\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch1}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull1}{OrderlyDifferentialPolynomialXmpPageEmpty1}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull1}{\hidepaste}
\tab{5}\spadcommand{dpol:= ODPOL(FRAC INT)\bound{dpol }}
\indentrel{3}\begin{verbatim}
   (1)  OrderlyDifferentialPolynomial(Fraction(Integer))
                                             Type: Type
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty1}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty1}{OrderlyDifferentialPolynomialXmpPagePatch1}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty1}{\showpaste}
\tab{5}\spadcommand{dpol:= ODPOL(FRAC INT)\bound{dpol }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch2}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull2}{OrderlyDifferentialPolynomialXmpPageEmpty2}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull2}{\hidepaste}
\tab{5}\spadcommand{w := makeVariable('w)$dpol\free{dpol }\bound{w }}
\indentrel{3}\begin{verbatim}
   (2)  theMap(DPOLCAT-;makeVariable;AM;17!0,303)
Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial(Fraction(Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty2}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty2}{OrderlyDifferentialPolynomialXmpPagePatch2}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty2}{\showpaste}
\tab{5}\spadcommand{w := makeVariable('w)$dpol\free{dpol }\bound{w }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch3}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull3}{OrderlyDifferentialPolynomialXmpPageEmpty3}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull3}{\hidepaste}
\tab{5}\spadcommand{z := makeVariable('z)$dpol\free{dpol }\bound{z }}
\indentrel{3}\begin{verbatim}
   (3)  theMap(DPOLCAT-;makeVariable;AM;17!0,303)
Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial(Fraction(Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty3}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty3}{OrderlyDifferentialPolynomialXmpPagePatch3}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty3}{\showpaste}
\tab{5}\spadcommand{z := makeVariable('z)$dpol\free{dpol }\bound{z }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch4}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull4}{OrderlyDifferentialPolynomialXmpPageEmpty4}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull4}{\hidepaste}
\tab{5}\spadcommand{w.5\free{w }}
\indentrel{3}\begin{verbatim}
   (4)  w
         5
 Type: OrderlyDifferentialPolynomial(Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty4}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty4}{OrderlyDifferentialPolynomialXmpPagePatch4}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty4}{\showpaste}
\tab{5}\spadcommand{w.5\free{w }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch5}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull5}{OrderlyDifferentialPolynomialXmpPageEmpty5}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull5}{\hidepaste}
\tab{5}\spadcommand{w 0\free{w }}
\indentrel{3}\begin{verbatim}
   (5)  w
 Type: OrderlyDifferentialPolynomial(Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty5}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty5}{OrderlyDifferentialPolynomialXmpPagePatch5}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty5}{\showpaste}
\tab{5}\spadcommand{w 0\free{w }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch6}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull6}{OrderlyDifferentialPolynomialXmpPageEmpty6}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull6}{\hidepaste}
\tab{5}\spadcommand{[z.i for i in 1..5]\free{z }}
\indentrel{3}\begin{verbatim}
   (6)  [z ,z ,z ,z ,z ]
          1  2  3  4  5
Type: List(OrderlyDifferentialPolynomial(Fraction(Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty6}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty6}{OrderlyDifferentialPolynomialXmpPagePatch6}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty6}{\showpaste}
\tab{5}\spadcommand{[z.i for i in 1..5]\free{z }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch7}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull7}{OrderlyDifferentialPolynomialXmpPageEmpty7}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull7}{\hidepaste}
\tab{5}\spadcommand{f:= w.4 - w.1 * w.1 * z.3\free{w }\free{z }\bound{f }}
\indentrel{3}\begin{verbatim}
               2
   (7)  w  - w  z
         4    1  3
 Type: OrderlyDifferentialPolynomial(Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty7}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty7}{OrderlyDifferentialPolynomialXmpPagePatch7}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty7}{\showpaste}
\tab{5}\spadcommand{f:= w.4 - w.1 * w.1 * z.3\free{w }\free{z }\bound{f }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch8}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull8}{OrderlyDifferentialPolynomialXmpPageEmpty8}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull8}{\hidepaste}
\tab{5}\spadcommand{g:=(z.1)^3 * (z.2)^2 - w.2\free{z }\free{w }\bound{g }}
