\begin{patch}{PolynomialGCDPagePatch1} \begin{paste}{PolynomialGCDPageFull1}{PolynomialGCDPageEmpty1} \pastebutton{PolynomialGCDPageFull1}{\hidepaste} \tab{5}\spadcommand{p := 3*x**8 + 2*x**7 + 6*x**2 + 7*x + 2\bound{p }} \indentrel{3}\begin{verbatim} 8 7 2 (1) 3x + 2x + 6x + 7x + 2 Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialGCDPageEmpty1} \begin{paste}{PolynomialGCDPageEmpty1}{PolynomialGCDPagePatch1} \pastebutton{PolynomialGCDPageEmpty1}{\showpaste} \tab{5}\spadcommand{p := 3*x**8 + 2*x**7 + 6*x**2 + 7*x + 2\bound{p }} \end{paste}\end{patch} \begin{patch}{PolynomialGCDPagePatch2} \begin{paste}{PolynomialGCDPageFull2}{PolynomialGCDPageEmpty2} \pastebutton{PolynomialGCDPageFull2}{\hidepaste} \tab{5}\spadcommand{q := 2*x**13 + 9*x**7 + 2*x**6 + 10*x + 5\bound{q }} \indentrel{3}\begin{verbatim} 13 7 6 (2) 2x + 9x + 2x + 10x + 5 Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialGCDPageEmpty2} \begin{paste}{PolynomialGCDPageEmpty2}{PolynomialGCDPagePatch2} \pastebutton{PolynomialGCDPageEmpty2}{\showpaste} \tab{5}\spadcommand{q := 2*x**13 + 9*x**7 + 2*x**6 + 10*x + 5\bound{q }} \end{paste}\end{patch} \begin{patch}{PolynomialGCDPagePatch3} \begin{paste}{PolynomialGCDPageFull3}{PolynomialGCDPageEmpty3} \pastebutton{PolynomialGCDPageFull3}{\hidepaste} \tab{5}\spadcommand{gcd(p,q)\free{p q }} \indentrel{3}\begin{verbatim} 7 (3) x + 2x + 1 Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialGCDPageEmpty3} \begin{paste}{PolynomialGCDPageEmpty3}{PolynomialGCDPagePatch3} \pastebutton{PolynomialGCDPageEmpty3}{\showpaste} \tab{5}\spadcommand{gcd(p,q)\free{p q }} \end{paste}\end{patch} \begin{patch}{PolynomialGCDPagePatch4} \begin{paste}{PolynomialGCDPageFull4}{PolynomialGCDPageEmpty4} \pastebutton{PolynomialGCDPageFull4}{\hidepaste} \tab{5}\spadcommand{resultant(p,q,x)\free{p q }} \indentrel{3}\begin{verbatim} (4) 0 Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialGCDPageEmpty4} \begin{paste}{PolynomialGCDPageEmpty4}{PolynomialGCDPagePatch4} \pastebutton{PolynomialGCDPageEmpty4}{\showpaste} \tab{5}\spadcommand{resultant(p,q,x)\free{p q }} \end{paste}\end{patch} \begin{patch}{PolynomialSubstitutionPagePatch1} \begin{paste}{PolynomialSubstitutionPageFull1}{PolynomialSubstitutionPageEmpty1} \pastebutton{PolynomialSubstitutionPageFull1}{\hidepaste} \tab{5}\spadcommand{p := x**2 + y**2\bound{p }} \indentrel{3}\begin{verbatim} 2 2 (1) y + x Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialSubstitutionPageEmpty1} \begin{paste}{PolynomialSubstitutionPageEmpty1}{PolynomialSubstitutionPagePatch1} \pastebutton{PolynomialSubstitutionPageEmpty1}{\showpaste} \tab{5}\spadcommand{p := x**2 + y**2\bound{p }} \end{paste}\end{patch} \begin{patch}{PolynomialSubstitutionPagePatch2} \begin{paste}{PolynomialSubstitutionPageFull2}{PolynomialSubstitutionPageEmpty2} \pastebutton{PolynomialSubstitutionPageFull2}{\hidepaste} \tab{5}\spadcommand{eval(p,x=5)\free{p }} \indentrel{3}\begin{verbatim} 2 (2) y + 25 Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialSubstitutionPageEmpty2} \begin{paste}{PolynomialSubstitutionPageEmpty2}{PolynomialSubstitutionPagePatch2} \pastebutton{PolynomialSubstitutionPageEmpty2}{\showpaste} \tab{5}\spadcommand{eval(p,x=5)\free{p }} \end{paste}\end{patch} \begin{patch}{PolynomialSubstitutionPagePatch3} \begin{paste}{PolynomialSubstitutionPageFull3}{PolynomialSubstitutionPageEmpty3} \pastebutton{PolynomialSubstitutionPageFull3}{\hidepaste} \tab{5}\spadcommand{eval(p,[x = a + b,y = c + d])\free{p }} \indentrel{3}\begin{verbatim} 2 2 2 2 (3) d + 2c d + c + b + 2a b + a Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialSubstitutionPageEmpty3} \begin{paste}{PolynomialSubstitutionPageEmpty3}{PolynomialSubstitutionPagePatch3} \pastebutton{PolynomialSubstitutionPageEmpty3}{\showpaste} \tab{5}\spadcommand{eval(p,[x = a + b,y = c + d])\free{p }} \end{paste}\end{patch} \begin{patch}{PolynomialSubstitutionPagePatch4} \begin{paste}{PolynomialSubstitutionPageFull4}{PolynomialSubstitutionPageEmpty4} \pastebutton{PolynomialSubstitutionPageFull4}{\hidepaste} \tab{5}\spadcommand{q := x**3 + 5*x - y**4\bound{q }} \indentrel{3}\begin{verbatim} 4 3 (4) - y + x + 5x Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialSubstitutionPageEmpty4} \begin{paste}{PolynomialSubstitutionPageEmpty4}{PolynomialSubstitutionPagePatch4} \pastebutton{PolynomialSubstitutionPageEmpty4}{\showpaste} \tab{5}\spadcommand{q := x**3 + 5*x - y**4\bound{q }} \end{paste}\end{patch} \begin{patch}{PolynomialSubstitutionPagePatch5} \begin{paste}{PolynomialSubstitutionPageFull5}{PolynomialSubstitutionPageEmpty5} \pastebutton{PolynomialSubstitutionPageFull5}{\hidepaste} \tab{5}\spadcommand{eval(q,[x=y,y=x])\free{q }} \indentrel{3}\begin{verbatim} 3 4 (5) y + 5y - x Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialSubstitutionPageEmpty5} \begin{paste}{PolynomialSubstitutionPageEmpty5}{PolynomialSubstitutionPagePatch5} \pastebutton{PolynomialSubstitutionPageEmpty5}{\showpaste} \tab{5}\spadcommand{eval(q,[x=y,y=x])\free{q }} \end{paste}\end{patch} \begin{patch}{PolynomialSubstitutionPagePatch6} \begin{paste}{PolynomialSubstitutionPageFull6}{PolynomialSubstitutionPageEmpty6} \pastebutton{PolynomialSubstitutionPageFull6}{\hidepaste} \tab{5}\spadcommand{px := eval(p, y = sin(2.0))\bound{px }\free{p }} \indentrel{3}\begin{verbatim} 2 (6) x + 0.8268218104 3180595732 Type: Polynomial Float \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialSubstitutionPageEmpty6} \begin{paste}{PolynomialSubstitutionPageEmpty6}{PolynomialSubstitutionPagePatch6} \pastebutton{PolynomialSubstitutionPageEmpty6}{\showpaste} \tab{5}\spadcommand{px := eval(p, y = sin(2.0))\bound{px }\free{p }} \end{paste}\end{patch} \begin{patch}{PolynomialSubstitutionPagePatch7} \begin{paste}{PolynomialSubstitutionPageFull7}{PolynomialSubstitutionPageEmpty7} \pastebutton{PolynomialSubstitutionPageFull7}{\hidepaste} \tab{5}\spadcommand{eval(px, x = cos(2.0))\free{px }} \indentrel{3}\begin{verbatim} (7) 1.0 Type: Polynomial Float \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialSubstitutionPageEmpty7} \begin{paste}{PolynomialSubstitutionPageEmpty7}{PolynomialSubstitutionPagePatch7} \pastebutton{PolynomialSubstitutionPageEmpty7}{\showpaste} \tab{5}\spadcommand{eval(px, x = cos(2.0))\free{px }} \end{paste}\end{patch} \begin{patch}{PolynomialBasicPagePatch1} \begin{paste}{PolynomialBasicPageFull1}{PolynomialBasicPageEmpty1} \pastebutton{PolynomialBasicPageFull1}{\hidepaste} \tab{5}\spadcommand{p := a*x**2 + b*x*y + c*y**2\bound{p }} \indentrel{3}\begin{verbatim} 2 2 (1) c y + b x y + a x Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialBasicPageEmpty1} \begin{paste}{PolynomialBasicPageEmpty1}{PolynomialBasicPagePatch1} \pastebutton{PolynomialBasicPageEmpty1}{\showpaste} \tab{5}\spadcommand{p := a*x**2 + b*x*y + c*y**2\bound{p }} \end{paste}\end{patch} \begin{patch}{PolynomialBasicPagePatch2} \begin{paste}{PolynomialBasicPageFull2}{PolynomialBasicPageEmpty2} \pastebutton{PolynomialBasicPageFull2}{\hidepaste} \tab{5}\spadcommand{q := 13*x**2 + 3*z\bound{q }} \indentrel{3}\begin{verbatim} 2 (2) 3z + 13x Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialBasicPageEmpty2} \begin{paste}{PolynomialBasicPageEmpty2}{PolynomialBasicPagePatch2} \pastebutton{PolynomialBasicPageEmpty2}{\showpaste} \tab{5}\spadcommand{q := 13*x**2 + 3*z\bound{q }} \end{paste}\end{patch} \begin{patch}{PolynomialBasicPagePatch3} \begin{paste}{PolynomialBasicPageFull3}{PolynomialBasicPageEmpty3} \pastebutton{PolynomialBasicPageFull3}{\hidepaste} \tab{5}\spadcommand{p + q\free{p q }} \indentrel{3}\begin{verbatim} 2 2 (3) 3z + c y + b x y + (a + 13)x Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialBasicPageEmpty3} \begin{paste}{PolynomialBasicPageEmpty3}{PolynomialBasicPagePatch3} \pastebutton{PolynomialBasicPageEmpty3}{\showpaste} \tab{5}\spadcommand{p + q\free{p q }} \end{paste}\end{patch} \begin{patch}{PolynomialBasicPagePatch4} \begin{paste}{PolynomialBasicPageFull4}{PolynomialBasicPageEmpty4} \pastebutton{PolynomialBasicPageFull4}{\hidepaste} \tab{5}\spadcommand{p - 3*q\free{p q }} \indentrel{3}\begin{verbatim} 2 2 (4) - 9z + c y + b x y + (a - 39)x Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialBasicPageEmpty4} \begin{paste}{PolynomialBasicPageEmpty4}{PolynomialBasicPagePatch4} \pastebutton{PolynomialBasicPageEmpty4}{\showpaste} \tab{5}\spadcommand{p - 3*q\free{p q }} \end{paste}\end{patch} \begin{patch}{PolynomialBasicPagePatch5} \begin{paste}{PolynomialBasicPageFull5}{PolynomialBasicPageEmpty5} \pastebutton{PolynomialBasicPageFull5}{\hidepaste} \tab{5}\spadcommand{p**2 + p*q\free{p q }} \indentrel{3}\begin{verbatim} (5) 2 2 2 4 3 (3c y + 3b x y + 3a x )z + c y + 2b c x y + 2 2 2 3 2 4 ((2a + 13)c + b )x y + (2a + 13)b x y + (a + 13a)x Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialBasicPageEmpty5} \begin{paste}{PolynomialBasicPageEmpty5}{PolynomialBasicPagePatch5} \pastebutton{PolynomialBasicPageEmpty5}{\showpaste} \tab{5}\spadcommand{p**2 + p*q\free{p q }} \end{paste}\end{patch} \begin{patch}{PolynomialBasicPagePatch6} \begin{paste}{PolynomialBasicPageFull6}{PolynomialBasicPageEmpty6} \pastebutton{PolynomialBasicPageFull6}{\hidepaste} \tab{5}\spadcommand{r := (p + q)**2\bound{r }\free{p q }} \indentrel{3}\begin{verbatim} (6) 2 2 2 2 4 9z + (6c y + 6b x y + (6a + 78)x )z + c y + 3 2 2 2 3 2b c x y + ((2a + 26)c + b )x y + (2a + 26)b x y + 2 4 (a + 26a + 169)x Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialBasicPageEmpty6} \begin{paste}{PolynomialBasicPageEmpty6}{PolynomialBasicPagePatch6} \pastebutton{PolynomialBasicPageEmpty6}{\showpaste} \tab{5}\spadcommand{r := (p + q)**2\bound{r }\free{p q }} \end{paste}\end{patch} \begin{patch}{PolynomialBasicPagePatch7} \begin{paste}{PolynomialBasicPageFull7}{PolynomialBasicPageEmpty7} \pastebutton{PolynomialBasicPageFull7}{\hidepaste} \tab{5}\spadcommand{setVariableOrder [a,b,c,x,y,z]\bound{vord }} \indentrel{3}\begin{verbatim} Type: Void \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialBasicPageEmpty7} \begin{paste}{PolynomialBasicPageEmpty7}{PolynomialBasicPagePatch7} \pastebutton{PolynomialBasicPageEmpty7}{\showpaste} \tab{5}\spadcommand{setVariableOrder [a,b,c,x,y,z]\bound{vord }} \end{paste}\end{patch} \begin{patch}{PolynomialBasicPagePatch8} \begin{paste}{PolynomialBasicPageFull8}{PolynomialBasicPageEmpty8} \pastebutton{PolynomialBasicPageFull8}{\hidepaste} \tab{5}\spadcommand{p\free{p vord }} \indentrel{3}\begin{verbatim} 2 2 (8) x a + y x b + y c Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialBasicPageEmpty8} \begin{paste}{PolynomialBasicPageEmpty8}{PolynomialBasicPagePatch8} \pastebutton{PolynomialBasicPageEmpty8}{\showpaste} \tab{5}\spadcommand{p\free{p vord }} \end{paste}\end{patch} \begin{patch}{PolynomialBasicPagePatch9} \begin{paste}{PolynomialBasicPageFull9}{PolynomialBasicPageEmpty9} \pastebutton{PolynomialBasicPageFull9}{\hidepaste} \tab{5}\spadcommand{q\free{q vord }} \indentrel{3}\begin{verbatim} 2 (9) 13x + 3z Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialBasicPageEmpty9} \begin{paste}{PolynomialBasicPageEmpty9}{PolynomialBasicPagePatch9} \pastebutton{PolynomialBasicPageEmpty9}{\showpaste} \tab{5}\spadcommand{q\free{q vord }} \end{paste}\end{patch} \begin{patch}{PolynomialBasicPagePatch10} \begin{paste}{PolynomialBasicPageFull10}{PolynomialBasicPageEmpty10} \pastebutton{PolynomialBasicPageFull10}{\hidepaste} \tab{5}\spadcommand{r\free{r vord }} \indentrel{3}\begin{verbatim} (10) 4 2 3 2 2 4 2 2 2 2 x a + (2y x b + 2y x c + 26x + 6z x )a + y x b + 3 3 4 2 (2y x c + 26y x + 6z y x)b + y c + 2 2 2 4 2 2 (26y x + 6z y )c + 169x + 78z x + 9z Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialBasicPageEmpty10} \begin{paste}{PolynomialBasicPageEmpty10}{PolynomialBasicPagePatch10} \pastebutton{PolynomialBasicPageEmpty10}{\showpaste} \tab{5}\spadcommand{r\free{r vord }} \end{paste}\end{patch} \begin{patch}{PolynomialBasicPagePatch11} \begin{paste}{PolynomialBasicPageFull11}{PolynomialBasicPageEmpty11} \pastebutton{PolynomialBasicPageFull11}{\hidepaste} \tab{5}\spadcommand{resetVariableOrder()\bound{rvord }} \indentrel{3}\begin{verbatim} Type: Void \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialBasicPageEmpty11} \begin{paste}{PolynomialBasicPageEmpty11}{PolynomialBasicPagePatch11} \pastebutton{PolynomialBasicPageEmpty11}{\showpaste} \tab{5}\spadcommand{resetVariableOrder()\bound{rvord }} \end{paste}\end{patch} \begin{patch}{PolynomialBasicPagePatch12} \begin{paste}{PolynomialBasicPageFull12}{PolynomialBasicPageEmpty12} \pastebutton{PolynomialBasicPageFull12}{\hidepaste} \tab{5}\spadcommand{p\free{p rvord }} \indentrel{3}\begin{verbatim} 2 2 (12) c y + b x y + a x Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialBasicPageEmpty12} \begin{paste}{PolynomialBasicPageEmpty12}{PolynomialBasicPagePatch12} \pastebutton{PolynomialBasicPageEmpty12}{\showpaste} \tab{5}\spadcommand{p\free{p rvord }} \end{paste}\end{patch} \begin{patch}{PolynomialBasicPagePatch13} \begin{paste}{PolynomialBasicPageFull13}{PolynomialBasicPageEmpty13} \pastebutton{PolynomialBasicPageFull13}{\hidepaste} \tab{5}\spadcommand{coefficient(q,x,2)\free{q }} \indentrel{3}\begin{verbatim} (13) 13 Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialBasicPageEmpty13} \begin{paste}{PolynomialBasicPageEmpty13}{PolynomialBasicPagePatch13} \pastebutton{PolynomialBasicPageEmpty13}{\showpaste} \tab{5}\spadcommand{coefficient(q,x,2)\free{q }} \end{paste}\end{patch} \begin{patch}{PolynomialBasicPagePatch14} \begin{paste}{PolynomialBasicPageFull14}{PolynomialBasicPageEmpty14} \pastebutton{PolynomialBasicPageFull14}{\hidepaste} \tab{5}\spadcommand{coefficient(r,x,3)\free{r }} \indentrel{3}\begin{verbatim} (14) (2a + 26)b y Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialBasicPageEmpty14} \begin{paste}{PolynomialBasicPageEmpty14}{PolynomialBasicPagePatch14} \pastebutton{PolynomialBasicPageEmpty14}{\showpaste} \tab{5}\spadcommand{coefficient(r,x,3)\free{r }} \end{paste}\end{patch} \begin{patch}{PolynomialBasicPagePatch15} \begin{paste}{PolynomialBasicPageFull15}{PolynomialBasicPageEmpty15} \pastebutton{PolynomialBasicPageFull15}{\hidepaste} \tab{5}\spadcommand{c := coefficient(r,z,1)\free{r }\bound{c }} \indentrel{3}\begin{verbatim} 2 2 (15) 6c y + 6b x y + (6a + 78)x Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialBasicPageEmpty15} \begin{paste}{PolynomialBasicPageEmpty15}{PolynomialBasicPagePatch15} \pastebutton{PolynomialBasicPageEmpty15}{\showpaste} \tab{5}\spadcommand{c := coefficient(r,z,1)\free{r }\bound{c }} \end{paste}\end{patch} \begin{patch}{PolynomialBasicPagePatch16} \begin{paste}{PolynomialBasicPageFull16}{PolynomialBasicPageEmpty16} \pastebutton{PolynomialBasicPageFull16}{\hidepaste} \tab{5}\spadcommand{coefficient(c,x,2)\free{c }} \indentrel{3}\begin{verbatim} (16) 6a + 78 Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialBasicPageEmpty16} \begin{paste}{PolynomialBasicPageEmpty16}{PolynomialBasicPagePatch16} \pastebutton{PolynomialBasicPageEmpty16}{\showpaste} \tab{5}\spadcommand{coefficient(c,x,2)\free{c }} \end{paste}\end{patch} \begin{patch}{PolynomialBasicPagePatch17} \begin{paste}{PolynomialBasicPageFull17}{PolynomialBasicPageEmpty17} \pastebutton{PolynomialBasicPageFull17}{\hidepaste} \tab{5}\spadcommand{coefficient(q**2, [x,z], [2,1])\free{q }} \indentrel{3}\begin{verbatim} (17) 78 Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialBasicPageEmpty17} \begin{paste}{PolynomialBasicPageEmpty17}{PolynomialBasicPagePatch17} \pastebutton{PolynomialBasicPageEmpty17}{\showpaste} \tab{5}\spadcommand{coefficient(q**2, [x,z], [2,1])\free{q }} \end{paste}\end{patch} \begin{patch}{PolynomialBasicPagePatch18} \begin{paste}{PolynomialBasicPageFull18}{PolynomialBasicPageEmpty18} \pastebutton{PolynomialBasicPageFull18}{\hidepaste} \tab{5}\spadcommand{coefficient(r, [x,y], [2,2])\free{r }} \indentrel{3}\begin{verbatim} 2 (18) (2a + 26)c + b Type: Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{PolynomialBasicPageEmpty18} \begin{paste}{PolynomialBasicPageEmpty18}{PolynomialBasicPagePatch18} \pastebutton{PolynomialBasicPageEmpty18}{\showpaste} \tab{5}\spadcommand{coefficient(r, [x,y], [2,2])\free{r }} \end{paste}\end{patch}