diff --git a/changelog b/changelog index b9f8022..539dea7 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100727 mxr src/axiom-website/patches.html 20100727.02.mxr.patch +20100727 mxr src/input/Makefile add guess.input regression tests +20100727 mxr src/input/guess.input test examples of the GUESS package 20100727 tpd src/axiom-website/patches.html 20100727.01.tpd.patch 20100727 tpd Makefile build src/input quietly 20100726 tpd src/axiom-website/patches.html 20100726.01.tpd.patch diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 244915a..eb6ce56 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -3029,5 +3029,7 @@ src/axiom-website/download.html upload source, add ubuntu binary
src/doc/axiom.sty consolidate latex macros
20100727.01.tpd.patch Makefile build src/input quietly
+20100727.02.mxr.patch +src/input/guess.input test examples of the GUESS package
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 0ebba87..feabb93 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -328,7 +328,8 @@ REGRESSTESTS= ackermann.regress \ fr2.regress frac.regress fr.regress free.regress \ function.regress galois.regress gamma.regress \ gbf.regress genups.regress gonshor.regress grpthry.regress \ - gstbl.regress heap.regress heat.regress help.regress \ + gstbl.regress guess.regress \ + heap.regress heat.regress help.regress \ herm.regress heugcd.regress \ hexadec.regress hyperbolicrules.regress \ hyperell.regress ico.regress ideal.regress \ @@ -681,7 +682,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/fr1.input ${OUT}/gary1.input \ ${OUT}/gbf.input ${OUT}/genups.input ${OUT}/gnarly1.input \ ${OUT}/gonshor.input ${OUT}/grdef.input \ - ${OUT}/gstbl.input \ + ${OUT}/gstbl.input ${OUT}/guess.input \ ${OUT}/heap.input ${OUT}/heat.input ${OUT}/helix.input \ ${OUT}/herm.input ${OUT}/heugcd.input \ ${OUT}/hexadec.input ${OUT}/huang.input \ @@ -1036,7 +1037,8 @@ DOCFILES= \ ${DOC}/genups.input.dvi ${DOC}/gnarly1.input.dvi \ ${DOC}/gonshor.input.dvi ${DOC}/graphics.input.dvi \ ${DOC}/grdef.input.dvi ${DOC}/grpthry.input.dvi \ - ${DOC}/gstbl.input.dvi ${DOC}/heap.input.dvi \ + ${DOC}/gstbl.input.dvi ${DOC}/guess.input.dvi \ + ${DOC}/heap.input.dvi \ ${DOC}/heat.input.dvi ${DOC}/helix.input.dvi \ ${DOC}/help.input.dvi ${DOC}/herm.input.dvi \ ${DOC}/heugcd.input.dvi \ diff --git a/src/input/guess.input.pamphlet b/src/input/guess.input.pamphlet new file mode 100644 index 0000000..f1b1193 --- /dev/null +++ b/src/input/guess.input.pamphlet @@ -0,0 +1,1349 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input guess.input} +\author{Martin Rubey} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)spool guess.output +)set message auto off +)clear all + +--S 1 of 102 +coeff:=FRAC(UP('k,Integer)) +--R +--R +--R (1) Fraction UnivariatePolynomial(k,Integer) +--R Type: Domain +--E 1 + +--S 2 of 102 +Uts:=UnivariateTaylorSeries(coeff,'x,0) +--R +--R +--R (2) UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Integer),x,0) +--R Type: Domain +--E 2 + +--S 3 of 102 +Ets:=EllipticFunctionsUnivariateTaylorSeries(coeff,Uts) +--R +--R +--R (3) +--R EllipticFunctionsUnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Integ +--R er),UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Integer),x,0)) +--R Type: Domain +--E 3 + +--S 4 of 102 +snk:=sn(x::Uts,k::coeff)$Ets +--R +--R +--R (4) +--R 2 4 2 6 4 2 +--R - k - 1 3 k + 14k + 1 5 - k - 135k - 135k - 1 7 +--R x + -------- x + ------------- x + ------------------------ x +--R 6 120 5040 +--R + +--R 8 6 4 2 +--R k + 1228k + 5478k + 1228k + 1 9 11 +--R --------------------------------- x + O(x ) +--R 362880 +--R Type: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Integer),x,0) +--E 4 + +--S 5 of 102 +ll:=entries(complete(first(coefficients(snk),25))) +--R +--R +--R (5) +--R 2 4 2 6 4 2 +--R - k - 1 k + 14k + 1 - k - 135k - 135k - 1 +--R [0, 1, 0, --------, 0, -------------, 0, ------------------------, 0, +--R 6 120 5040 +--R 8 6 4 2 +--R k + 1228k + 5478k + 1228k + 1 +--R ---------------------------------, 0, +--R 362880 +--R 10 8 6 4 2 +--R - k - 11069k - 165826k - 165826k - 11069k - 1 +--R ---------------------------------------------------, 0, +--R 39916800 +--R 12 10 8 6 4 2 +--R k + 99642k + 4494351k + 13180268k + 4494351k + 99642k + 1 +--R -----------------------------------------------------------------, 0, +--R 6227020800 +--R +--R 14 12 10 8 6 +--R - k - 896803k - 116294673k - 834687179k - 834687179k +--R + +--R 4 2 +--R - 116294673k - 896803k - 1 +--R / +--R 1307674368000 +--R , +--R 0, +--R +--R 16 14 12 10 8 +--R k + 8071256k + 2949965020k + 47152124264k + 109645021894k +--R + +--R 6 4 2 +--R 47152124264k + 2949965020k + 8071256k + 1 +--R / +--R 355687428096000 +--R , +--R 0, +--R +--R 18 16 14 12 +--R - k - 72641337k - 74197080276k - 2504055894564k +--R + +--R 10 8 6 +--R - 11966116940238k - 11966116940238k - 2504055894564k +--R + +--R 4 2 +--R - 74197080276k - 72641337k - 1 +--R / +--R 121645100408832000 +--R , +--R 0, +--R +--R 20 18 16 14 +--R k + 653772070k + 1859539731885k + 128453495887560k +--R + +--R 12 10 8 +--R 1171517154238290k + 2347836365864484k + 1171517154238290k +--R + +--R 6 4 2 +--R 128453495887560k + 1859539731885k + 653772070k + 1 +--R / +--R 51090942171709440000 +--R , +--R 0, +--R +--R 22 20 18 16 +--R - k - 5883948671k - 46535238000235k - 6460701405171285k +--R + +--R 14 12 10 +--R - 107266611330420090k - 393938089395885894k - 393938089395885894k +--R + +--R 8 6 4 +--R - 107266611330420090k - 6460701405171285k - 46535238000235k +--R + +--R 2 +--R - 5883948671k - 1 +--R / +--R 25852016738884976640000 +--R , +--R 0] +--R Type: List Fraction UnivariatePolynomial(k,Integer) +--E 5 + +--S 6 of 102 +r1:=guessADE(ll,maxDegree==0,safety==5) +--R +--R +--R (6) +--R [ +--R [ +--R function = +--R BRACKET +--R n +--R [x ]f(x): +--R ,, 2 3 2 , +--R f (x) - 2k f(x) + (k + 1)f(x)= 0,f(0)= 0(0)!,f (0)= 1(1)! +--R +--R , +--R order= 0] +--R ] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 6 + +)clear all + +--S 7 of 102 +t1:=[0,1,0,1,1,0,0,0,0,0,0,0,0,0,0] +--R +--R +--R (1) [0,1,0,1,1,0,0,0,0,0,0,0,0,0,0] +--R Type: List NonNegativeInteger +--E 7 + +--S 8 of 102 +t2:=first guessADE first(t1,10) +--R +--R +--R n 4 3 +--R (2) [function= [[x ]f(x): f(x) - x - x - x= 0],order= 0] +--R Type: Record(function: Expression Integer,order: NonNegativeInteger) +--E 8 + +)clear all + +--S 9 of 102 +t1:=guessRat [0,1,4] +--R +--R +--R (1) [] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 9 + +--S 10 of 102 +t2:=guessRat [0] +--R +--R +--R (2) [] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 10 + +--S 11 of 102 +t3:=guessRat [1,1] +--R +--R +--R (3) [[function= 1,order= 0]] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 11 + +--S 12 of 102 +t4:=guessRat [0,0] +--R +--R +--R (4) [[function= 0,order= 0]] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 12 + +--S 13 of 102 +t5:=guessRat([0,1,2], allDegrees==false)$GUESSAN +--R +--R +--R (5) [[function= n,order= 0]] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 13 + +--S 14 of 102 +t6:=guessRat([1,2,3], allDegrees==false) +--R +--R +--R (6) [[function= n + 1,order= 0]] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 14 + +--S 15 of 102 +t7:=guessRat([1,1/2,1/3], allDegrees==false)$GUESSAN +--R +--R +--R 1 +--R (7) [[function= -----,order= 0]] +--R n + 1 +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 15 + +--S 16 of 102 +t8:=guessRat([0,1,4,9])$GUESSAN +--R +--R +--R 2 +--R (8) [[function= n ,order= 0]] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 16 + +--S 17 of 102 +t9:=guessRat([0,1/2,2/3,3/4], allDegrees==false)$GUESSAN +--R +--R +--R n +--R (9) [[function= -----,order= 0]] +--R n + 1 +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 17 + +--S 18 of 102 +t10:=guessRat([1/2,2/3,3/4,4/5], allDegrees==false) +--R +--R +--R n + 1 +--R (10) [[function= -----,order= 0]] +--R n + 2 +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 18 + +--S 19 of 102 +t11:=guessRat([0,1,4,9,16], safety==2) +--R +--R +--R 2 +--R (11) [[function= n ,order= 0]] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 19 + +)clear all + +--S 20 of 102 +t1:=guessRat(q)([1,q,q^2], []) +--R +--R +--R n +--R (1) [[function= q ,order= 0]] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 20 + +--S 21 of 102 +t2:=guessRat(q)([i^3*q^i + q^(2*i) for i in 0..6], maxMixedDegree==2) +--R +--R There are no library operations named maxMixedDegree +--R Use HyperDoc Browse or issue +--R )what op maxMixedDegree +--R to learn if there is any operation containing " maxMixedDegree " +--R in its name. +--R +--R Cannot find a definition or applicable library operation named +--R maxMixedDegree with argument type(s) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 21 + +--S 22 of 102 +t3:=guessRat([(i+1)*z for i in 0..5]::List POLY PF 5) +--R +--R There are 12 exposed and 0 unexposed library operations named +--R guessRat having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op guessRat +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R guessRat with argument type(s) +--R List Polynomial PrimeField 5 +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 22 + +)clear all + +--S 23 of 102 +t1:=guessRat([1,0,1])$GUESSF(PF 2) +--R +--R +--R (1) [[function= - n - 1,order= 0]] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 23 + +--S 24 of 102 +t2:=guessRat([1,0,1,0])$GUESSF(PF 2) +--R +--R +--R >> Error detected within library code: +--R not invertible +--R +--R Continuing to read the file... +--R +--E 24 + +--S 25 of 102 +t3:=guessRat([1,0,1,1], one==false)$GUESSF(PF 2) +--R +--R +--R >> Error detected within library code: +--R not invertible +--R +--R Continuing to read the file... +--R +--E 25 + +--S 26 of 102 +t4:=guessRat([binomial(2*n, n) for n in 0..6])$GUESSF(PF 3) +--R +--R +--R >> Error detected within library code: +--R not invertible +--R +--R Continuing to read the file... +--R +--E 26 + +--S 27 of 102 +t5:=guessRat([1,0,1,0,1,0,1])$GUESSF(PF 