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-rw-r--r--src/hyper/pages/CONTFRAC.pht437
1 files changed, 437 insertions, 0 deletions
diff --git a/src/hyper/pages/CONTFRAC.pht b/src/hyper/pages/CONTFRAC.pht
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+++ b/src/hyper/pages/CONTFRAC.pht
@@ -0,0 +1,437 @@
+\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 ³ 1 ³ 1 ³ 1 ³ 1 ³ 1 ³
+ 3 + ÚÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÙ
+ ³ 7 ³ 15 ³ 1 ³ 25 ³ 1 ³ 7
+ +
+ 1 ³
+ ÚÄÄÄÙ
+ ³ 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,ÄÄ,ÄÄÄ,ÄÄÄ,ÄÄÄÄ,ÄÄÄÄ,ÄÄÄÄÄ,ÄÄÄÄÄÄ]
+ 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,ÄÄ,ÄÄÄ,ÄÄÄ,ÄÄÄÄ,ÄÄÄÄ,ÄÄÄÄÄ,ÄÄÄÄÄÄ]
+ 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 ³ 1 ³ 1 ³ 1 ³ 1 ³ 1 ³
+ ÚÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÙ
+ ³ 3 ³ 7 ³ 15 ³ 1 ³ 25 ³ 1
+ +
+ 1 ³ 1 ³
+ ÚÄÄÄÙ + ÚÄÄÄÙ
+ ³ 7 ³ 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 ³ 1 ³ 1 ³ 1 ³ 1 ³ 1 ³
+ 3 + ÚÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÙ
+ ³ 3 ³ 6 ³ 3 ³ 6 ³ 3 ³ 6
+ +
+ 1 ³ 1 ³ 1 ³ 1 ³
+ ÚÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÙ + ...
+ ³ 3 ³ 6 ³ 3 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 ³ 1 ³ 1 ³ 1 ³ 1 ³ 1 ³
+ ÚÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÄÙ
+ ³ 1 ³ 6 ³ 10 ³ 14 ³ 18 ³ 22
+ +
+ 1 ³ 1 ³ 1 ³ 1 ³
+ ÚÄÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÄÙ + ...
+ ³ 26 ³ 30 ³ 34 ³ 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, Ä, ÄÄ, ÄÄÄÄ, ÄÄÄÄÄ, ÄÄÄÄÄÄ, ÄÄÄÄÄÄÄÄ,
+ 7 71 1001 18089 398959 10391023
+ 268163352 9126481321
+ ÄÄÄÄÄÄÄÄÄ, ÄÄÄÄÄÄÄÄÄÄÄ, ...]
+ 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, ÄÄ, ÄÄÄ, ÄÄÄÄ, ÄÄÄÄÄ, ÄÄÄÄÄÄÄ, ÄÄÄÄÄÄÄÄ,
+ 7 71 1001 18089 398959 10391023
+ 848456353 28875761731
+ ÄÄÄÄÄÄÄÄÄ, ÄÄÄÄÄÄÄÄÄÄÄ, ...]
+ 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 ³ 9 ³ 25 ³ 49 ³ 81 ³
+ 1 + ÚÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÄÙ
+ ³ 2 ³ 2 ³ 2 ³ 2 ³ 2
+ +
+ 121 ³ 169 ³ 225 ³ 289 ³ 361 ³
+ ÚÄÄÄÄÄÙ + ÚÄÄÄÄÄÙ + ÚÄÄÄÄÄÙ + ÚÄÄÄÄÄÙ + ÚÄÄÄÄÄÙ + ...
+ ³ 2 ³ 2 ³ 2 ³ 2 ³ 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,Ä,ÄÄ,ÄÄÄ,ÄÄÄ,ÄÄÄÄ,ÄÄÄÄÄ,ÄÄÄÄÄ,ÄÄÄÄÄÄ,ÄÄÄÄÄÄÄÄ,...]
+ 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, Ä, ÄÄ, ÄÄÄ, ÄÄÄÄ, ÄÄÄÄÄ, ÄÄÄÄÄÄ, ÄÄÄÄÄÄ, ÄÄÄÄÄÄÄ,
+ 3 15 105 315 3465 45045 45045 765765
+ 44257352
+ ÄÄÄÄÄÄÄÄ, ...]
+ 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 ³ 1 ³
+ (18) - 90 + 59%i + ÚÄÄÄÄÄÄÄÄÄÙ + ÚÄÄÄÄÄÄÄÄÄÄÄÙ
+ ³ 1 - 2%i ³ - 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) ÄÄÄÄÄÄÄÄÄÄÄÄ
+ 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 ³ 1 ³
+ (21) 1 + ÚÄÄÄÄÄÄÄÄÄÙ + ÚÄÄÄÄÄÄÄÄÄÄÄÙ
+ ³ 1 9 ³ 16 40
+ ³ Ä x - Ä ³ ÄÄ x - ÄÄ
+ ³ 4 8 ³ 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}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ContinuedFractionXmpPageEmpty22}
+\begin{paste}{ContinuedFractionXmpPageEmpty22}{ContinuedFractionXmpPagePatch22}
+\pastebutton{ContinuedFractionXmpPageEmpty22}{\showpaste}
+\tab{5}\spadcommand{[i*i for i in convergents(z) :: Stream Float]\free{z }}
+\end{paste}\end{patch}
+