1\begin{patch}{PartialFractionXmpPagePatch1}
2\begin{paste}{PartialFractionXmpPageFull1}{PartialFractionXmpPageEmpty1}
3\pastebutton{PartialFractionXmpPageFull1}{\hidepaste}
4\tab{5}\spadcommand{partialFraction(1,factorial 10)\bound{prev1 }}
5\indentrel{3}\begin{verbatim}
6        159   23   12   1
7   (1)  --- - -- - -- + -
8          8    4    2   7
9         2    3    5
10                         Type: PartialFraction(Integer)
11\end{verbatim}
12\indentrel{-3}\end{paste}\end{patch}
13
14\begin{patch}{PartialFractionXmpPageEmpty1}
15\begin{paste}{PartialFractionXmpPageEmpty1}{PartialFractionXmpPagePatch1}
16\pastebutton{PartialFractionXmpPageEmpty1}{\showpaste}
17\tab{5}\spadcommand{partialFraction(1,factorial 10)\bound{prev1 }}
18\end{paste}\end{patch}
19
20\begin{patch}{PartialFractionXmpPagePatch2}
21\begin{paste}{PartialFractionXmpPageFull2}{PartialFractionXmpPageEmpty2}
22\pastebutton{PartialFractionXmpPageFull2}{\hidepaste}
23\tab{5}\spadcommand{f := padicFraction(\%)\free{prev1 }\bound{f }}
24\indentrel{3}\begin{verbatim}
25   (2)
26   1    1    1    1    1    1    2    1    2   2    2   1
27   - + -- + -- + -- + -- + -- - -- - -- - -- - - - -- + -
28   2    4    5    6    7    8    2    3    4   5    2   7
29       2    2    2    2    2    3    3    3        5
30                         Type: PartialFraction(Integer)
31\end{verbatim}
32\indentrel{-3}\end{paste}\end{patch}
33
34\begin{patch}{PartialFractionXmpPageEmpty2}
35\begin{paste}{PartialFractionXmpPageEmpty2}{PartialFractionXmpPagePatch2}
36\pastebutton{PartialFractionXmpPageEmpty2}{\showpaste}
37\tab{5}\spadcommand{f := padicFraction(\%)\free{prev1 }\bound{f }}
38\end{paste}\end{patch}
39
40\begin{patch}{PartialFractionXmpPagePatch3}
41\begin{paste}{PartialFractionXmpPageFull3}{PartialFractionXmpPageEmpty3}
42\pastebutton{PartialFractionXmpPageFull3}{\hidepaste}
43\tab{5}\spadcommand{compactFraction(f)\free{f }}
44\indentrel{3}\begin{verbatim}
45        159   23   12   1
46   (3)  --- - -- - -- + -
47          8    4    2   7
48         2    3    5
49                         Type: PartialFraction(Integer)
50\end{verbatim}
51\indentrel{-3}\end{paste}\end{patch}
52
53\begin{patch}{PartialFractionXmpPageEmpty3}
54\begin{paste}{PartialFractionXmpPageEmpty3}{PartialFractionXmpPagePatch3}
55\pastebutton{PartialFractionXmpPageEmpty3}{\showpaste}
56\tab{5}\spadcommand{compactFraction(f)\free{f }}
57\end{paste}\end{patch}
58
59\begin{patch}{PartialFractionXmpPagePatch4}
60\begin{paste}{PartialFractionXmpPageFull4}{PartialFractionXmpPageEmpty4}
61\pastebutton{PartialFractionXmpPageFull4}{\hidepaste}
62\tab{5}\spadcommand{numberOfFractionalTerms(f)\free{f }}
63\indentrel{3}\begin{verbatim}
64   (4)  12
65                                  Type: PositiveInteger
66\end{verbatim}
67\indentrel{-3}\end{paste}\end{patch}
68
69\begin{patch}{PartialFractionXmpPageEmpty4}
70\begin{paste}{PartialFractionXmpPageEmpty4}{PartialFractionXmpPagePatch4}
71\pastebutton{PartialFractionXmpPageEmpty4}{\showpaste}
72\tab{5}\spadcommand{numberOfFractionalTerms(f)\free{f }}
73\end{paste}\end{patch}
74
75\begin{patch}{PartialFractionXmpPagePatch5}
76\begin{paste}{PartialFractionXmpPageFull5}{PartialFractionXmpPageEmpty5}
77\pastebutton{PartialFractionXmpPageFull5}{\hidepaste}
78\tab{5}\spadcommand{fractionalTerms(f).3\free{f }}
79\indentrel{3}\begin{verbatim}
80                         5
81   (5)  [num = 1, den = 2 ]
82      Type: Record(num: Integer,den: Factored(Integer))
83\end{verbatim}
84\indentrel{-3}\end{paste}\end{patch}
85
86\begin{patch}{PartialFractionXmpPageEmpty5}
87\begin{paste}{PartialFractionXmpPageEmpty5}{PartialFractionXmpPagePatch5}
88\pastebutton{PartialFractionXmpPageEmpty5}{\showpaste}
89\tab{5}\spadcommand{fractionalTerms(f).3\free{f }}
90\end{paste}\end{patch}
91
92\begin{patch}{PartialFractionXmpPagePatch6}
93\begin{paste}{PartialFractionXmpPageFull6}{PartialFractionXmpPageEmpty6}
94\pastebutton{PartialFractionXmpPageFull6}{\hidepaste}
95\tab{5}\spadcommand{partialFraction(1,- 13 + 14 * \%i)\bound{prev2 }}
96\indentrel{3}\begin{verbatim}
97              1          4
98   (6)  - -------- + --------
99          1 + 2 %i   3 + 8 %i
100                Type: PartialFraction(Complex(Integer))
101\end{verbatim}
102\indentrel{-3}\end{paste}\end{patch}
103
104\begin{patch}{PartialFractionXmpPageEmpty6}