\indentrel{3}\begin{verbatim}
          3  2
   (8)  z  z   - w
         1  2     2
 Type: OrderlyDifferentialPolynomial(Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty8}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty8}{OrderlyDifferentialPolynomialXmpPagePatch8}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty8}{\showpaste}
\tab{5}\spadcommand{g:=(z.1)^3 * (z.2)^2 - w.2\free{z }\free{w }\bound{g }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch9}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull9}{OrderlyDifferentialPolynomialXmpPageEmpty9}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull9}{\hidepaste}
\tab{5}\spadcommand{D(f)\free{f }}
\indentrel{3}\begin{verbatim}
               2
   (9)  w  - w  z  - 2w w z
         5    1  4     1 2 3
 Type: OrderlyDifferentialPolynomial(Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty9}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty9}{OrderlyDifferentialPolynomialXmpPagePatch9}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty9}{\showpaste}
\tab{5}\spadcommand{D(f)\free{f }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch10}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull10}{OrderlyDifferentialPolynomialXmpPageEmpty10}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull10}{\hidepaste}
\tab{5}\spadcommand{D(f,4)\free{f }}
\indentrel{3}\begin{verbatim}
   (10)
            2                               2
     w  - w  z  - 8w w z  + (- 12w w  - 12w  )z  - 2w z w
      8    1  7     1 2 6         1 3      2   5     1 3 5
   + 
                                         2
     (- 8w w  - 24w w )z  - 8w z w  - 6w  z
          1 4      2 3  4     2 3 4     3  3
 Type: OrderlyDifferentialPolynomial(Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty10}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty10}{OrderlyDifferentialPolynomialXmpPagePatch10}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty10}{\showpaste}
\tab{5}\spadcommand{D(f,4)\free{f }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch11}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull11}{OrderlyDifferentialPolynomialXmpPageEmpty11}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull11}{\hidepaste}
\tab{5}\spadcommand{df:=makeVariable(f)$dpol\free{f }\bound{df }}
\indentrel{3}\begin{verbatim}
   (11)  theMap(DPOLCAT-;makeVariable;AM;17!0,303)
Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial(Fraction(Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty11}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty11}{OrderlyDifferentialPolynomialXmpPagePatch11}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty11}{\showpaste}
\tab{5}\spadcommand{df:=makeVariable(f)$dpol\free{f }\bound{df }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch12}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull12}{OrderlyDifferentialPolynomialXmpPageEmpty12}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull12}{\hidepaste}
\tab{5}\spadcommand{df.4\free{df }}
\indentrel{3}\begin{verbatim}
   (12)
            2                               2
     w  - w  z  - 8w w z  + (- 12w w  - 12w  )z  - 2w z w
      8    1  7     1 2 6         1 3      2   5     1 3 5
   + 
                                         2
     (- 8w w  - 24w w )z  - 8w z w  - 6w  z
          1 4      2 3  4     2 3 4     3  3
 Type: OrderlyDifferentialPolynomial(Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty12}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty12}{OrderlyDifferentialPolynomialXmpPagePatch12}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty12}{\showpaste}
\tab{5}\spadcommand{df.4\free{df }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch13}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull13}{OrderlyDifferentialPolynomialXmpPageEmpty13}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull13}{\hidepaste}
\tab{5}\spadcommand{order(g)\free{g }}
\indentrel{3}\begin{verbatim}
   (13)  2
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty13}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty13}{OrderlyDifferentialPolynomialXmpPagePatch13}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty13}{\showpaste}
\tab{5}\spadcommand{order(g)\free{g }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch14}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull14}{OrderlyDifferentialPolynomialXmpPageEmpty14}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull14}{\hidepaste}
\tab{5}\spadcommand{order(g, 'w)\free{g }}
\indentrel{3}\begin{verbatim}
   (14)  2
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty14}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty14}{OrderlyDifferentialPolynomialXmpPagePatch14}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty14}{\showpaste}
\tab{5}\spadcommand{order(g, 'w)\free{g }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch15}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull15}{OrderlyDifferentialPolynomialXmpPageEmpty15}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull15}{\hidepaste}
