diff --git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet index 804c802..d74c207 100644 --- a/books/bookvolbib.pamphlet +++ b/books/bookvolbib.pamphlet @@ -431,6 +431,9 @@ Capriotti, O. and Carlisle, D. Capriotti, Olga, Cohen, Arjeh M., Cuypers, Hans, and Sterk, Hans ``OpenMath Technology for Interactive Mathematical Documents'' \verb|www.win.tue.nl/~hansc/lisbon.pdf| +\bibitem[Che86]{Che86} +G.W. Cherry "Integration in Finite Terms with Special Functions: The Logarithmic Integral" +SIAM J. Comput. Vol 15 No 1 February 1986 \bibitem[Chu89]{Chu89} Chudnovsky, D.V. and Chudnovsky, G.V. ``The computation of classical constants'' diff --git a/changelog b/changelog index 125f42d..e3a3fe8 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20130106 tpd books/bookvolbib add Che86 +20130106 tpd src/input/Makefile add cherry.input +20130106 tpd src/input/cherry.input added 20120815 tpd src/axiom-website/patches.html 20120815.01.tpd.patch 20120815 tpd src/axiom-website/documentation.html 20120615 tpd src/axiom-website/patches.html 20120615.01.tpd.patch diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index dfd1044..557209b 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -3943,5 +3943,7 @@ src/axiom-website/download.html add binaries
Makefile.pamphlet add mint stanza
20120815.01.tpd.patch src/axiom-website/documentation.html +20130105.01.tpd.patch +src/input/cherry.input added diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index a64803e..49f9a1a 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -299,6 +299,7 @@ REGRESSTESTS= ackermann.regress \ cachedf.regress calcprob.regress \ calculus2.regress calculus.regress cardinal.regress card.regress \ carten.regress cclass.regress char.regress ch.regress \ + cherry.regress \ chtheorem.regress classtalk.regress clements.regress \ clifford.regress clif.regress cmds.regress \ coercels.regress collect.regress cohen.regress \ @@ -645,7 +646,8 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/calcprob.input ${OUT}/calculus.input \ ${OUT}/cardinal.input ${OUT}/card.input ${OUT}/carten.input \ ${OUT}/cclass.input ${OUT}/cdraw.input ${OUT}/char.input \ - ${OUT}/ch.input ${OUT}/chtheorem.input ${OUT}/classtalk.input \ + ${OUT}/ch.input ${OUT}/cherry.input \ + ${OUT}/chtheorem.input ${OUT}/classtalk.input \ ${OUT}/clifford.input ${OUT}/clements.input \ ${OUT}/clif.input ${OUT}/cmds.input \ ${OUT}/coercels.input ${OUT}/collect.input ${OUT}/color.input \ @@ -934,6 +936,7 @@ DOCFILES= \ ${DOC}/card.input.dvi ${DOC}/carten.input.dvi \ ${DOC}/cclass.input.dvi ${DOC}/cdraw.input.dvi \ ${DOC}/char.input.dvi ${DOC}/ch.input.dvi \ + ${DOC}/cherry.input.dvi \ ${DOC}/chtheorem.input.dvi ${DOC}/classtalk.input.dvi \ ${DOC}/clifford.input.dvi ${DOC}/clements.input.dvi \ ${DOC}/clif.input.dvi ${DOC}/cmds.input.dvi \ diff --git a/src/input/cherry.input.pamphlet b/src/input/cherry.input.pamphlet new file mode 100644 index 0000000..9798414 --- /dev/null +++ b/src/input/cherry.input.pamphlet @@ -0,0 +1,827 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input cherry.input} +\author{G. W. Cherry} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm cherry.output +)spool cherry.output +)set message test on +)set message auto off +)clear