105\begin{paste}{PartialFractionXmpPageEmpty6}{PartialFractionXmpPagePatch6}
106\pastebutton{PartialFractionXmpPageEmpty6}{\showpaste}
107\tab{5}\spadcommand{partialFraction(1,- 13 + 14 * \%i)\bound{prev2 }}
108\end{paste}\end{patch}
109
110\begin{patch}{PartialFractionXmpPagePatch7}
111\begin{paste}{PartialFractionXmpPageFull7}{PartialFractionXmpPageEmpty7}
112\pastebutton{PartialFractionXmpPageFull7}{\hidepaste}
113\tab{5}\spadcommand{\% :: Fraction Complex Integer\free{prev2 }}
114\indentrel{3}\begin{verbatim}
115              %i
116   (7)  - ----------
117          14 + 13 %i
118                       Type: Fraction(Complex(Integer))
119\end{verbatim}
120\indentrel{-3}\end{paste}\end{patch}
121
122\begin{patch}{PartialFractionXmpPageEmpty7}
123\begin{paste}{PartialFractionXmpPageEmpty7}{PartialFractionXmpPagePatch7}
124\pastebutton{PartialFractionXmpPageEmpty7}{\showpaste}
125\tab{5}\spadcommand{\% :: Fraction Complex Integer\free{prev2 }}
126\end{paste}\end{patch}
127
128\begin{patch}{PartialFractionXmpPagePatch8}
129\begin{paste}{PartialFractionXmpPageFull8}{PartialFractionXmpPageEmpty8}
130\pastebutton{PartialFractionXmpPageFull8}{\hidepaste}
131\tab{5}\spadcommand{u : FR UP(x, FRAC INT) := reduce(*,[primeFactor(x+i,i) for i in 1..4])\bound{u }}
132\indentrel{3}\begin{verbatim}
133                      2       3       4
134   (8)  (x + 1)(x + 2) (x + 3) (x + 4)
135Type: Factored(UnivariatePolynomial(x,Fraction(Integer)))
136\end{verbatim}
137\indentrel{-3}\end{paste}\end{patch}
138
139\begin{patch}{PartialFractionXmpPageEmpty8}
140\begin{paste}{PartialFractionXmpPageEmpty8}{PartialFractionXmpPagePatch8}
141\pastebutton{PartialFractionXmpPageEmpty8}{\showpaste}
142\tab{5}\spadcommand{u : FR UP(x, FRAC INT) := reduce(*,[primeFactor(x+i,i) for i in 1..4])\bound{u }}
143\end{paste}\end{patch}
144
145\begin{patch}{PartialFractionXmpPagePatch9}
146\begin{paste}{PartialFractionXmpPageFull9}{PartialFractionXmpPageEmpty9}
147\pastebutton{PartialFractionXmpPageFull9}{\hidepaste}
148\tab{5}\spadcommand{partialFraction(1,u)\free{u }\bound{prev3 }}
149\indentrel{3}\begin{verbatim}
150   (9)
151       1     1      7     17  2          139
152      ---    - x + --   - -- x  - 12 x - ---
153      648    4     16      8              8
154     ----- + -------- + --------------------
155     x + 1          2                3
156             (x + 2)          (x + 3)
157   +
158     607  3   10115  2   391     44179
159     --- x  + ----- x  + --- x + -----
160     324       432        4       324
161     ---------------------------------
162                         4
163                  (x + 4)
164Type: PartialFraction(UnivariatePolynomial(x,Fraction(Integer)))
165\end{verbatim}
166\indentrel{-3}\end{paste}\end{patch}
167
168\begin{patch}{PartialFractionXmpPageEmpty9}
169\begin{paste}{PartialFractionXmpPageEmpty9}{PartialFractionXmpPagePatch9}
170\pastebutton{PartialFractionXmpPageEmpty9}{\showpaste}
171\tab{5}\spadcommand{partialFraction(1,u)\free{u }\bound{prev3 }}
172\end{paste}\end{patch}
173
174\begin{patch}{PartialFractionXmpPagePatch10}
175\begin{paste}{PartialFractionXmpPageFull10}{PartialFractionXmpPageEmpty10}
176\pastebutton{PartialFractionXmpPageFull10}{\hidepaste}
177\tab{5}\spadcommand{padicFraction \%\free{prev3 }}
178\indentrel{3}\begin{verbatim}
179   (10)
180       1       1         1        17        3
181      ---      -        --        --        -
182      648      4        16         8        4
183     ----- + ----- - -------- - ----- + --------
184     x + 1   x + 2          2   x + 3          2
185                     (x + 2)            (x + 3)
186   +
187           1       607       403        13          1
188           -       ---       ---        --         --
189           2       324       432        36         12
190     - -------- + ----- + -------- + -------- + --------
191              3   x + 4          2          3          4
192       (x + 3)            (x + 4)    (x + 4)    (x + 4)
193Type: PartialFraction(UnivariatePolynomial(x,Fraction(Integer)))
194\end{verbatim}
195\indentrel{-3}\end{paste}\end{patch}
196
197\begin{patch}{PartialFractionXmpPageEmpty10}
198\begin{paste}{PartialFractionXmpPageEmpty10}{PartialFractionXmpPagePatch10}
199\pastebutton{PartialFractionXmpPageEmpty10}{\showpaste}
200\tab{5}\spadcommand{padicFraction \%\free{prev3 }}
201\end{paste}\end{patch}
202
203