\tab{5}\spadcommand{differentialVariables(g)\free{g }}
\indentrel{3}\begin{verbatim}
   (15)  [z,w]
                                     Type: List(Symbol)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty15}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty15}{OrderlyDifferentialPolynomialXmpPagePatch15}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty15}{\showpaste}
\tab{5}\spadcommand{differentialVariables(g)\free{g }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch16}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull16}{OrderlyDifferentialPolynomialXmpPageEmpty16}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull16}{\hidepaste}
\tab{5}\spadcommand{degree(g)\free{g }}
\indentrel{3}\begin{verbatim}
           2  3
   (16)  z  z
          2  1
Type: IndexedExponents(OrderlyDifferentialVariable(Symbol))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty16}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty16}{OrderlyDifferentialPolynomialXmpPagePatch16}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty16}{\showpaste}
\tab{5}\spadcommand{degree(g)\free{g }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch17}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull17}{OrderlyDifferentialPolynomialXmpPageEmpty17}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull17}{\hidepaste}
\tab{5}\spadcommand{degree(g, 'w)\free{g }}
\indentrel{3}\begin{verbatim}
   (17)  1
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty17}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty17}{OrderlyDifferentialPolynomialXmpPagePatch17}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty17}{\showpaste}
\tab{5}\spadcommand{degree(g, 'w)\free{g }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch18}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull18}{OrderlyDifferentialPolynomialXmpPageEmpty18}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull18}{\hidepaste}
\tab{5}\spadcommand{weights(g)\free{g }}
\indentrel{3}\begin{verbatim}
   (18)  [7,2]
                         Type: List(NonNegativeInteger)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty18}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty18}{OrderlyDifferentialPolynomialXmpPagePatch18}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty18}{\showpaste}
\tab{5}\spadcommand{weights(g)\free{g }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch19}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull19}{OrderlyDifferentialPolynomialXmpPageEmpty19}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull19}{\hidepaste}
\tab{5}\spadcommand{weights(g,'w)\free{g }}
\indentrel{3}\begin{verbatim}
   (19)  [2]
                         Type: List(NonNegativeInteger)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty19}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty19}{OrderlyDifferentialPolynomialXmpPagePatch19}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty19}{\showpaste}
\tab{5}\spadcommand{weights(g,'w)\free{g }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch20}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull20}{OrderlyDifferentialPolynomialXmpPageEmpty20}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull20}{\hidepaste}
\tab{5}\spadcommand{weight(g)\free{g }}
\indentrel{3}\begin{verbatim}
   (20)  7
                                  Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty20}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty20}{OrderlyDifferentialPolynomialXmpPagePatch20}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty20}{\showpaste}
\tab{5}\spadcommand{weight(g)\free{g }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch21}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull21}{OrderlyDifferentialPolynomialXmpPageEmpty21}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull21}{\hidepaste}
\tab{5}\spadcommand{isobaric?(g)\free{g }}
\indentrel{3}\begin{verbatim}
   (21)  false
                                          Type: Boolean
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty21}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty21}{OrderlyDifferentialPolynomialXmpPagePatch21}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty21}{\showpaste}
\tab{5}\spadcommand{isobaric?(g)\free{g }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch22}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull22}{OrderlyDifferentialPolynomialXmpPageEmpty22}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull22}{\hidepaste}
\tab{5}\spadcommand{eval(g,['w::Symbol],[f])\free{f }\free{g }}
\indentrel{3}\begin{verbatim}
   (22)
            2                           2        3  2
   - w  + w  z  + 4w w z  + (2w w  + 2w  )z  + z  z
      6    1  5     1 2 4      1 3     2   3    1  2
 Type: OrderlyDifferentialPolynomial(Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty22}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty22}{OrderlyDifferentialPolynomialXmpPagePatch22}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty22}{\showpaste}
