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|
\begin{patch}{ContinuedFractionXmpPagePatch1}
\begin{paste}{ContinuedFractionXmpPageFull1}{ContinuedFractionXmpPageEmpty1}
\pastebutton{ContinuedFractionXmpPageFull1}{\hidepaste}
\tab{5}\spadcommand{c := continuedFraction(314159/100000)\bound{c }}
\indentrel{3}\begin{verbatim}
(1)
1 � 1 � 1 � 1 � 1 � 1 �
3 + ����� + ������ + ����� + ������ + ����� + �����
� 7 � 15 � 1 � 25 � 1 � 7
+
1 �
�����
� 4
Type: ContinuedFraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty1}
\begin{paste}{ContinuedFractionXmpPageEmpty1}{ContinuedFractionXmpPagePatch1}
\pastebutton{ContinuedFractionXmpPageEmpty1}{\showpaste}
\tab{5}\spadcommand{c := continuedFraction(314159/100000)\bound{c }}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch2}
\begin{paste}{ContinuedFractionXmpPageFull2}{ContinuedFractionXmpPageEmpty2}
\pastebutton{ContinuedFractionXmpPageFull2}{\hidepaste}
\tab{5}\spadcommand{partialQuotients c\free{c }}
\indentrel{3}\begin{verbatim}
(2) [3,7,15,1,25,1,7,4]
Type: Stream Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty2}
\begin{paste}{ContinuedFractionXmpPageEmpty2}{ContinuedFractionXmpPagePatch2}
\pastebutton{ContinuedFractionXmpPageEmpty2}{\showpaste}
\tab{5}\spadcommand{partialQuotients c\free{c }}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch3}
\begin{paste}{ContinuedFractionXmpPageFull3}{ContinuedFractionXmpPageEmpty3}
\pastebutton{ContinuedFractionXmpPageFull3}{\hidepaste}
\tab{5}\spadcommand{convergents c\free{c }}
\indentrel{3}\begin{verbatim}
22 333 355 9208 9563 76149 314159
(3) [3,��,���,���,����,����,�����,������]
7 106 113 2931 3044 24239 100000
Type: Stream Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty3}
\begin{paste}{ContinuedFractionXmpPageEmpty3}{ContinuedFractionXmpPagePatch3}
\pastebutton{ContinuedFractionXmpPageEmpty3}{\showpaste}
\tab{5}\spadcommand{convergents c\free{c }}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch4}
\begin{paste}{ContinuedFractionXmpPageFull4}{ContinuedFractionXmpPageEmpty4}
\pastebutton{ContinuedFractionXmpPageFull4}{\hidepaste}
\tab{5}\spadcommand{approximants c\free{c }}
\indentrel{3}\begin{verbatim}
______
22 333 355 9208 9563 76149 314159
(4) [3,��,���,���,����,����,�����,������]
7 106 113 2931 3044 24239 100000
Type: Stream Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty4}
\begin{paste}{ContinuedFractionXmpPageEmpty4}{ContinuedFractionXmpPagePatch4}
\pastebutton{ContinuedFractionXmpPageEmpty4}{\showpaste}
\tab{5}\spadcommand{approximants c\free{c }}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch5}
\begin{paste}{ContinuedFractionXmpPageFull5}{ContinuedFractionXmpPageEmpty5}
\pastebutton{ContinuedFractionXmpPageFull5}{\hidepaste}
\tab{5}\spadcommand{pq := partialQuotients(1/c)\free{c }\bound{pq }}
\indentrel{3}\begin{verbatim}
(5) [0,3,7,15,1,25,1,7,4]
Type: Stream Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty5}
\begin{paste}{ContinuedFractionXmpPageEmpty5}{ContinuedFractionXmpPagePatch5}
\pastebutton{ContinuedFractionXmpPageEmpty5}{\showpaste}
\tab{5}\spadcommand{pq := partialQuotients(1/c)\free{c }\bound{pq }}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch6}
\begin{paste}{ContinuedFractionXmpPageFull6}{ContinuedFractionXmpPageEmpty6}
\pastebutton{ContinuedFractionXmpPageFull6}{\hidepaste}
\tab{5}\spadcommand{continuedFraction(first pq,repeating [1],rest pq)\free{pq }}
\indentrel{3}\begin{verbatim}
(6)
1 � 1 � 1 � 1 � 1 � 1 �
����� + ����� + ������ + ����� + ������ + �����
� 3 � 7 � 15 � 1 � 25 � 1
+
1 � 1 �
����� + �����
� 7 � 4
Type: ContinuedFraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty6}
\begin{paste}{ContinuedFractionXmpPageEmpty6}{ContinuedFractionXmpPagePatch6}
\pastebutton{ContinuedFractionXmpPageEmpty6}{\showpaste}
\tab{5}\spadcommand{continuedFraction(first pq,repeating [1],rest pq)\free{pq }}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch7}
\begin{paste}{ContinuedFractionXmpPageFull7}{ContinuedFractionXmpPageEmpty7}
\pastebutton{ContinuedFractionXmpPageFull7}{\hidepaste}
\tab{5}\spadcommand{z:=continuedFraction(3,repeating [1],repeating [3,6])\bound{z }}
\indentrel{3}\begin{verbatim}
(7)
1 � 1 � 1 � 1 � 1 � 1 �
3 + ����� + ����� + ����� + ����� + ����� + �����
� 3 � 6 � 3 � 6 � 3 � 6
+
1 � 1 � 1 � 1 �
����� + ����� + ����� + ����� + ...
