 1, y + %A  - %A - 1,
                3
          z - %A  + 2 %A + 1, t - %A]
       ]
     ,

     [complexRoots = ? + 1,
      coordinates = [x - 1, y - 1, z, t - %A]]
     ,

                      6      3      2
     [complexRoots = ?  + 2 ?  + 3 ?  - 3,

         coordinates
       = 
                  3                           3
         [2 x - %A  - %A - 1, y + %A, 2 z - %A  - %A - 1,
          t + %A]
       ]
     ,

     [
         complexRoots
       = 
          6       4       3       2
         ?  + 12 ?  + 20 ?  - 45 ?  - 42 ? - 953
       ,

         coordinates
       = 
         [
                            5        4        3         2
             12609 x + 23 %A  + 49 %A  - 46 %A  + 362 %A
           + 
             - 5015 %A - 8239
           ,

                            5        4        3         2
             25218 y + 23 %A  + 49 %A  - 46 %A  + 362 %A
           + 
             7594 %A - 8239
           ,

                            5        4        3         2
             25218 z + 23 %A  + 49 %A  - 46 %A  + 362 %A
           + 
             7594 %A - 8239
           ,

                            5        4        3         2
             12609 t + 23 %A  + 49 %A  - 46 %A  + 362 %A
           + 
             - 5015 %A - 8239
           ]
       ]
     ,

                      5       3       2
     [complexRoots = ?  + 12 ?  - 16 ?  + 48 ? - 96,

         coordinates
       = 
                  3
         [8 x + %A  + 8 %A - 8, 2 y - %A, 2 z - %A,
          2 t - %A]
       ]
     ,

                      5    4      3      2
     [complexRoots = ?  + ?  - 5 ?  - 3 ?  + 9 ? + 3,

         coordinates
       = 
                  3                     3
         [2 x - %A  + 2 %A - 1, 2 y + %A  - 4 %A + 1,
                  3                     3
          2 z - %A  + 2 %A - 1, 2 t - %A  + 2 %A - 1]
       ]
     ,

                      4      3      2
     [complexRoots = ?  - 3 ?  + 4 ?  - 6 ? + 13,

         coordinates
       = 
                    3       2
         [9 x - 2 %A  + 4 %A  - %A + 2,
                  3       2
          9 y + %A  - 2 %A  + 5 %A - 1,
                  3       2
          9 z + %A  - 2 %A  + 5 %A - 1,
                  3       2
          9 t + %A  - 2 %A  - 4 %A - 1]
       ]
     ,

                      4       2
     [complexRoots = ?  - 11 ?  + 37,

         coordinates
       = 
                  2              2
         [3 x - %A  + 7, 6 y + %A  + 3 %A - 7,
                  2              2
          3 z - %A  + 7, 6 t + %A  - 3 %A - 7]
       ]
     ,

     [complexRoots = ? + 1,
      coordinates = [x - 1, y, z - 1, t + 1]]
     ,

     [complexRoots = ? + 2,
      coordinates = [x, y - 1, z - 1, t + 1]]
     ,

     [complexRoots = ? - 2,
      coordinates = [x, y - 1, z + 1, t - 1]]
     ,

     [complexRoots = ?,
      coordinates = [x, y + 1, z - 1, t - 1]]
     ,

     [complexRoots = ? - 2,
      coordinates = [x - 1, y, z + 1, t - 1]]
     ,

     [complexRoots = ?,
      coordinates = [x + 1, y, z - 1, t - 1]]
     ,

                      4      3       2
     [complexRoots = ?  + 5 ?  + 16 ?  + 30 ? + 57,

         coordinates
       = 
                       3        2
         [151 x + 15 %A  + 54 %A  + 104 %A + 93,
                       3        2
          151 y - 10 %A  - 36 %A  - 19 %A - 62,
                      3        2
          151 z - 5 %A  - 18 %A  - 85 %A - 31,
                      3        2
          151 t - 5 %A  - 18 %A  - 85 %A - 31]
       ]
     ,

                      4    3      2
     [complexRoots = ?  - ?  - 2 ?  + 3,

         coordinates
       = 
                3                   3
         [x - %A  + 2 %A + 1, y + %A  - %A - 1, z - %A,
                3
          t + %A  - %A - 1]
       ]
     ,

                      4      3      2
     [complexRoots = ?  + 2 ?  - 8 ?  + 48,

         coordinates
       = 
                  3
         [8 x - %A  + 4 %A - 8, 2 y + %A,
                  3                     3
          8 z + %A  - 8 %A + 8, 8 t - %A  + 4 %A - 8]
       ]
     ,

                      5    4      3      2
     [complexRoots = ?  + ?  - 2 ?  - 4 ?  + 5 ? + 8,

         coordinates
       = 
                  3              3              3
         [3 x + %A  - 1, 3 y + %A  - 1, 3 z + %A  - 1,
          t - %A]
       ]
     ,

                      3
     [complexRoots = ?  + 3 ? - 1,
      coordinates = [x - %A, y - %A, z - %A, t - %A]]
     ]
Type: List(Record(complexRoots: SparseUnivariatePolynomial(Integer),coordinates: List(Polynomial(Integer))))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty21}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty21}{ZeroDimensionalSolvePackageXmpPagePatch21}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty21}{\showpaste}
\tab{5}\spadcommand{univariateSolve(lf)$pack\free{lf }\free{pack }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch22}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull22}{ZeroDimensionalSolvePackageXmpPageEmpty22}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull22}{\hidepaste}
\tab{5}\spadcommand{ts := lts.1\free{lts }\bound{ts }}
\indentrel{3}\begin{verbatim}
   (22)
     2           3        3
   {t  + t + 1, z  - z - t  + t,