all + +\end{chunk} +Examples taken from: +"INTEGRATION IN FINITE TERMS WITH SPECIAL FUNCTIONS: THE LOGARITHMIC INTEGRAL" +written by G. W. CHERRY +published in SIAM J. COMPUT. Vol. 15, No. 1, February 1986 + +Page 1 Example 1.1 +\begin{chunk}{*} + +--S 1 of 61 +i := x/log(x)^2 +--R +--R +--R x +--R (1) ------- +--R 2 +--R log(x) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 61 +I := integrate(i, x) +--R +--R +--R 2 +--R 2log(x)Ei(2log(x)) - x +--R (2) ----------------------- +--R log(x) +--R Type: Union(Expression(Integer),...) +--E 2 + +--S 3 of 61 +Ic := 2*li(x^2) - x^2/log(x) +--R +--R +--R 2 2 +--R 2li(x )log(x) - x +--R (3) ------------------ +--R log(x) +--R Type: Expression(Integer) +--E 3 + +--S 4 of 61 +D(Ic, x) +--R +--R +--R 2 2 +--R (- 2x log(x) + x)log(x ) + 4x log(x) +--R (4) ------------------------------------- +--R 2 2 +--R log(x) log(x ) +--R Type: Expression(Integer) +--E 4 +\end{chunk} +Page 16, Example 5.1 +\begin{chunk}{*} + +--S 5 of 61 +i := x^3 / log(x^2-1) +--R +--R +--R 3 +--R x +--R (5) ----------- +--R 2 +--R log(x - 1) +--R Type: Expression(Integer) +--E 5 + +--S 6 of 61 +I := integrate(i, x) +--R +--R +--R x 3 +--R ++ %I +--R (6) | ------------ d%I +--R ++ 2 +--R log(%I - 1) +--R Type: Union(Expression(Integer),...) +--E 6 + +--S 7 of 61 +Ic := li(x^4-2*x^2+1)/2 + li(x^2-1)/2 +--R +--R +--R 4 2 2 +--R li(x - 2x + 1) + li(x - 1) +--R (7) ----------------------------- +--R 2 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 61 +D(Ic, x) +--R +--R +--R 4 2 3 2 +--R x log(x - 2x + 1) + (2x - 2x)log(x - 1) +--R (8) ------------------------------------------- +--R 2 4 2 +--R log(x - 1)log(x - 2x + 1) +--R Type: Expression(Integer) +--E 8 +\end{chunk} +Example 5.2 +\begin{chunk}{*} + +--S 9 of 61 +i := x^2 / log(x^2-1) +--R +--R +--R 2 +--R x +--R (9) ----------- +--R 2 +--R log(x - 1) +--R Type: Expression(Integer) +--E 9 + +--S 10 of 61 +I := integrate(i, x) +--R +--R +--R x 2 +--R ++ %I +--R (10) | ------------ d%I +--R ++ 2 +--R log(%I - 1) +--R Type: Union(Expression(Integer),...) +--E 10 +\end{chunk} +No closed form + +Page 17, Example 5.3 +\begin{chunk}{*} + +--S 11 of 61 +i := (2*x+3)/(3*log(x)+2*x) * exp(log(x)/2+x) + 1/(x+1)*(exp(log(x)/2+x))^2 +--R +--R +--R log(x) + 2x 2 log(x) + 2x +--R ----------- ----------- +--R 2 2 2 +--R (3log(x) + 2x)(%e ) + (2x + 5x + 3)%e +--R (11) ------------------------------------------------------------ +--R 2 +--R (3x + 3)log(x) + 2x + 2x +--R Type: Expression(Integer) +--E 11 + +--S 12 of 61 +I := integrate(i, x) +--R +--R +--R (12) +--R INTSIGN +--R , +--R x +--R , +--R log(%I) + 2%I 2 log(%I) + 2%I +--R ------------- ------------- +--R 2 2 2 +--R (3log(%I) + 2%I)(%e ) + (2%I + 5%I + 3)%e +--R -------------------------------------------------------------------- d%I +--R 2 +--R (3%I + 3)log(%I) + 2%I + 2%I +--R Type: Union(Expression(Integer),...) +--E 12 +\end{chunk} +Example 5.3a +\begin{chunk}{*} + +--S 13 of 61 +i := (2*x+3)/(3*log(x)+2*x) * exp(log(x)/2+x) +--R +--R +--R log(x) + 2x +--R ----------- +--R 2 +--R (2x + 3)%e +--R (13) --------------------- +--R 3log(x) + 2x +--R Type: Expression(Integer) +--E 13 + +--S 14 of 61 +I := integrate(i, x) +--R +--R +--R log(%I) + 2%I +--R ------------- +--R