� 3 � 6 � 3 � 6
Type: ContinuedFraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty7}
\begin{paste}{ContinuedFractionXmpPageEmpty7}{ContinuedFractionXmpPagePatch7}
\pastebutton{ContinuedFractionXmpPageEmpty7}{\showpaste}
\tab{5}\spadcommand{z:=continuedFraction(3,repeating [1],repeating [3,6])\bound{z }}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch8}
\begin{paste}{ContinuedFractionXmpPageFull8}{ContinuedFractionXmpPageEmpty8}
\pastebutton{ContinuedFractionXmpPageFull8}{\hidepaste}
\tab{5}\spadcommand{dens:Stream Integer := cons(1,generate((x+->x+4),6))\bound{dens }}
\indentrel{3}\begin{verbatim}
(8) [1,6,10,14,18,22,26,30,34,38,...]
Type: Stream Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty8}
\begin{paste}{ContinuedFractionXmpPageEmpty8}{ContinuedFractionXmpPagePatch8}
\pastebutton{ContinuedFractionXmpPageEmpty8}{\showpaste}
\tab{5}\spadcommand{dens:Stream Integer := cons(1,generate((x+->x+4),6))\bound{dens }}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch9}
\begin{paste}{ContinuedFractionXmpPageFull9}{ContinuedFractionXmpPageEmpty9}
\pastebutton{ContinuedFractionXmpPageFull9}{\hidepaste}
\tab{5}\spadcommand{cf := continuedFraction(0,repeating [1],dens)\free{dens }\bound{cf }}
\indentrel{3}\begin{verbatim}
(9)
1 � 1 � 1 � 1 � 1 � 1 �
����� + ����� + ������ + ������ + ������ + ������
� 1 � 6 � 10 � 14 � 18 � 22
+
1 � 1 � 1 � 1 �
������ + ������ + ������ + ������ + ...
� 26 � 30 � 34 � 38
Type: ContinuedFraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty9}
\begin{paste}{ContinuedFractionXmpPageEmpty9}{ContinuedFractionXmpPagePatch9}
\pastebutton{ContinuedFractionXmpPageEmpty9}{\showpaste}
\tab{5}\spadcommand{cf := continuedFraction(0,repeating [1],dens)\free{dens }\bound{cf }}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch10}
\begin{paste}{ContinuedFractionXmpPageFull10}{ContinuedFractionXmpPageEmpty10}
\pastebutton{ContinuedFractionXmpPageFull10}{\hidepaste}
\tab{5}\spadcommand{ccf := convergents cf\free{cf }\bound{ccf }}
\indentrel{3}\begin{verbatim}
(10)
6 61 860 15541 342762 8927353
[0, 1, �, ��, ����, �����, ������, ��������,
7 71 1001 18089 398959 10391023
268163352 9126481321
���������, �����������, ...]
312129649 10622799089
Type: Stream Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty10}
\begin{paste}{ContinuedFractionXmpPageEmpty10}{ContinuedFractionXmpPagePatch10}
\pastebutton{ContinuedFractionXmpPageEmpty10}{\showpaste}
\tab{5}\spadcommand{ccf := convergents cf\free{cf }\bound{ccf }}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch11}
\begin{paste}{ContinuedFractionXmpPageFull11}{ContinuedFractionXmpPageEmpty11}
\pastebutton{ContinuedFractionXmpPageFull11}{\hidepaste}
\tab{5}\spadcommand{eConvergents := [2*e + 1 for e in ccf]\bound{ec }\free{ccf }}
\indentrel{3}\begin{verbatim}
(11)
19 193 2721 49171 1084483 28245729
[1, 3, ��, ���, ����, �����, �������, ��������,
7 71 1001 18089 398959 10391023
848456353 28875761731
���������, �����������, ...]
