1\begin{patch}{XPolynomialXmpPagePatch1} 2\begin{paste}{XPolynomialXmpPageFull1}{XPolynomialXmpPageEmpty1} 3\pastebutton{XPolynomialXmpPageFull1}{\hidepaste} 4\tab{5}\spadcommand{poly := XPolynomial(Integer)\bound{poly }} 5\indentrel{3}\begin{verbatim} 6 (1) XPolynomial(Integer) 7 Type: Type 8\end{verbatim} 9\indentrel{-3}\end{paste}\end{patch} 10 11\begin{patch}{XPolynomialXmpPageEmpty1} 12\begin{paste}{XPolynomialXmpPageEmpty1}{XPolynomialXmpPagePatch1} 13\pastebutton{XPolynomialXmpPageEmpty1}{\showpaste} 14\tab{5}\spadcommand{poly := XPolynomial(Integer)\bound{poly }} 15\end{paste}\end{patch} 16 17\begin{patch}{XPolynomialXmpPagePatch2} 18\begin{paste}{XPolynomialXmpPageFull2}{XPolynomialXmpPageEmpty2} 19\pastebutton{XPolynomialXmpPageFull2}{\hidepaste} 20\tab{5}\spadcommand{pr: poly := 2*x + 3*y-5\free{poly }\bound{pr }} 21\indentrel{3}\begin{verbatim} 22 (2) - 5 + x 2 + y 3 23 Type: XPolynomial(Integer) 24\end{verbatim} 25\indentrel{-3}\end{paste}\end{patch} 26 27\begin{patch}{XPolynomialXmpPageEmpty2} 28\begin{paste}{XPolynomialXmpPageEmpty2}{XPolynomialXmpPagePatch2} 29\pastebutton{XPolynomialXmpPageEmpty2}{\showpaste} 30\tab{5}\spadcommand{pr: poly := 2*x + 3*y-5\free{poly }\bound{pr }} 31\end{paste}\end{patch} 32 33\begin{patch}{XPolynomialXmpPagePatch3} 34\begin{paste}{XPolynomialXmpPageFull3}{XPolynomialXmpPageEmpty3} 35\pastebutton{XPolynomialXmpPageFull3}{\hidepaste} 36\tab{5}\spadcommand{pr2: poly := pr*pr\free{poly }\bound{pr2 }} 37\indentrel{3}\begin{verbatim} 38 (3) 25 + x(- 20 + x 4 + y 6) + y(- 30 + x 6 + y 9) 39 Type: XPolynomial(Integer) 40\end{verbatim} 41\indentrel{-3}\end{paste}\end{patch} 42 43\begin{patch}{XPolynomialXmpPageEmpty3} 44\begin{paste}{XPolynomialXmpPageEmpty3}{XPolynomialXmpPagePatch3} 45\pastebutton{XPolynomialXmpPageEmpty3}{\showpaste} 46\tab{5}\spadcommand{pr2: poly := pr*pr\free{poly }\bound{pr2 }} 47\end{paste}\end{patch} 48 49\begin{patch}{XPolynomialXmpPagePatch4} 50\begin{paste}{XPolynomialXmpPageFull4}{XPolynomialXmpPageEmpty4} 51\pastebutton{XPolynomialXmpPageFull4}{\hidepaste} 52\tab{5}\spadcommand{pd := expand pr\free{pr }\bound{pd }} 53\indentrel{3}\begin{verbatim} 54 (4) - 5 + 2 x + 3 y 55 Type: XDistributedPolynomial(Symbol,Integer) 56\end{verbatim} 57\indentrel{-3}\end{paste}\end{patch} 58 59\begin{patch}{XPolynomialXmpPageEmpty4} 60\begin{paste}{XPolynomialXmpPageEmpty4}{XPolynomialXmpPagePatch4} 61\pastebutton{XPolynomialXmpPageEmpty4}{\showpaste} 62\tab{5}\spadcommand{pd := expand pr\free{pr }\bound{pd }} 63\end{paste}\end{patch} 64 65\begin{patch}{XPolynomialXmpPagePatch5} 66\begin{paste}{XPolynomialXmpPageFull5}{XPolynomialXmpPageEmpty5} 67\pastebutton{XPolynomialXmpPageFull5}{\hidepaste} 68\tab{5}\spadcommand{pd2 := pd*pd\free{pd }\bound{pd2 }} 69\indentrel{3}\begin{verbatim} 70 2 2 71 (5) 25 - 20 x - 30 y + 4 x + 6 x y + 6 y x + 9 y 72 Type: XDistributedPolynomial(Symbol,Integer) 73\end{verbatim} 74\indentrel{-3}\end{paste}\end{patch} 75 76\begin{patch}{XPolynomialXmpPageEmpty5} 77\begin{paste}{XPolynomialXmpPageEmpty5}{XPolynomialXmpPagePatch5} 78\pastebutton{XPolynomialXmpPageEmpty5}{\showpaste} 