\tab{5}\spadcommand{eval(g,['w::Symbol],[f])\free{f }\free{g }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch23}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull23}{OrderlyDifferentialPolynomialXmpPageEmpty23}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull23}{\hidepaste}
\tab{5}\spadcommand{eval(g,variables(w.0),[f])\free{f }\free{g }}
\indentrel{3}\begin{verbatim}
           3  2
   (23)  z  z   - w
          1  2     2
 Type: OrderlyDifferentialPolynomial(Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty23}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty23}{OrderlyDifferentialPolynomialXmpPagePatch23}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty23}{\showpaste}
\tab{5}\spadcommand{eval(g,variables(w.0),[f])\free{f }\free{g }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch24}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull24}{OrderlyDifferentialPolynomialXmpPageEmpty24}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull24}{\hidepaste}
\tab{5}\spadcommand{monomials(g)\free{g }}
\indentrel{3}\begin{verbatim}
            3  2
   (24)  [z  z  ,- w ]
           1  2     2
Type: List(OrderlyDifferentialPolynomial(Fraction(Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty24}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty24}{OrderlyDifferentialPolynomialXmpPagePatch24}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty24}{\showpaste}
\tab{5}\spadcommand{monomials(g)\free{g }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch25}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull25}{OrderlyDifferentialPolynomialXmpPageEmpty25}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull25}{\hidepaste}
\tab{5}\spadcommand{variables(g)\free{g }}
\indentrel{3}\begin{verbatim}
   (25)  [z ,w ,z ]
           2  2  1
        Type: List(OrderlyDifferentialVariable(Symbol))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty25}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty25}{OrderlyDifferentialPolynomialXmpPagePatch25}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty25}{\showpaste}
\tab{5}\spadcommand{variables(g)\free{g }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch26}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull26}{OrderlyDifferentialPolynomialXmpPageEmpty26}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull26}{\hidepaste}
\tab{5}\spadcommand{gcd(f,g)\free{f }\free{g }}
\indentrel{3}\begin{verbatim}
   (26)  1
 Type: OrderlyDifferentialPolynomial(Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty26}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty26}{OrderlyDifferentialPolynomialXmpPagePatch26}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty26}{\showpaste}
\tab{5}\spadcommand{gcd(f,g)\free{f }\free{g }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch27}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull27}{OrderlyDifferentialPolynomialXmpPageEmpty27}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull27}{\hidepaste}
\tab{5}\spadcommand{groebner([f,g])\free{f }\free{g }}
\indentrel{3}\begin{verbatim}
                 2     3  2
   (27)  [w  - w  z ,z  z   - w ]
           4    1  3  1  2     2
Type: List(OrderlyDifferentialPolynomial(Fraction(Integer)))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty27}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty27}{OrderlyDifferentialPolynomialXmpPagePatch27}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty27}{\showpaste}
\tab{5}\spadcommand{groebner([f,g])\free{f }\free{g }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch28}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull28}{OrderlyDifferentialPolynomialXmpPageEmpty28}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull28}{\hidepaste}
\tab{5}\spadcommand{lg:=leader(g)\free{g }\bound{lg }}
\indentrel{3}\begin{verbatim}
   (28)  z
          2
              Type: OrderlyDifferentialVariable(Symbol)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty28}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty28}{OrderlyDifferentialPolynomialXmpPagePatch28}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty28}{\showpaste}
\tab{5}\spadcommand{lg:=leader(g)\free{g }\bound{lg }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch29}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull29}{OrderlyDifferentialPolynomialXmpPageEmpty29}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull29}{\hidepaste}
\tab{5}\spadcommand{sg:=separant(g)\free{g }\bound{sg }}
\indentrel{3}\begin{verbatim}
            3
   (29)  2z  z
           1  2
 Type: OrderlyDifferentialPolynomial(Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty29}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty29}{OrderlyDifferentialPolynomialXmpPagePatch29}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty29}{\showpaste}
\tab{5}\spadcommand{sg:=separant(g)\free{g }\bound{sg }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch30}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull30}{OrderlyDifferentialPolynomialXmpPageEmpty30}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull30}{\hidepaste}
\tab{5}\spadcommand{ig:=initial(g)\free{g }\bound{ig }}