312129649 10622799089
Type: Stream Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty11}
\begin{paste}{ContinuedFractionXmpPageEmpty11}{ContinuedFractionXmpPagePatch11}
\pastebutton{ContinuedFractionXmpPageEmpty11}{\showpaste}
\tab{5}\spadcommand{eConvergents := [2*e + 1 for e in ccf]\bound{ec }\free{ccf }}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch12}
\begin{paste}{ContinuedFractionXmpPageFull12}{ContinuedFractionXmpPageEmpty12}
\pastebutton{ContinuedFractionXmpPageFull12}{\hidepaste}
\tab{5}\spadcommand{eConvergents :: Stream Float\free{ec }}
\indentrel{3}\begin{verbatim}
(12)
[1.0, 3.0, 2.7142857142 857142857,
2.7183098591 549295775, 2.7182817182 817182817,
2.7182818287 356957267, 2.7182818284 585634113,
2.7182818284 590458514, 2.7182818284 590452348,
2.7182818284 590452354, ...]
Type: Stream Float
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty12}
\begin{paste}{ContinuedFractionXmpPageEmpty12}{ContinuedFractionXmpPagePatch12}
\pastebutton{ContinuedFractionXmpPageEmpty12}{\showpaste}
\tab{5}\spadcommand{eConvergents :: Stream Float\free{ec }}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch13}
\begin{paste}{ContinuedFractionXmpPageFull13}{ContinuedFractionXmpPageEmpty13}
\pastebutton{ContinuedFractionXmpPageFull13}{\hidepaste}
\tab{5}\spadcommand{exp 1.0}
\indentrel{3}\begin{verbatim}
(13) 2.7182818284 590452354
Type: Float
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty13}
\begin{paste}{ContinuedFractionXmpPageEmpty13}{ContinuedFractionXmpPagePatch13}
\pastebutton{ContinuedFractionXmpPageEmpty13}{\showpaste}
\tab{5}\spadcommand{exp 1.0}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch14}
\begin{paste}{ContinuedFractionXmpPageFull14}{ContinuedFractionXmpPageEmpty14}
\pastebutton{ContinuedFractionXmpPageFull14}{\hidepaste}
\tab{5}\spadcommand{cf := continuedFraction(1,[(2*i+1)**2 for i in 0..],repeating [2])\bound{cf1 }}
\indentrel{3}\begin{verbatim}
(14)
1 � 9 � 25 � 49 � 81 �
1 + ����� + ����� + ������ + ������ + ������
� 2 � 2 � 2 � 2 � 2
+
121 � 169 � 225 � 289 � 361 �
������� + ������� + ������� + ������� + ������� + ...
� 2 � 2 � 2 � 2 � 2
Type: ContinuedFraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty14}
\begin{paste}{ContinuedFractionXmpPageEmpty14}{ContinuedFractionXmpPagePatch14}
\pastebutton{ContinuedFractionXmpPageEmpty14}{\showpaste}
\tab{5}\spadcommand{cf := continuedFraction(1,[(2*i+1)**2 for i in 0..],repeating [2])\bound{cf1 }}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch15}
\begin{paste}{ContinuedFractionXmpPageFull15}{ContinuedFractionXmpPageEmpty15}
\pastebutton{ContinuedFractionXmpPageFull15}{\hidepaste}
\tab{5}\spadcommand{ccf := convergents cf\free{cf1 }\bound{ccf1 }}
\indentrel{3}\begin{verbatim}
(15)
3 15 105 315 3465 45045 45045 765765 14549535
[1,�,��,���,���,����,�����,�����,������,��������,...]
2 13 76 263 2578 36979 33976 622637 11064338
Type: Stream Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty15}
\begin{paste}{ContinuedFractionXmpPageEmpty15}{ContinuedFractionXmpPagePatch15}
\pastebutton{ContinuedFractionXmpPageEmpty15}{\showpaste}
\tab{5}\spadcommand{ccf := convergents cf\free{cf1 }\bound{ccf1 }}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch16}
\begin{paste}{ContinuedFractionXmpPageFull16}{ContinuedFractionXmpPageEmpty16}
\pastebutton{ContinuedFractionXmpPageFull16}{\hidepaste}
\tab{5}\spadcommand{piConvergents := [4/p for p in ccf]\bound{piConvergents }\free{ccf1 }}
\indentrel{3}\begin{verbatim}
(16)
8 52 304 1052 10312 147916 135904 2490548
[4, �, ��, ���, ����, �����, ������, ������, �������,
3 15 105 315 3465 45045 45045 765765
44257352
��������, ...]
14549535
Type: Stream Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty16}
\begin{paste}{ContinuedFractionXmpPageEmpty16}{ContinuedFractionXmpPagePatch16}
\pastebutton{ContinuedFractionXmpPageEmpty16}{\showpaste}
\tab{5}\spadcommand{piConvergents := [4/p for p in ccf]\bound{piConvergents }\free{ccf1 }}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch17}
\begin{paste}{ContinuedFractionXmpPageFull17}{ContinuedFractionXmpPageEmpty17}
\pastebutton{ContinuedFractionXmpPageFull17}{\hidepaste}
\tab{5}\spadcommand{piConvergents :: Stream Float\free{piConvergents }}
\indentrel{3}\begin{verbatim}
(17)
[4.0, 2.6666666666 666666667, 3.4666666666 666666667,
2.8952380952 380952381, 3.3396825396 825396825,
2.9760461760 461760462, 3.2837384837 384837385,
3.0170718170 718170718, 3.2523659347 188758953,
3.0418396189 294022111, ...]