79\tab{5}\spadcommand{pd2 := pd*pd\free{pd }\bound{pd2 }} 80\end{paste}\end{patch} 81 82\begin{patch}{XPolynomialXmpPagePatch6} 83\begin{paste}{XPolynomialXmpPageFull6}{XPolynomialXmpPageEmpty6} 84\pastebutton{XPolynomialXmpPageFull6}{\hidepaste} 85\tab{5}\spadcommand{expand(pr2) - pd2\free{pr2 }\free{pd2 }} 86\indentrel{3}\begin{verbatim} 87 (6) 0 88 Type: XDistributedPolynomial(Symbol,Integer) 89\end{verbatim} 90\indentrel{-3}\end{paste}\end{patch} 91 92\begin{patch}{XPolynomialXmpPageEmpty6} 93\begin{paste}{XPolynomialXmpPageEmpty6}{XPolynomialXmpPagePatch6} 94\pastebutton{XPolynomialXmpPageEmpty6}{\showpaste} 95\tab{5}\spadcommand{expand(pr2) - pd2\free{pr2 }\free{pd2 }} 96\end{paste}\end{patch} 97 98\begin{patch}{XPolynomialXmpPagePatch7} 99\begin{paste}{XPolynomialXmpPageFull7}{XPolynomialXmpPageEmpty7} 100\pastebutton{XPolynomialXmpPageFull7}{\hidepaste} 101\tab{5}\spadcommand{qr := pr^3\free{pr }\bound{qr }} 102\indentrel{3}\begin{verbatim} 103 (7) 104 - 125 105 + 106 x(150 + x(- 60 + x 8 + y 12) + y(- 90 + x 12 + y 18)) 107 + 108 y(225 + x(- 90 + x 12 + y 18) + y(- 135 + x 18 + y 27)) 109 Type: XPolynomial(Integer) 110\end{verbatim} 111\indentrel{-3}\end{paste}\end{patch} 112 113\begin{patch}{XPolynomialXmpPageEmpty7} 114\begin{paste}{XPolynomialXmpPageEmpty7}{XPolynomialXmpPagePatch7} 115\pastebutton{XPolynomialXmpPageEmpty7}{\showpaste} 116\tab{5}\spadcommand{qr := pr^3\free{pr }\bound{qr }} 117\end{paste}\end{patch} 118 119\begin{patch}{XPolynomialXmpPagePatch8} 120\begin{paste}{XPolynomialXmpPageFull8}{XPolynomialXmpPageEmpty8} 121\pastebutton{XPolynomialXmpPageFull8}{\hidepaste} 122\tab{5}\spadcommand{qd := pd^3\free{pd }\bound{qd }} 123\indentrel{3}\begin{verbatim} 124 (8) 125 2 126 - 125 + 150 x + 225 y - 60 x - 90 x y - 90 y x 127 + 128 2 3 2 2 129 - 135 y + 8 x + 12 x y + 12 x y x + 18 x y 130 + 131 2 2 3 132 12 y x + 18 y x y + 18 y x + 27 y 133 Type: XDistributedPolynomial(Symbol,Integer) 134\end{verbatim} 135\indentrel{-3}\end{paste}\end{patch} 136 137\begin{patch}{XPolynomialXmpPageEmpty8} 138\begin{paste}{XPolynomialXmpPageEmpty8}{XPolynomialXmpPagePatch8} 139\pastebutton{XPolynomialXmpPageEmpty8}{\showpaste} 140\tab{5}\spadcommand{qd := pd^3\free{pd }\bound{qd }} 141\end{paste}\end{patch} 142 143\begin{patch}{XPolynomialXmpPagePatch9} 144\begin{paste}{XPolynomialXmpPageFull9}{XPolynomialXmpPageEmpty9} 145\pastebutton{XPolynomialXmpPageFull9}{\hidepaste} 146\tab{5}\spadcommand{trunc(qd,2)\free{qd }} 147\indentrel{3}\begin{verbatim} 148 (9) 149 2 150 - 125 + 150 x + 225 y - 60 x - 90 x y - 90 y x 151 + 152 2 153 - 135 y 154 Type: XDistributedPolynomial(Symbol,Integer) 155\end{verbatim} 156\indentrel{-3}\end{paste}\end{patch} 157 158\begin{patch}{XPolynomialXmpPageEmpty9} 159\begin{paste}{XPolynomialXmpPageEmpty9}{XPolynomialXmpPagePatch9} 160\pastebutton{XPolynomialXmpPageEmpty9}{\showpaste} 161\tab{5}\spadcommand{trunc(qd,2)\free{qd }} 162\end{paste}\end{patch} 163 164\begin{patch}{XPolynomialXmpPagePatch10} 165\begin{paste}{XPolynomialXmpPageFull10}{XPolynomialXmpPageEmpty10} 