                 3      2
       (3 z + 3 t  - 3)y
     + 
           2       3            6      3
       (3 z  + (6 t  - 6)z + 3 t  - 6 t  + 3)y
     + 
           3      2       6      3          9      6
       (3 t  - 3)z  + (3 t  - 6 t  + 3)z + t  - 3 t
     + 
          3
       5 t  - 3 t
     ,
    x + y + z}
                  Type: RegularChain(Integer,[x,y,z,t])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty22}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty22}{ZeroDimensionalSolvePackageXmpPagePatch22}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty22}{\showpaste}
\tab{5}\spadcommand{ts := lts.1\free{lts }\bound{ts }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch23}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull23}{ZeroDimensionalSolvePackageXmpPageEmpty23}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull23}{\hidepaste}
\tab{5}\spadcommand{univariateSolve(ts)$pack\free{ts }\free{pack }}
\indentrel{3}\begin{verbatim}
   (23)
   [
                      4      3       2
     [complexRoots = ?  + 5 ?  + 16 ?  + 30 ? + 57,

         coordinates
       = 
                       3        2
         [151 x + 15 %A  + 54 %A  + 104 %A + 93,
                       3        2
          151 y - 10 %A  - 36 %A  - 19 %A - 62,
                      3        2
          151 z - 5 %A  - 18 %A  - 85 %A - 31,
                      3        2
          151 t - 5 %A  - 18 %A  - 85 %A - 31]
       ]
     ,

                      4    3      2
     [complexRoots = ?  - ?  - 2 ?  + 3,

         coordinates
       = 
                3                   3
         [x - %A  + 2 %A + 1, y + %A  - %A - 1, z - %A,
                3
          t + %A  - %A - 1]
       ]
     ,

                      4      3      2
     [complexRoots = ?  + 2 ?  - 8 ?  + 48,

         coordinates
       = 
                  3
         [8 x - %A  + 4 %A - 8, 2 y + %A,
                  3                     3
          8 z + %A  - 8 %A + 8, 8 t - %A  + 4 %A - 8]
       ]
     ]
Type: List(Record(complexRoots: SparseUnivariatePolynomial(Integer),coordinates: List(Polynomial(Integer))))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty23}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty23}{ZeroDimensionalSolvePackageXmpPagePatch23}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty23}{\showpaste}
\tab{5}\spadcommand{univariateSolve(ts)$pack\free{ts }\free{pack }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch24}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull24}{ZeroDimensionalSolvePackageXmpPageEmpty24}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull24}{\hidepaste}
\tab{5}\spadcommand{realSolve(ts)$pack\free{ts }\free{pack }}
\indentrel{3}\begin{verbatim}
   (24)  []
       Type: List(List(RealClosure(Fraction(Integer))))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty24}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty24}{ZeroDimensionalSolvePackageXmpPagePatch24}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty24}{\showpaste}
\tab{5}\spadcommand{realSolve(ts)$pack\free{ts }\free{pack }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch25}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull25}{ZeroDimensionalSolvePackageXmpPageEmpty25}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull25}{\hidepaste}
\tab{5}\spadcommand{lr2 := realSolve(lf)$pack;\free{lf }\free{pack }\bound{lr2 }}
\indentrel{3}\begin{verbatim}
       Type: List(List(RealClosure(Fraction(Integer))))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty25}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty25}{ZeroDimensionalSolvePackageXmpPagePatch25}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty25}{\showpaste}
\tab{5}\spadcommand{lr2 := realSolve(lf)$pack;\free{lf }\free{pack }\bound{lr2 }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch26}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull26}{ZeroDimensionalSolvePackageXmpPageEmpty26}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull26}{\hidepaste}
\tab{5}\spadcommand{\#lr2\free{lr2 }}
\indentrel{3}\begin{verbatim}
   (26)  27
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty26}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty26}{ZeroDimensionalSolvePackageXmpPagePatch26}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty26}{\showpaste}
\tab{5}\spadcommand{\#lr2\free{lr2 }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch27}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull27}{ZeroDimensionalSolvePackageXmpPageEmpty27}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull27}{\hidepaste}
\tab{5}\spadcommand{lpr2 := positiveSolve(lf)$pack\free{lf }\free{pack }\bound{lpr2 }}
\indentrel{3}\begin{verbatim}
   (27)
             1     3   1    1     3   1    1     3   1
   [[%B40, - - %B40  + -, - - %B40  + -, - - %B40  + -]]
             3         3    3         3    3         3
       Type: List(List(RealClosure(Fraction(Integer))))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty27}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty27}{ZeroDimensionalSolvePackageXmpPagePatch27}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty27}{\showpaste}
\tab{5}\spadcommand{lpr2 := positiveSolve(lf)$pack\free{lf }\free{pack }\bound{lpr2 }}
\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPagePatch28}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageFull28}{ZeroDimensionalSolvePackageXmpPageEmpty28}
\pastebutton{ZeroDimensionalSolvePackageXmpPageFull28}{\hidepaste}
\tab{5}\spadcommand{[approximate(r,1/10^21)::Float for r in lpr2.1]\free{lpr2 }}
\indentrel{3}\begin{verbatim}
   (28)
   [0.3221853546_2608559291, 0.3221853546_2608559291,
    0.3221853546_2608559291, 0.3221853546_2608559291]
                                      Type: List(Float)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{ZeroDimensionalSolvePackageXmpPageEmpty28}
\begin{paste}{ZeroDimensionalSolvePackageXmpPageEmpty28}{ZeroDimensionalSolvePackageXmpPagePatch28}
\pastebutton{ZeroDimensionalSolvePackageXmpPageEmpty28}{\showpaste}
\tab{5}\spadcommand{[approximate(r,1/10^21)::Float for r in lpr2.1]\free{lpr2 }}
\end{paste}\end{patch}

