diff options
Diffstat (limited to 'src/hyper/pages/CONTFRAC.pht')
-rw-r--r-- | src/hyper/pages/CONTFRAC.pht | 437 |
1 files changed, 437 insertions, 0 deletions
diff --git a/src/hyper/pages/CONTFRAC.pht b/src/hyper/pages/CONTFRAC.pht new file mode 100644 index 00000000..fb95eff0 --- /dev/null +++ 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} + |