\begin{patch}{UnivariatePolynomialXmpPagePatch1} \begin{paste}{UnivariatePolynomialXmpPageFull1}{UnivariatePolynomialXmpPageEmpty1} \pastebutton{UnivariatePolynomialXmpPageFull1}{\hidepaste} \tab{5}\spadcommand{(p,q) : UP(x,INT)\bound{pdec }\bound{qdec }} \indentrel{3}\begin{verbatim} Type: Void \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty1} \begin{paste}{UnivariatePolynomialXmpPageEmpty1}{UnivariatePolynomialXmpPagePatch1} \pastebutton{UnivariatePolynomialXmpPageEmpty1}{\showpaste} \tab{5}\spadcommand{(p,q) : UP(x,INT)\bound{pdec }\bound{qdec }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch2} \begin{paste}{UnivariatePolynomialXmpPageFull2}{UnivariatePolynomialXmpPageEmpty2} \pastebutton{UnivariatePolynomialXmpPageFull2}{\hidepaste} \tab{5}\spadcommand{p := (3*x-1)**2 * (2*x + 8)\free{pdec }\bound{p }} \indentrel{3}\begin{verbatim} 3 2 (2) 18x + 60x - 46x + 8 Type: UnivariatePolynomial(x,Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty2} \begin{paste}{UnivariatePolynomialXmpPageEmpty2}{UnivariatePolynomialXmpPagePatch2} \pastebutton{UnivariatePolynomialXmpPageEmpty2}{\showpaste} \tab{5}\spadcommand{p := (3*x-1)**2 * (2*x + 8)\free{pdec }\bound{p }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch3} \begin{paste}{UnivariatePolynomialXmpPageFull3}{UnivariatePolynomialXmpPageEmpty3} \pastebutton{UnivariatePolynomialXmpPageFull3}{\hidepaste} \tab{5}\spadcommand{q := (1 - 6*x + 9*x**2)**2\free{qdec }\bound{q }} \indentrel{3}\begin{verbatim} 4 3 2 (3) 81x - 108x + 54x - 12x + 1 Type: UnivariatePolynomial(x,Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty3} \begin{paste}{UnivariatePolynomialXmpPageEmpty3}{UnivariatePolynomialXmpPagePatch3} \pastebutton{UnivariatePolynomialXmpPageEmpty3}{\showpaste} \tab{5}\spadcommand{q := (1 - 6*x + 9*x**2)**2\free{qdec }\bound{q }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch4} \begin{paste}{UnivariatePolynomialXmpPageFull4}{UnivariatePolynomialXmpPageEmpty4} \pastebutton{UnivariatePolynomialXmpPageFull4}{\hidepaste} \tab{5}\spadcommand{p**2 + p*q\free{p q }} \indentrel{3}\begin{verbatim} (4) 7 6 5 4 3 2 1458x + 3240x - 7074x + 10584x - 9282x + 4120x + - 878x + 72 Type: UnivariatePolynomial(x,Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty4} \begin{paste}{UnivariatePolynomialXmpPageEmpty4}{UnivariatePolynomialXmpPagePatch4} \pastebutton{UnivariatePolynomialXmpPageEmpty4}{\showpaste} \tab{5}\spadcommand{p**2 + p*q\free{p q }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch5} \begin{paste}{UnivariatePolynomialXmpPageFull5}{UnivariatePolynomialXmpPageEmpty5} \pastebutton{UnivariatePolynomialXmpPageFull5}{\hidepaste} \tab{5}\spadcommand{leadingCoefficient p\free{p }} \indentrel{3}\begin{verbatim} (5) 18 Type: PositiveInteger \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty5} \begin{paste}{UnivariatePolynomialXmpPageEmpty5}{UnivariatePolynomialXmpPagePatch5} \pastebutton{UnivariatePolynomialXmpPageEmpty5}{\showpaste} \tab{5}\spadcommand{leadingCoefficient p\free{p }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch6} \begin{paste}{UnivariatePolynomialXmpPageFull6}{UnivariatePolynomialXmpPageEmpty6} \pastebutton{UnivariatePolynomialXmpPageFull6}{\hidepaste} \tab{5}\spadcommand{degree p\free{p }} \indentrel{3}\begin{verbatim} (6) 3 Type: PositiveInteger \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty6} \begin{paste}{UnivariatePolynomialXmpPageEmpty6}{UnivariatePolynomialXmpPagePatch6} \pastebutton{UnivariatePolynomialXmpPageEmpty6}{\showpaste} \tab{5}\spadcommand{degree