diff options
Diffstat (limited to 'src/hyper/pages/ODPOL.pht')
| -rw-r--r-- | src/hyper/pages/ODPOL.pht | 626 |
1 files changed, 626 insertions, 0 deletions
diff --git a/src/hyper/pages/ODPOL.pht b/src/hyper/pages/ODPOL.pht new file mode 100644 index 00000000..2c37bab9 --- /dev/null +++ b/src/hyper/pages/ODPOL.pht @@ -0,0 +1,626 @@ +\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: Domain +\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)$dpol\free{dpol }\bound{w }} +\indentrel{3}\begin{verbatim} + (2) theMap(DPOLCAT-;makeVariable;AM;17!0,62) +Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty2} +\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty2}{OrderlyDifferentialPolynomialXmpPagePatch2} +\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{w := makeVariable('w)$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)$dpol\free{dpol }\bound{z }} +\indentrel{3}\begin{verbatim} + (3) theMap(DPOLCAT-;makeVariable;AM;17!0,187) +Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty3} +\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty3}{OrderlyDifferentialPolynomialXmpPagePatch3} +\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{z := makeVariable('z)$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)$dpol\free{f }\bound{df }} +\indentrel{3}\begin{verbatim} + (11) theMap(DPOLCAT-;makeVariable;AM;17!0,488) +Type: (NonNegativeInteger -> OrderlyDifferentialPolynomial Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OrderlyDifferentialPolynomialXmpPageEmpty11} +\begin{paste}{OrderlyDifferentialPolynomialXmpPageEmpty11}{OrderlyDifferentialPolynomialXmpPagePatch11} +\pastebutton{OrderlyDifferentialPolynomialXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{df:=makeVariable(f)$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} + |