x 2 +--R ++ (2%I + 3)%e +--R (14) | ------------------------ d%I +--R ++ 3log(%I) + 2%I +--R Type: Union(Expression(Integer),...) +--E 14 + +--S 15 of 61 +Ic := li(x*exp(log(x)/2+x)) +--R +--R +--R log(x) + 2x +--R ----------- +--R 2 +--R (15) li(x %e ) +--R Type: Expression(Integer) +--E 15 + +--S 16 of 61 +D(Ic, x) +--R +--R +--R log(x) + 2x +--R ----------- +--R 2 +--R (2x + 3)%e +--R (16) --------------------- +--R log(x) + 2x +--R ----------- +--R 2 +--R 2log(x %e ) +--R Type: Expression(Integer) +--E 16 +\end{chunk} +Example 5.3b +\begin{chunk}{*} + +--S 17 of 61 +i := 1/(x+1)*(exp(log(x)/2+x))^2 +--R +--R +--R log(x) + 2x 2 +--R ----------- +--R 2 +--R (%e ) +--R (17) ---------------- +--R x + 1 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 61 +I := integrate(i, x) +--R +--R +--R log(%I) + 2%I 2 +--R ------------- +--R x 2 +--R ++ (%e ) +--R (18) | ------------------ d%I +--R ++ %I + 1 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 61 +i := x/(x+1)*exp(2*x) +--R +--R +--R 2x +--R x %e +--R (19) ------ +--R x + 1 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 61 +I := integrate(i, x) +--R +--R +--R x 2%I +--R ++ %I %e +--R (20) | -------- d%I +--R ++ %I + 1 +--R Type: Union(Expression(Integer),...) +--E 20 + +--S 21 of 61 +Ic := exp(2*x)/2 - exp(-2)*li(exp(2*x+2)) +--R +--R +--R 2 2x +--R %e %e - 2Ei(2x + 2) +--R (21) --------------------- +--R 2 +--R 2%e +--R Type: Expression(Integer) +--E 21 + +--S 22 of 61 +D(Ic, x) +--R +--R +--R 2x + 2 2 2x +--R - %e + (x + 1)%e %e +--R (22) --------------------------- +--R 2 +--R (x + 1)%e +--R Type: Expression(Integer) +--E 22 +\end{chunk} +Page 18, Example 5.4 +\begin{chunk}{*} + +--S 23 of 61 +i := ((2*x^3-x^2-6*x)/(x^2+3*x+2) + (2*x-3)/(log(x)+1)) * exp(x*log(x)+x) +--R +--R +--R 3 2 3 2 x log(x) + x +--R ((2x - x - 6x)log(x) + 4x + 2x - 11x - 6)%e +--R (23) ----------------------------------------------------------- +--R 2 2 +--R (x + 3x + 2)log(x) + x + 3x + 2 +--R Type: Expression(Integer) +--E 23 + +--S 24 of 61 +I := integrate(i, x) +--R +--R +--R (24) +--R INTSIGN +--R , +--R x +--R , +--R 3 2 3 2 %I log(%I) + %I +--R ((2%I - %I - 6%I)log(%I) + 4%I + 2%I - 11%I - 6)%e +--R --------------------------------------------------------------------- d%I +--R 2 2 +--R (%I + 3%I + 2)log(%I) + %I + 3%I + 2 +--R Type: Union(Expression(Integer),...) +--E 24 + +--S 25 of 61 +Ic := -3/exp(1)*li(exp(x*log(x)+x+log(x)+1)) + 2/exp(2)*li(exp(x*log(x)+x+2*log(x)+2)) +--R +--R +--R 2 +--R 2%e Ei((x + 2)log(x) + x + 2) - 3%e Ei((x + 1)log(x) + x + 1) +--R (25) ------------------------------------------------------------- +--R 2 +--R %e %e +--R Type: Expression(Integer) +--E 25 + +--S 26 of 61 +D(Ic, x) +--R +--R +--R (26) +--R 2 2 (x + 2)log(x) + x + 2 +--R ((2x + 2x)%e log(x) + (4x + 8x + 4)%e)%e +--R + +--R 2 2 2 2 (x + 1)log(x) + x + 1 +--R ((- 3x - 6x)%e log(x) + (- 6x - 15x - 6)%e )%e +--R / +--R 3 2 2 3 2 2 +--R (x + 3x + 2x)%e %e log(x) + (x + 3x + 2x)%e %e +--R Type: Expression(Integer) +--E 26 +\end{chunk} +Page 19, Example 6 +\begin{chunk}{*} + +--S 27 of 61 +i := cos(x)^2 / x^3 +--R +--R +--R 2 +--R cos(x) +--R (27) ------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 27 + +--S 28 of 61 +I := integrate(i, x) +--R +--R +--R x 2 +--R ++ cos(%I) +--R (28) | -------- d%I +--R ++ 3 +--R %I +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 61 +Ic := -Ci(2*x) + sin(2*x)/(2*x) - cos(2*x)/(4*x^2) - 1/(4*x^2) +--R +--R +--R 2 +--R 2x sin(2x) - cos(2x) - 4x Ci(2x) - 1 +--R (29) ------------------------------------ +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 29 + +--S 30 of 61 +D(Ic, x) +--R +--R +--R cos(2x) + 1 +--R (30) ----------- +--R 3 +--R 2x +--R Type: Expression(Integer) +--E 30 +\end{chunk} +Appendix, Example d1 (same as 1.1) +\begin{chunk}{*} + +--S 31 of 61 +i := x/log(x)^2 +--R +--R +--R x +--R (31) ------- +--R 2 +--R log(x) +--R Type: Expression(Integer) +--E 31 + +--S 32 of 61 +I := integrate(i, x) +--R +--R +--R 2 +--R 2log(x)Ei(2log(x)) - x +--R (32) ----------------------- +--R log(x) +--R Type: Union(Expression(Integer),...) +--E 32 +\end{chunk} +Example d2 +\begin{chunk}{*} + +--S 33 of 61 +i := 1/(log(x)+3) +--R +--R +--R 1 +--R (33) ---------- +--R log(x) + 3 +--R Type: Expression(Integer) +--E 33 + +--S 34 of 61 +I := integrate(i, x) +--R +--R +--R x +--R ++ 1 +--R (34) | ----------- d%I +--R ++ log(%I) + 3 +--R Type: Union(Expression(Integer),...) +--E 34 + +--S 35 of 61 +Ic := exp(-3)*li(exp(3)*x) +--R +--R +--R 3 +--R li(x %e ) +--R (35) --------- +--R 3 +--R %e +--R Type: Expression(Integer) +--E 35 + +--S 36 of 61 +D(Ic, x) +--R +--R +--R 1 +--R (36) ---------- +--R 3 +--R log(x %e ) +--R Type: Expression(Integer) +--E 36 +\end{chunk} +Example d3 +\begin{chunk}{*} + +--S 37 of 61 +i := x^2 / log(x+1) +--R +--R +--R 2 +--R x +--R (37) ---------- +--R log(x + 1) +--R Type: Expression(Integer) +--E 37 + +--S 38 of 61 +I := integrate(i, x) +--R +--R +--R x 2 +--R ++ %I +--R (38) | ----------- d%I +--R ++ log(%I + 1) +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 61 +Ic := li(x^3+3*x^2+3*x+1) - 2*li(x^2+2*x+1) + li(x+1) +--R +--R +--R 3 2 2 +--R (39) li(x + 3x + 3x + 1) - 2li(x + 2x + 1) + li(x + 1) +--R Type: Expression(Integer) +--E 39 + +--S 40 of 61 +D(Ic, x) +--R +--R +--R (40) +--R 2 3 2 +--R (log(x + 2x + 1) + (- 4x - 4)log(x + 1))log(x + 3x + 3x + 1) +--R + +--R 2 2 +--R (3x + 6x + 3)log(x + 1)log(x + 2x + 1) +--R / +--R 2 3 2 +--R log(x + 1)log(x + 2x + 1)log(x + 3x + 3x + 1) +--R Type: Expression(Integer) +--E 40 +\end{chunk} +Example d4 +\begin{chunk}{*} + +--S 41 of 61 +i := (log(x)^2+3)/(log(x)^2+3*log(x)+2) +--R +--R +--R 2 +--R log(x) + 3 +--R (41) --------------------- +--R 2 +--R log(x) + 3log(x) + 2 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 61 +I := integrate(i, x) +--R +--R +--R x 2 +--R ++ log(%I) + 3 +--R (42) | ----------------------- d%I +--R ++ 2 +--R log(%I) + 3log(%I) + 2 +--R Type: Union(Expression(Integer),...) +--E 42 + +--S 43 of 61 +Ic := -7*exp(-2)*li(exp(2)*x)+4*exp(-1)*li(exp(1)*x)+x +--R +--R +--R 2 2 2 +--R - 7%e li(x %e ) + 4%e li(x %e) + x %e %e +--R (43) ----------------------------------------- +--R 2 +--R %e %e +--R Type: Expression(Integer) +--E 43 + +--S 44 of 61 +D(Ic, x) +--R +--R +--R 2 +--R (log(x %e) + 4)log(x %e ) - 7log(x %e) +--R (44) -------------------------------------- +--R 2 +--R log(x %e)log(x %e ) +--R Type: Expression(Integer) +--E 44 +\end{chunk} +Example d5, d6, d7 +\begin{chunk}{*} + +--S 45 of 61 +I := li(x*exp(x)/log(x)) +--R +--R +--R x +--R x %e +--R (45) li(------) +--R log(x) +--R Type: Expression(Integer) +--E 45 + +--S 46 of 61 +i := D(I, x) +--R +--R +--R x x +--R (x + 1)%e log(x) - %e +--R (46) ---------------------- +--R x +--R 2 x %e +--R log(x) log(------) +--R log(x) +--R Type: Expression(Integer) +--E 46 + +--S 47 of 61 +I := integrate(i, x) +--R +--R +--R x +--R x %e +--R (47) li(------) +--R log(x) +--R Type: Union(Expression(Integer),...) +--E 47 +\end{chunk} +Example d8 +\begin{chunk}{*} + +--S 48 of 61 +i := exp(x)/(x+1)^2 +--R +--R +--R x +--R %e +--R (48) ----------- +--R 2 +--R x + 2x + 1 +--R Type: Expression(Integer) +--E 48 + +--S 49 of 61 +I := integrate(i, x) +--R +--R +--R x %I +--R ++ %e +--R (49) | ------------- d%I +--R ++ 2 +--R %I + 2%I + 1 +--R Type: Union(Expression(Integer),...) +--E 49 + +--S 50 of 61 +Ic := exp(-1)*Ei(x+1) - exp(x)/(x+1) +--R +--R +--R x +--R - %e %e + (x + 1)Ei(x + 1) +--R (50) --------------------------- +--R (x + 1)%e +--R Type: Expression(Integer) +--E 50 + +--S 51 of 61 +D(Ic, x) +--R +--R +--R x + 1 x +--R (x + 1)%e - x %e %e +--R (51) ------------------------- +--R 2 +--R (x + 2x + 1)%e +--R Type: Expression(Integer) +--E 51 +\end{chunk} +Example d9 +\begin{chunk}{*} + +--S 52 of 61 +i := sin(x)/x +--R +--R +--R sin(x) +--R (52) ------ +--R x +--R Type: Expression(Integer) +--E 52 + +--S 53 of 61 +I := integrate(i, x) +--R +--R +--R (53) Si(x) +--R Type: Union(Expression(Integer),...) +--E 53 +\end{chunk} +Example d10 (same as 6) +\begin{chunk}{*} + +--S 54 of 61 +i := cos(x)^2/x^3 +--R +--R +--R 2 +--R cos(x) +--R (54) ------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 54 + +--S 55 of 61 +I := integrate(i, x) +--R +--R +--R x 2 +--R ++ cos(%I) +--R (55) | -------- d%I +--R ++ 3 +--R %I +--R Type: Union(Expression(Integer),...) +--E 55 +\end{chunk} +Example d11 +\begin{chunk}{*} + +--S 56 of 61 +i := (x^2+3)*exp(x)/(x^2+3*x+2) +--R +--R +--R 2 x +--R (x + 3)%e +--R (56) ----------- +--R 2 +--R x + 3x + 2 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 61 +I := integrate(i, x) +--R +--R +--R x 2 %I +--R ++ (%I + 3)%e +--R (57) | ------------- d%I +--R ++ 2 +--R %I + 3%I + 2 +--R Type: Union(Expression(Integer),...) +--E 57 + +--S 58 of 61 +Ic := -7*exp(-2)*Ei(x+2) + 4*exp(-1)*Ei(x+1) + exp(x) +--R +--R +--R 2 x 2 +--R %e %e %e - 7%e Ei(x + 2) + 4%e Ei(x + 1) +--R (58) ----------------------------------------- +--R 2 +--R %e %e +--R Type: Expression(Integer) +--E 58 + +--S 59 of 61 +D(Ic, x) +--R +--R +--R x + 2 2 x + 1 2 2 x +--R (- 7x - 7)%e %e + (4x + 8)%e %e + (x + 3x + 2)%e %e %e +--R (59) ------------------------------------------------------------------ +--R 2 2 +--R (x + 3x + 2)%e %e +--R Type: Expression(Integer) +--E 59 +\end{chunk} +Example d12 +\begin{chunk}{*} + +--S 60 of 61 +i := (x^2+1)*exp(x)/(x^2+x+1) +--R +--R +--R 2 x +--R (x + 1)%e +--R (60) ----------- +--R 2 +--R x + x + 1 +--R Type: Expression(Integer) +--E 60 + +--S 61 of 61 +I := integrate(i, x) +--R +--R +--R x 2 %I +--R ++ (%I + 1)%e +--R (61) | ------------- d%I +--R ++ 2 +--R %I + %I + 1 +--R Type: Union(Expression(Integer),...) +--E 61 +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} +