p\free{p }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch7} \begin{paste}{UnivariatePolynomialXmpPageFull7}{UnivariatePolynomialXmpPageEmpty7} \pastebutton{UnivariatePolynomialXmpPageFull7}{\hidepaste} \tab{5}\spadcommand{reductum p\free{p }} \indentrel{3}\begin{verbatim} 2 (7) 60x - 46x + 8 Type: UnivariatePolynomial(x,Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty7} \begin{paste}{UnivariatePolynomialXmpPageEmpty7}{UnivariatePolynomialXmpPagePatch7} \pastebutton{UnivariatePolynomialXmpPageEmpty7}{\showpaste} \tab{5}\spadcommand{reductum p\free{p }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch8} \begin{paste}{UnivariatePolynomialXmpPageFull8}{UnivariatePolynomialXmpPageEmpty8} \pastebutton{UnivariatePolynomialXmpPageFull8}{\hidepaste} \tab{5}\spadcommand{gcd(p,q)\free{p q }} \indentrel{3}\begin{verbatim} 2 (8) 9x - 6x + 1 Type: UnivariatePolynomial(x,Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty8} \begin{paste}{UnivariatePolynomialXmpPageEmpty8}{UnivariatePolynomialXmpPagePatch8} \pastebutton{UnivariatePolynomialXmpPageEmpty8}{\showpaste} \tab{5}\spadcommand{gcd(p,q)\free{p q }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch9} \begin{paste}{UnivariatePolynomialXmpPageFull9}{UnivariatePolynomialXmpPageEmpty9} \pastebutton{UnivariatePolynomialXmpPageFull9}{\hidepaste} \tab{5}\spadcommand{lcm(p,q)\free{p q }} \indentrel{3}\begin{verbatim} 5 4 3 2 (9) 162x + 432x - 756x + 408x - 94x + 8 Type: UnivariatePolynomial(x,Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty9} \begin{paste}{UnivariatePolynomialXmpPageEmpty9}{UnivariatePolynomialXmpPagePatch9} \pastebutton{UnivariatePolynomialXmpPageEmpty9}{\showpaste} \tab{5}\spadcommand{lcm(p,q)\free{p q }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch10} \begin{paste}{UnivariatePolynomialXmpPageFull10}{UnivariatePolynomialXmpPageEmpty10} \pastebutton{UnivariatePolynomialXmpPageFull10}{\hidepaste} \tab{5}\spadcommand{resultant(p,q)\free{p q }} \indentrel{3}\begin{verbatim} (10) 0 Type: NonNegativeInteger \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty10} \begin{paste}{UnivariatePolynomialXmpPageEmpty10}{UnivariatePolynomialXmpPagePatch10} \pastebutton{UnivariatePolynomialXmpPageEmpty10}{\showpaste} \tab{5}\spadcommand{resultant(p,q)\free{p q }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch11} \begin{paste}{UnivariatePolynomialXmpPageFull11}{UnivariatePolynomialXmpPageEmpty11} \pastebutton{UnivariatePolynomialXmpPageFull11}{\hidepaste} \tab{5}\spadcommand{D p\free{p }} \indentrel{3}\begin{verbatim} 2 (11) 54x + 120x - 46 Type: UnivariatePolynomial(x,Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty11} \begin{paste}{UnivariatePolynomialXmpPageEmpty11}{UnivariatePolynomialXmpPagePatch11} \pastebutton{UnivariatePolynomialXmpPageEmpty11}{\showpaste} \tab{5}\spadcommand{D p\free{p }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch12} \begin{paste}{UnivariatePolynomialXmpPageFull12}{UnivariatePolynomialXmpPageEmpty12} \pastebutton{UnivariatePolynomialXmpPageFull12}{\hidepaste} \tab{5}\spadcommand{p(2)\free{p }} \indentrel{3}\begin{verbatim} (12) 300 Type: PositiveInteger \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty12} \begin{paste}{UnivariatePolynomialXmpPageEmpty12}{UnivariatePolynomialXmpPagePatch12} \pastebutton{UnivariatePolynomialXmpPageEmpty12}{\showpaste} \tab{5}\spadcommand{p(2)\free{p }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch13} \begin{paste}{UnivariatePolynomialXmpPageFull13}{UnivariatePolynomialXmpPageEmpty13} \pastebutton{UnivariatePolynomialXmpPageFull13}{\hidepaste} \tab{5}\spadcommand{p(q)\free{p