166\pastebutton{XPolynomialXmpPageFull10}{\hidepaste} 167\tab{5}\spadcommand{trunc(qr,2)\free{qr }} 168\indentrel{3}\begin{verbatim} 169 (10) 170 - 125 + x(150 + x(- 60) + y(- 90)) 171 + 172 y(225 + x(- 90) + y(- 135)) 173 Type: XPolynomial(Integer) 174\end{verbatim} 175\indentrel{-3}\end{paste}\end{patch} 176 177\begin{patch}{XPolynomialXmpPageEmpty10} 178\begin{paste}{XPolynomialXmpPageEmpty10}{XPolynomialXmpPagePatch10} 179\pastebutton{XPolynomialXmpPageEmpty10}{\showpaste} 180\tab{5}\spadcommand{trunc(qr,2)\free{qr }} 181\end{paste}\end{patch} 182 183\begin{patch}{XPolynomialXmpPagePatch11} 184\begin{paste}{XPolynomialXmpPageFull11}{XPolynomialXmpPageEmpty11} 185\pastebutton{XPolynomialXmpPageFull11}{\hidepaste} 186\tab{5}\spadcommand{Word := FreeMonoid Symbol\bound{Word }} 187\indentrel{3}\begin{verbatim} 188 (11) FreeMonoid(Symbol) 189 Type: Type 190\end{verbatim} 191\indentrel{-3}\end{paste}\end{patch} 192 193\begin{patch}{XPolynomialXmpPageEmpty11} 194\begin{paste}{XPolynomialXmpPageEmpty11}{XPolynomialXmpPagePatch11} 195\pastebutton{XPolynomialXmpPageEmpty11}{\showpaste} 196\tab{5}\spadcommand{Word := FreeMonoid Symbol\bound{Word }} 197\end{paste}\end{patch} 198 199\begin{patch}{XPolynomialXmpPagePatch12} 200\begin{paste}{XPolynomialXmpPageFull12}{XPolynomialXmpPageEmpty12} 201\pastebutton{XPolynomialXmpPageFull12}{\hidepaste} 202\tab{5}\spadcommand{w: Word := x*y^2\free{Word }\bound{w }} 203\indentrel{3}\begin{verbatim} 204 2 205 (12) x y 206 Type: FreeMonoid(Symbol) 207\end{verbatim} 208\indentrel{-3}\end{paste}\end{patch} 209 210\begin{patch}{XPolynomialXmpPageEmpty12} 211\begin{paste}{XPolynomialXmpPageEmpty12}{XPolynomialXmpPagePatch12} 212\pastebutton{XPolynomialXmpPageEmpty12}{\showpaste} 213\tab{5}\spadcommand{w: Word := x*y^2\free{Word }\bound{w }} 214\end{paste}\end{patch} 215 216\begin{patch}{XPolynomialXmpPagePatch13} 217\begin{paste}{XPolynomialXmpPageFull13}{XPolynomialXmpPageEmpty13} 218\pastebutton{XPolynomialXmpPageFull13}{\hidepaste} 219\tab{5}\spadcommand{rquo(qr,w)\free{qr }\free{w }} 220\indentrel{3}\begin{verbatim} 221 (13) 18 222 Type: XPolynomial(Integer) 223\end{verbatim} 224\indentrel{-3}\end{paste}\end{patch} 225 226\begin{patch}{XPolynomialXmpPageEmpty13} 227\begin{paste}{XPolynomialXmpPageEmpty13}{XPolynomialXmpPagePatch13} 228\pastebutton{XPolynomialXmpPageEmpty13}{\showpaste} 229\tab{5}\spadcommand{rquo(qr,w)\free{qr }\free{w }} 230\end{paste}\end{patch} 231 232\begin{patch}{XPolynomialXmpPagePatch14} 233\begin{paste}{XPolynomialXmpPageFull14}{XPolynomialXmpPageEmpty14} 234\pastebutton{XPolynomialXmpPageFull14}{\hidepaste} 235\tab{5}\spadcommand{sh(pr,w::poly)\free{pr }\free{w }} 236\indentrel{3}\begin{verbatim} 237 (14) 238 x(x y y 4 + y(x y 2 + y(- 5 + x 2 + y 9))) + y x y y 3 239 Type: XPolynomial(Integer) 240\end{verbatim} 241\indentrel{-3}\end{paste}\end{patch} 242 243\begin{patch}{XPolynomialXmpPageEmpty14} 244\begin{paste}{XPolynomialXmpPageEmpty14}{XPolynomialXmpPagePatch14} 245\pastebutton{XPolynomialXmpPageEmpty14}{\showpaste} 246\tab{5}\spadcommand{sh(pr,w::poly)\free{pr }\free{w }} 247\end{paste}\end{patch} 248 249