Type: Stream Float
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty17}
\begin{paste}{ContinuedFractionXmpPageEmpty17}{ContinuedFractionXmpPagePatch17}
\pastebutton{ContinuedFractionXmpPageEmpty17}{\showpaste}
\tab{5}\spadcommand{piConvergents :: Stream Float\free{piConvergents }}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch18}
\begin{paste}{ContinuedFractionXmpPageFull18}{ContinuedFractionXmpPageEmpty18}
\pastebutton{ContinuedFractionXmpPageFull18}{\hidepaste}
\tab{5}\spadcommand{continuedFraction((- 122 + 597*\%i)/(4 - 4*\%i))}
\indentrel{3}\begin{verbatim}
1 � 1 �
(18) - 90 + 59%i + ����������� + �������������
� 1 - 2%i � - 1 + 2%i
Type: ContinuedFraction Complex Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty18}
\begin{paste}{ContinuedFractionXmpPageEmpty18}{ContinuedFractionXmpPagePatch18}
\pastebutton{ContinuedFractionXmpPageEmpty18}{\showpaste}
\tab{5}\spadcommand{continuedFraction((- 122 + 597*\%i)/(4 - 4*\%i))}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch19}
\begin{paste}{ContinuedFractionXmpPageFull19}{ContinuedFractionXmpPageEmpty19}
\pastebutton{ContinuedFractionXmpPageFull19}{\hidepaste}
\tab{5}\spadcommand{r : Fraction UnivariatePolynomial(x,Fraction Integer)\bound{rdec }}
\indentrel{3}\begin{verbatim}
Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty19}
\begin{paste}{ContinuedFractionXmpPageEmpty19}{ContinuedFractionXmpPagePatch19}
\pastebutton{ContinuedFractionXmpPageEmpty19}{\showpaste}
\tab{5}\spadcommand{r : Fraction UnivariatePolynomial(x,Fraction Integer)\bound{rdec }}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch20}
\begin{paste}{ContinuedFractionXmpPageFull20}{ContinuedFractionXmpPageEmpty20}
\pastebutton{ContinuedFractionXmpPageFull20}{\hidepaste}
\tab{5}\spadcommand{r := ((x - 1) * (x - 2)) / ((x-3) * (x-4))\free{rdec }\bound{r }}
\indentrel{3}\begin{verbatim}
2
x - 3x + 2
(20) ������������
2
x - 7x + 12
Type: Fraction UnivariatePolynomial(x,Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty20}
\begin{paste}{ContinuedFractionXmpPageEmpty20}{ContinuedFractionXmpPagePatch20}
\pastebutton{ContinuedFractionXmpPageEmpty20}{\showpaste}
\tab{5}\spadcommand{r := ((x - 1) * (x - 2)) / ((x-3) * (x-4))\free{rdec }\bound{r }}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch21}
\begin{paste}{ContinuedFractionXmpPageFull21}{ContinuedFractionXmpPageEmpty21}
\pastebutton{ContinuedFractionXmpPageFull21}{\hidepaste}
\tab{5}\spadcommand{continuedFraction r\free{r }}
\indentrel{3}\begin{verbatim}
1 � 1 �
(21) 1 + ����������� + �������������
� 1 9 � 16 40
� � x - � � �� x - ��
� 4 8 � 3 3
Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPageEmpty21}
\begin{paste}{ContinuedFractionXmpPageEmpty21}{ContinuedFractionXmpPagePatch21}
\pastebutton{ContinuedFractionXmpPageEmpty21}{\showpaste}
\tab{5}\spadcommand{continuedFraction r\free{r }}
\end{paste}\end{patch}
\begin{patch}{ContinuedFractionXmpPagePatch22}
\begin{paste}{ContinuedFractionXmpPageFull22}{ContinuedFractionXmpPageEmpty22}
\pastebutton{ContinuedFractionXmpPageFull22}{\hidepaste}
\tab{5}\spadcommand{[i*i for i in convergents(z) :: Stream Float]\free{z }}
\indentrel{3}\begin{verbatim}
(22)
[9.0, 11.1111111111 11111111, 10.9944598337 9501385,
11.0002777777 77777778, 10.9999860763 98799786,
11.0000006979 29731039, 10.9999999650 15834446,
11.0000000017 53603304, 10.9999999999 12099531,
11.0000000000 04406066, ...]
Type: Stream Float
\end{verbatim}
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