q }} \indentrel{3}\begin{verbatim} (13) 12 11 10 9 9565938x - 38263752x + 70150212x - 77944680x + 8 7 6 5 58852170x - 32227632x + 13349448x - 4280688x + 4 3 2 1058184x - 192672x + 23328x - 1536x + 40 Type: UnivariatePolynomial(x,Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty13} \begin{paste}{UnivariatePolynomialXmpPageEmpty13}{UnivariatePolynomialXmpPagePatch13} \pastebutton{UnivariatePolynomialXmpPageEmpty13}{\showpaste} \tab{5}\spadcommand{p(q)\free{p q }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch14} \begin{paste}{UnivariatePolynomialXmpPageFull14}{UnivariatePolynomialXmpPageEmpty14} \pastebutton{UnivariatePolynomialXmpPageFull14}{\hidepaste} \tab{5}\spadcommand{q(p)\free{p q }} \indentrel{3}\begin{verbatim} (14) 12 11 10 8503056x + 113374080x + 479950272x + 9 8 7 404997408x - 1369516896x - 626146848x + 6 5 4 2939858712x - 2780728704x + 1364312160x + 3 2 - 396838872x + 69205896x - 6716184x + 279841 Type: UnivariatePolynomial(x,Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty14} \begin{paste}{UnivariatePolynomialXmpPageEmpty14}{UnivariatePolynomialXmpPagePatch14} \pastebutton{UnivariatePolynomialXmpPageEmpty14}{\showpaste} \tab{5}\spadcommand{q(p)\free{p q }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch15} \begin{paste}{UnivariatePolynomialXmpPageFull15}{UnivariatePolynomialXmpPageEmpty15} \pastebutton{UnivariatePolynomialXmpPageFull15}{\hidepaste} \tab{5}\spadcommand{l := coefficients p\free{p }\bound{l }} \indentrel{3}\begin{verbatim} (15) [18,60,- 46,8] Type: List Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty15} \begin{paste}{UnivariatePolynomialXmpPageEmpty15}{UnivariatePolynomialXmpPagePatch15} \pastebutton{UnivariatePolynomialXmpPageEmpty15}{\showpaste} \tab{5}\spadcommand{l := coefficients p\free{p }\bound{l }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch16} \begin{paste}{UnivariatePolynomialXmpPageFull16}{UnivariatePolynomialXmpPageEmpty16} \pastebutton{UnivariatePolynomialXmpPageFull16}{\hidepaste} \tab{5}\spadcommand{reduce(gcd,l)\free{l }} \indentrel{3}\begin{verbatim} (16) 2 Type: PositiveInteger \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty16} \begin{paste}{UnivariatePolynomialXmpPageEmpty16}{UnivariatePolynomialXmpPagePatch16} \pastebutton{UnivariatePolynomialXmpPageEmpty16}{\showpaste} \tab{5}\spadcommand{reduce(gcd,l)\free{l }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch17} \begin{paste}{UnivariatePolynomialXmpPageFull17}{UnivariatePolynomialXmpPageEmpty17} \pastebutton{UnivariatePolynomialXmpPageFull17}{\hidepaste} \tab{5}\spadcommand{content p\free{p }} \indentrel{3}\begin{verbatim} (17) 2 Type: PositiveInteger \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty17} \begin{paste}{UnivariatePolynomialXmpPageEmpty17}{UnivariatePolynomialXmpPagePatch17} \pastebutton{UnivariatePolynomialXmpPageEmpty17}{\showpaste} \tab{5}\spadcommand{content p\free{p }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch18} \begin{paste}{UnivariatePolynomialXmpPageFull18}{UnivariatePolynomialXmpPageEmpty18} \pastebutton{UnivariatePolynomialXmpPageFull18}{\hidepaste} \tab{5}\spadcommand{ux := (x**4+2*x+3)::UP(x,INT)\bound{ux }} \indentrel{3}\begin{verbatim} 4 (18) x + 2x + 3 Type: UnivariatePolynomial(x,Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty18} \begin{paste}{UnivariatePolynomialXmpPageEmpty18}{UnivariatePolynomialXmpPagePatch18} \pastebutton{UnivariatePolynomialXmpPageEmpty18}{\showpaste} \tab{5}\spadcommand{ux := (x**4+2*x+3)::UP(x,INT)\bound{ux }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch19} \begin{paste}{UnivariatePolynomialXmpPageFull19}{UnivariatePolynomialXmpPageEmpty19} \pastebutton{UnivariatePolynomialXmpPageFull19}{\hidepaste} \tab{5}\spadcommand{vectorise(ux,5)\free{ux }} \indentrel{3}\begin{verbatim} (19) [3,2,0,0,1] Type: Vector Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty19} \begin{paste}{UnivariatePolynomialXmpPageEmpty19}{UnivariatePolynomialXmpPagePatch19} \pastebutton{UnivariatePolynomialXmpPageEmpty19}{\showpaste} \tab{5}\spadcommand{vectorise(ux,5)\free{ux }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch20} \begin{paste}{UnivariatePolynomialXmpPageFull20}{UnivariatePolynomialXmpPageEmpty20} \pastebutton{UnivariatePolynomialXmpPageFull20}{\hidepaste} \tab{5}\spadcommand{squareTerms(p) == reduce(+,[t**2 for t in monomials p]) \bound{squareTerms }} \indentrel{3}\begin{verbatim} Type: Void \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty20} \begin{paste}{UnivariatePolynomialXmpPageEmpty20}{UnivariatePolynomialXmpPagePatch20} \pastebutton{UnivariatePolynomialXmpPageEmpty20}{\showpaste} \tab{5}\spadcommand{squareTerms(p) == reduce(+,[t**2 for t in monomials p]) \bound{squareTerms }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch21} \begin{paste}{UnivariatePolynomialXmpPageFull21}{UnivariatePolynomialXmpPageEmpty21} \pastebutton{UnivariatePolynomialXmpPageFull21}{\hidepaste} \tab{5}\spadcommand{p\free{p }} \indentrel{3}\begin{verbatim} 3 2 (21) 18x + 60x - 46x + 8 Type: UnivariatePolynomial(x,Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty21} \begin{paste}{UnivariatePolynomialXmpPageEmpty21}{UnivariatePolynomialXmpPagePatch21} \pastebutton{UnivariatePolynomialXmpPageEmpty21}{\showpaste} \tab{5}\spadcommand{p\free{p }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch22} \begin{paste}{UnivariatePolynomialXmpPageFull22}{UnivariatePolynomialXmpPageEmpty22} \pastebutton{UnivariatePolynomialXmpPageFull22}{\hidepaste} \tab{5}\spadcommand{squareTerms p\free{p }\free{squareTerms }} \indentrel{3}\begin{verbatim} 6 4 2 (22) 324x + 3600x + 2116x + 64 Type: UnivariatePolynomial(x,Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty22} \begin{paste}{UnivariatePolynomialXmpPageEmpty22}{UnivariatePolynomialXmpPagePatch22} \pastebutton{UnivariatePolynomialXmpPageEmpty22}{\showpaste} \tab{5}\spadcommand{squareTerms p\free{p }\free{squareTerms }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch23} \begin{paste}{UnivariatePolynomialXmpPageFull23}{UnivariatePolynomialXmpPageEmpty23} \pastebutton{UnivariatePolynomialXmpPageFull23}{\hidepaste} \tab{5}\spadcommand{(r,s) : UP(a1,FRAC INT)\bound{rdec }\bound{sdec }} \indentrel{3}\begin{verbatim} Type: Void \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty23} \begin{paste}{UnivariatePolynomialXmpPageEmpty23}{UnivariatePolynomialXmpPagePatch23} \pastebutton{UnivariatePolynomialXmpPageEmpty23}{\showpaste} \tab{5}\spadcommand{(r,s) : UP(a1,FRAC INT)\bound{rdec }\bound{sdec }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch24} \begin{paste}{UnivariatePolynomialXmpPageFull24}{UnivariatePolynomialXmpPageEmpty24} \pastebutton{UnivariatePolynomialXmpPageFull24}{\hidepaste} \tab{5}\spadcommand{r := a1**2 - 2/3\free{rdec }\bound{r }} \indentrel{3}\begin{verbatim} 2 2 (24) a1 - Ä 3 Type: UnivariatePolynomial(a1,Fraction Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty24} \begin{paste}{UnivariatePolynomialXmpPageEmpty24}{UnivariatePolynomialXmpPagePatch24} \pastebutton{UnivariatePolynomialXmpPageEmpty24}{\showpaste} \tab{5}\spadcommand{r := a1**2 - 2/3\free{rdec }\bound{r }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch25} \begin{paste}{UnivariatePolynomialXmpPageFull25}{UnivariatePolynomialXmpPageEmpty25} \pastebutton{UnivariatePolynomialXmpPageFull25}{\hidepaste} \tab{5}\spadcommand{s := a1 + 4\free{sdec }\bound{s }} \indentrel{3}\begin{verbatim} (25) a1 + 4 Type: UnivariatePolynomial(a1,Fraction Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty25} \begin{paste}{UnivariatePolynomialXmpPageEmpty25}{UnivariatePolynomialXmpPagePatch25} \pastebutton{UnivariatePolynomialXmpPageEmpty25}{\showpaste} \tab{5}\spadcommand{s := a1 + 4\free{sdec }\bound{s }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch26} \begin{paste}{UnivariatePolynomialXmpPageFull26}{UnivariatePolynomialXmpPageEmpty26} \pastebutton{UnivariatePolynomialXmpPageFull26}{\hidepaste} \tab{5}\spadcommand{r quo s\free{r s }} \indentrel{3}\begin{verbatim} (26) a1 - 4 Type: UnivariatePolynomial(a1,Fraction Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty26} \begin{paste}{UnivariatePolynomialXmpPageEmpty26}{UnivariatePolynomialXmpPagePatch26} \pastebutton{UnivariatePolynomialXmpPageEmpty26}{\showpaste} \tab{5}\spadcommand{r quo s\free{r s }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch27} \begin{paste}{UnivariatePolynomialXmpPageFull27}{UnivariatePolynomialXmpPageEmpty27} \pastebutton{UnivariatePolynomialXmpPageFull27}{\hidepaste} \tab{5}\spadcommand{r rem s\free{r s }} \indentrel{3}\begin{verbatim} 46 (27) ÄÄ 3 Type: UnivariatePolynomial(a1,Fraction Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty27} \begin{paste}{UnivariatePolynomialXmpPageEmpty27}{UnivariatePolynomialXmpPagePatch27} \pastebutton{UnivariatePolynomialXmpPageEmpty27}{\showpaste} \tab{5}\spadcommand{r rem s\free{r s }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch28} \begin{paste}{UnivariatePolynomialXmpPageFull28}{UnivariatePolynomialXmpPageEmpty28} \pastebutton{UnivariatePolynomialXmpPageFull28}{\hidepaste} \tab{5}\spadcommand{d := divide(r, s)\free{r s }\bound{d }} \indentrel{3}\begin{verbatim} 46 (28) [quotient= a1 - 4,remainder= ÄÄ] 3 Type: Record(quotient: UnivariatePolynomial(a1,Fraction Integer),remainder: UnivariatePolynomial(a1,Fraction Integer)) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty28} \begin{paste}{UnivariatePolynomialXmpPageEmpty28}{UnivariatePolynomialXmpPagePatch28} \pastebutton{UnivariatePolynomialXmpPageEmpty28}{\showpaste} \tab{5}\spadcommand{d := divide(r, s)\free{r s }\bound{d }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch29} \begin{paste}{UnivariatePolynomialXmpPageFull29}{UnivariatePolynomialXmpPageEmpty29} \pastebutton{UnivariatePolynomialXmpPageFull29}{\hidepaste} \tab{5}\spadcommand{r - (d.quotient * s + d.remainder)\free{r s d }} \indentrel{3}\begin{verbatim} (29) 0 Type: UnivariatePolynomial(a1,Fraction Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty29} \begin{paste}{UnivariatePolynomialXmpPageEmpty29}{UnivariatePolynomialXmpPagePatch29} \pastebutton{UnivariatePolynomialXmpPageEmpty29}{\showpaste} \tab{5}\spadcommand{r - (d.quotient * s + d.remainder)\free{r s d }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch30} \begin{paste}{UnivariatePolynomialXmpPageFull30}{UnivariatePolynomialXmpPageEmpty30} \pastebutton{UnivariatePolynomialXmpPageFull30}{\hidepaste} \tab{5}\spadcommand{integrate r\free{r }} \indentrel{3}\begin{verbatim} 1 3 2 (30) Ä a1 - Ä a1 3 3 Type: UnivariatePolynomial(a1,Fraction Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty30} \begin{paste}{UnivariatePolynomialXmpPageEmpty30}{UnivariatePolynomialXmpPagePatch30} \pastebutton{UnivariatePolynomialXmpPageEmpty30}{\showpaste} \tab{5}\spadcommand{integrate r\free{r }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch31} \begin{paste}{UnivariatePolynomialXmpPageFull31}{UnivariatePolynomialXmpPageEmpty31} \pastebutton{UnivariatePolynomialXmpPageFull31}{\hidepaste} \tab{5}\spadcommand{integrate s\free{s }} \indentrel{3}\begin{verbatim} 1 2 (31) Ä a1 + 4a1 2 Type: UnivariatePolynomial(a1,Fraction Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty31} \begin{paste}{UnivariatePolynomialXmpPageEmpty31}{UnivariatePolynomialXmpPagePatch31} \pastebutton{UnivariatePolynomialXmpPageEmpty31}{\showpaste} \tab{5}\spadcommand{integrate s\free{s }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch32} \begin{paste}{UnivariatePolynomialXmpPageFull32}{UnivariatePolynomialXmpPageEmpty32} \pastebutton{UnivariatePolynomialXmpPageFull32}{\hidepaste} \tab{5}\spadcommand{t : UP(a1,FRAC POLY INT)\bound{tdec }} \indentrel{3}\begin{verbatim} Type: Void \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty32} \begin{paste}{UnivariatePolynomialXmpPageEmpty32}{UnivariatePolynomialXmpPagePatch32} \pastebutton{UnivariatePolynomialXmpPageEmpty32}{\showpaste} \tab{5}\spadcommand{t : UP(a1,FRAC POLY INT)\bound{tdec }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch33} \begin{paste}{UnivariatePolynomialXmpPageFull33}{UnivariatePolynomialXmpPageEmpty33} \pastebutton{UnivariatePolynomialXmpPageFull33}{\hidepaste} \tab{5}\spadcommand{t := a1**2 - a1/b2 + (b1**2-b1)/(b2+3)\free{tdec }\bound{t }} \indentrel{3}\begin{verbatim} 2 2 1 b1 - b1 (33) a1 - ÄÄ a1 + ÄÄÄÄÄÄÄÄ b2 b2 + 3 Type: UnivariatePolynomial(a1,Fraction Polynomial Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty33} \begin{paste}{UnivariatePolynomialXmpPageEmpty33}{UnivariatePolynomialXmpPagePatch33} \pastebutton{UnivariatePolynomialXmpPageEmpty33}{\showpaste} \tab{5}\spadcommand{t := a1**2 - a1/b2 + (b1**2-b1)/(b2+3)\free{tdec }\bound{t }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch34} \begin{paste}{UnivariatePolynomialXmpPageFull34}{UnivariatePolynomialXmpPageEmpty34} \pastebutton{UnivariatePolynomialXmpPageFull34}{\hidepaste} \tab{5}\spadcommand{u : FRAC POLY INT := t\bound{u }\free{t }} \indentrel{3}\begin{verbatim} 2 2 2 2 a1 b2 + (b1 - b1 + 3a1 - a1)b2 - 3a1 (34) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ 2 b2 + 3b2 Type: Fraction Polynomial Integer \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty34} \begin{paste}{UnivariatePolynomialXmpPageEmpty34}{UnivariatePolynomialXmpPagePatch34} \pastebutton{UnivariatePolynomialXmpPageEmpty34}{\showpaste} \tab{5}\spadcommand{u : FRAC POLY INT := t\bound{u }\free{t }} \end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPagePatch35} \begin{paste}{UnivariatePolynomialXmpPageFull35}{UnivariatePolynomialXmpPageEmpty35} \pastebutton{UnivariatePolynomialXmpPageFull35}{\hidepaste} \tab{5}\spadcommand{u :: UP(b1,?)\free{u }} \indentrel{3}\begin{verbatim} 2 1 2 1 a1 b2 - a1 (35) ÄÄÄÄÄÄ b1 - ÄÄÄÄÄÄ b1 + ÄÄÄÄÄÄÄÄÄÄ b2 + 3 b2 + 3 b2 Type: UnivariatePolynomial(b1,Fraction Polynomial Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{UnivariatePolynomialXmpPageEmpty35} \begin{paste}{UnivariatePolynomialXmpPageEmpty35}{UnivariatePolynomialXmpPagePatch35} \pastebutton{UnivariatePolynomialXmpPageEmpty35}{\showpaste} \tab{5}\spadcommand{u :: UP(b1,?)\free{u }} \end{paste}\end{patch}