\indentrel{3}\begin{verbatim}
           3
   (30)  z
          1
 Type: OrderlyDifferentialPolynomial(Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty30}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty30}{OrderlyDifferentialPolynomialXmpPagePatch30}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty30}{\showpaste}
\tab{5}\spadcommand{ig:=initial(g)\free{g }\bound{ig }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch31}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull31}{OrderlyDifferentialPolynomialXmpPageEmpty31}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull31}{\hidepaste}
\tab{5}\spadcommand{g1 := D g\free{g }\bound{g1 }}
\indentrel{3}\begin{verbatim}
            3               2  3
   (31)  2z  z z  - w  + 3z  z
           1  2 3    3     1  2
 Type: OrderlyDifferentialPolynomial(Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty31}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty31}{OrderlyDifferentialPolynomialXmpPagePatch31}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty31}{\showpaste}
\tab{5}\spadcommand{g1 := D g\free{g }\bound{g1 }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch32}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull32}{OrderlyDifferentialPolynomialXmpPageEmpty32}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull32}{\hidepaste}
\tab{5}\spadcommand{lg1:= leader g1\free{g1 }\bound{lg1 }}
\indentrel{3}\begin{verbatim}
   (32)  z
          3
              Type: OrderlyDifferentialVariable(Symbol)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty32}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty32}{OrderlyDifferentialPolynomialXmpPagePatch32}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty32}{\showpaste}
\tab{5}\spadcommand{lg1:= leader g1\free{g1 }\bound{lg1 }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch33}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull33}{OrderlyDifferentialPolynomialXmpPageEmpty33}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull33}{\hidepaste}
\tab{5}\spadcommand{pdf:=D(f, lg1)\free{f }\free{lg1 }\bound{pdf }}
\indentrel{3}\begin{verbatim}
             2
   (33)  - w
            1
 Type: OrderlyDifferentialPolynomial(Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty33}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty33}{OrderlyDifferentialPolynomialXmpPagePatch33}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty33}{\showpaste}
\tab{5}\spadcommand{pdf:=D(f, lg1)\free{f }\free{lg1 }\bound{pdf }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch34}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull34}{OrderlyDifferentialPolynomialXmpPageEmpty34}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull34}{\hidepaste}
\tab{5}\spadcommand{prf:=sg * f- pdf * g1\free{f }\free{sg }\free{pdf }\free{g1 }\bound{prf }}
\indentrel{3}\begin{verbatim}
            3         2        2  2  3
   (34)  2z  z w  - w  w  + 3w  z  z
           1  2 4    1  3     1  1  2
 Type: OrderlyDifferentialPolynomial(Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty34}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty34}{OrderlyDifferentialPolynomialXmpPagePatch34}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty34}{\showpaste}
\tab{5}\spadcommand{prf:=sg * f- pdf * g1\free{f }\free{sg }\free{pdf }\free{g1 }\bound{prf }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch35}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull35}{OrderlyDifferentialPolynomialXmpPageEmpty35}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull35}{\hidepaste}
\tab{5}\spadcommand{lcf:=leadingCoefficient univariate(prf, lg)\free{prf }\free{lg }\bound{lcf }}
\indentrel{3}\begin{verbatim}
            2  2
   (35)  3w  z
           1  1
 Type: OrderlyDifferentialPolynomial(Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty35}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty35}{OrderlyDifferentialPolynomialXmpPagePatch35}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty35}{\showpaste}
\tab{5}\spadcommand{lcf:=leadingCoefficient univariate(prf, lg)\free{prf }\free{lg }\bound{lcf }}
\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPagePatch36}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageFull36}{OrderlyDifferentialPolynomialXmpPageEmpty36}
\pastebutton{OrderlyDifferentialPolynomialXmpPageFull36}{\hidepaste}
\tab{5}\spadcommand{ig * prf - lcf * g * lg\free{ig }\free{prf }\free{lcf }\free{g }\free{lg }}
\indentrel{3}\begin{verbatim}
            6         2  3        2  2
   (36)  2z  z w  - w  z  w  + 3w  z  w z
           1  2 4    1  1  3     1  1  2 2
 Type: OrderlyDifferentialPolynomial(Fraction(Integer))
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}

\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty36}
\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty36}{OrderlyDifferentialPolynomialXmpPagePatch36}
\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty36}{\showpaste}
\tab{5}\spadcommand{ig * prf - lcf * g * lg\free{ig }\free{prf }\free{lcf }\free{g }\free{lg }}
\end{paste}\end{patch}