7) +--R +--R +--R (2) [] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 27 + +--S 28 of 102 +f := operator 'f; +--R +--R +--R Type: BasicOperator +--E 28 + +--S 29 of 102 +t6:=guessPade([1,1,1]) +--R +--R +--R n +--R (4) [[function= [[x ]f(x): (x - 1)f(x) + 1= 0],order= 0]] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 29 + +--S 30 of 102 +t7:=getEq first t6 +--R +--R There are 1 exposed and 0 unexposed library operations named getEq +--R having 1 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op getEq +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named getEq +--R with argument type(s) +--R Record(function: Expression Integer,order: NonNegativeInteger) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 30 + +--S 31 of 102 +t8:=guessPade([1,1,2,3], allDegrees==false) +--R +--R +--R (5) [] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 31 + +--S 32 of 102 +t9:=guessPade([1,1,2,3], allDegrees==true) +--R +--R +--R n 2 +--R (6) [[function= [[x ]f(x): (x + x - 1)f(x) + 1= 0],order= 0]] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 32 + +--S 33 of 102 +t10:=getEq first t9 +--R +--R There are 1 exposed and 0 unexposed library operations named getEq +--R having 1 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op getEq +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named getEq +--R with argument type(s) +--R Record(function: Expression Integer,order: NonNegativeInteger) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 33 + +)clear all + +--S 34 of 102 +g 0 == 0; +--R +--R Type: Void +--E 34 + +--S 35 of 102 +g 1 == 1; +--R +--R Type: Void +--E 35 + +--S 36 of 102 +g 2 == 1; +--R +--R Type: Void +--E 36 + +--S 37 of 102 +g n == sqrt 2*g(n-1)+3*g(n-2)+g(n-3); +--R +--R Type: Void +--E 37 + +--S 38 of 102 +guessPade([g i for i in 0..6])$GUESSAN +--R +--R Compiling function g with type Integer -> AlgebraicNumber +--R Compiling function g as a recurrence relation. +--R +--R (5) +--R [ +--R n +-+ 3 2 2 +-+ 2 +--R [function= [[x ]f(x): (x\|2 + x + 3x - 1)f(x) - x \|2 + x + x= 0], +--R order= 0] +--R ] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 38 + +)clear all + +--S 39 of 102 +g 0 == z; +--R +--R Type: Void +--E 39 + +--S 40 of 102 +g 1 == 1; +--R +--R Type: Void +--E 40 + +--S 41 of 102 +g 2 == 1; +--R +--R Type: Void +--E 41 + +--S 42 of 102 +g n == sqrt 2*g(n-1)+3*g(n-2)+g(n-3); +--R +--R Type: Void +--E 42 + +--S 43 of 102 +guessPade [g i for i in 0..6] +--R +--R Compiling function g with type Integer -> Polynomial AlgebraicNumber +--R +--R Compiling function g as a recurrence relation. +--R +--R (5) +--R SUB +--R guessPade +--R , +--R z +--R , +--R 1 +--R , +--R 1 +--R , +--R +-+ +--R z + \|2 + 3 +--R , +--R +-+ +-+ +--R \|2 z + 3\|2 + 6 +--R , +--R +-+ +--R 5z + 9\|2 + 16 +--R , +--R +-+ +-+ +--R (8\|2 + 1)z + 26\|2 + 39 +--R Type: Symbol +--E 43 + +)clear all + +--S 44 of 102 +guessAlg([1/(2*n+1)*binomial(2*n+1, n) for n in 0..3], allDegrees==true) +--R +--R +--R (1) +--R [ +--R [ +--R function = +--R BRACKET +--R n +--R [x ]f(x): +--R 2 , ,, +--R x f(x) - f(x) + 1= 0,f(0)= 1(0)!,f (0)= 1(1)!,f (0)= 2(2)! +--R +--R , +--R ,,, +--R f (0)= 5(3)! +--R +--R , +--R order= 0] +--R ] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 44 + +)clear all + +--S 45 of 102 +guessAlg [1/(2*n+1)*binomial(2*n+1, n) for n in 0..5] +--R +--R +--R (1) +--R [ +--R [ +--R function = +--R BRACKET +--R n +--R [x ]f(x): +--R 2 , ,, +--R x f(x) - f(x) + 1= 0,f(0)= 1(0)!,f (0)= 1(1)!,f (0)= 2(2)! +--R +--R , +--R ,,, (iv) +--R f (0)= 5(3)!,f (0)= 14(4)! +--R +--R , +--R order= 0] +--R ] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 45 + +)clear all + +--S 46 of 102 +guessPRec([1,2,6,20,70]) +--R +--R +--R (1) [] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 46 + +)clear all + +--S 47 of 102 +guessPRec([1,2,6,20], homogeneous==true, allDegrees==true) +--R +--R +--R (1) [] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 47 + +--S 48 of 102 +guessPRec([1,2,6,20,70], homogeneous==true) +--R +--R +--R (2) +--R [[function= [f(n): (n + 1)f(n + 1) + (- 4n - 2)f(n)= 0,f(0)= 1],order= 0]] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 48 + +--S 49 of 102 +guessPRec([1,2,6,20,70], allDegrees==true) +--R +--R +--R (3) +--R [[function= [f(n): (n + 1)f(n + 1) + (- 4n - 2)f(n)= 0,f(0)= 1],order= 0]] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 49 + +)clear all + +--S 50 of 102 +guessPRec [0,0,0,1,2,3,4,5] +--R +--R +--R (1) [[function= n - 2,order= 2]] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 50 + +)clear all + +--S 51 of 102 +r: INT -> POLY INT +--R +--R Type: Void +--E 51 + +--S 52 of 102 +r(0)==1 +--R +--R Type: Void +--E 52 + +--S 53 of 102 +r(1)==1 +--R +--R Type: Void +--E 53 + +--S 54 of 102 +r(n)==q^(n-1)*r(n-1)+(n-2)*r(n-2) +--R +--R Type: Void +--E 54 + +--S 55 of 102 +guessPRec(q)([r m for m in 0..7], maxMixedDegree==1, maxDegree==1, _ + homogeneous==true) +--R +--R Compiling function r with type Integer -> Polynomial Integer +--R Compiling function r as a recurrence relation. +--R There are no library operations named maxMixedDegree +--R Use HyperDoc Browse or issue +--R )what op maxMixedDegree +--R to learn if there is any operation containing " maxMixedDegree " +--R in its name. +--R +--R Cannot find a definition or applicable library operation named +--R maxMixedDegree with argument type(s) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 55 + +)clear all + +)set function cache all r + +--S 56 of 102 +r: INT -> POLY INT +--R +--R Type: Void +--E 56 + +--S 57 of 102 +r 0 == a00 +--R +--R Type: Void +--E 57 + +--S 58 of 102 +r 1 == a01 +--R +--R Type: Void +--E 58 + +--S 59 of 102 +r 2 == a02 +--R +--R Type: Void +--E 59 + +--S 60 of 102 +r 3 == a03 +--R +--R Type: Void +--E 60 + +--S 61 of 102 +r 4 == a04 +--R +--R Type: Void +--E 61 + +--S 62 of 102 +r n == reduce(+, [r(n-i)::POLY INT for i in 1..4]) +--R +--R Type: Void +--E 62 + +--S 63 of 102 +guessPRec [r i for i in 0..11] +--R +--R Compiling function r with type Integer -> Polynomial Integer +--R r will cache all previously computed values. +--R +--R (8) +--R [ +--R [ +--R function = +--R BRACKET +--R f(n): +--R f(n + 5) - f(n + 4) - f(n + 3) - f(n + 2) - f(n + 1)= 0 +--R , +--R f(0)= a00,f(1)= a01,f(2)= a02,f(3)= a03 +--R , +--R order= 0] +--R ] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 63 + +)clear all + +--S 64 of 102 +guessPRec([1,0,0,0,0,0,0,0], homogeneous==true) +--R +--R +--R (1) [] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 64 + +--S 65 of 102 +guessPRec([0,1,0,0,0,0,0,0], homogeneous==true) +--R +--R +--R (2) [] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 65 + +--S 66 of 102 +guessPRec([0,0,1,0,0,0,0,0], homogeneous==true) +--R +--R +--R (3) [] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 66 + +)clear all + +--S 67 of 102 +guessADE([n^n/factorial n for n in 0..6], allDegrees==true) +--R +--R +--R (1) +--R n , 3 2 +--R [[function= [[x ]f(x): xf (x) - f(x) + f(x) = 0,f(0)= 1(0)!],order= 0]] +--R +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 67 + +)clear all + +--S 68 of 102 +t1 := [1, 1, q+1, q^3+q^2+2*q+1, q^6+q^5+2*q^4+3*q^3+3*q^2+3*q+1, _ + q^10+q^9+2*q^8+3*q^7+5*q^6+5*q^5+7*q^4+7*q^3+6*q^2+4*q+1] +--R +--R +--R (1) +--R 3 2 6 5 4 3 2 +--R [1, 1, q + 1, q + q + 2q + 1, q + q + 2q + 3q + 3q + 3q + 1, +--R 10 9 8 7 6 5 4 3 2 +--R q + q + 2q + 3q + 5q + 5q + 7q + 7q + 6q + 4q + 1] +--R Type: List Polynomial Integer +--E 68 + +--S 69 of 102 +guessADE(q)(t1, maxPower==2, allDegrees==true) +--R +--R +--R n +--R (2) [[function= [[x ]f(x): x f(x)f(q x) - f(x) + 1= 0],order= 0]] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 69 + +)clear all + +--S 70 of 102 +guessADE(q)(first(t1, 4), maxPower==2, allDegrees==true) +--R +--R There are 1 exposed and 0 unexposed library operations named first +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op first +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named first +--R with argument type(s) +--R Variable t1 +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 70 + +)clear all + +--S 71 of 102 +s: INT -> INT +--R +--R Type: Void +--E 71 + +--S 72 of 102 +s(0)==1 +--R +--R Type: Void +--E 72 + +--S 73 of 102 +s(1)==1 +--R +--R Type: Void +--E 73 + +--S 74 of 102 +s(2)==1 +--R +--R Type: Void +--E 74 + +--S 75 of 102 +s(3)==1 +--R +--R Type: Void +--E 75 + +--S 76 of 102 +s(n)==(s(n-1)*s(n-3)+s(n-2)^2)/s(n-4) +--R +--R Type: Void +--E 76 + +--S 77 of 102 +guessRec([s m for m in 0..18], maxPower==2) +--R +--R Compiling function s with type Integer -> Integer +--R Compiling function s as a recurrence relation. +--R +--R (7) +--R [ +--R [ +--R function = +--R BRACKET +--R f(n): +--R 2 +--R f(n)f(n + 4) - f(n + 1)f(n + 3) - f(n + 2) = 0,f(0)= 1,f(1)= 1 +--R , +--R f(2)= 1,f(3)= 1 +--R , +--R order= 0] +--R ] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 77 + +--S 78 of 102 +guessRec([s m for m in 0..12], maxPower==2, homogeneous==true) +--R +--R +--R (8) [] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 78 + +--S 79 of 102 +guessRec([s m for m in 0..6], Somos==4, homogeneous==2) +--R +--R There are no library operations named Somos +--R Use HyperDoc Browse or issue +--R )what op Somos +--R to learn if there is any operation containing " Somos " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Somos +--R with argument type(s) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 79 + +)clear all + +)clear values s + +--S 80 of 102 +s n == reduce(*,[reduce(*,[factorial i for i in 0..j-1],1) for j in 0..n-1],1) +--R +--R Type: Void +--E 80 + +--S 81 of 102 +guess [s l for l in 0..6] +--R +--R Compiling function s with type NonNegativeInteger -> Integer +--R s will cache all previously computed values. +--R +--R (2) +--R [ +--R [ +--R function = +--R PI2 +--R p = 0 +--R 7 +--R , +--R n - 1 +--R , +--R PI2 +--R p = 0 +--R 6 +--R , +--R p - 1 +--R 7 +--R , +--R BRACKET +--R p +--R 6 +--R [x ]f(x): +--R 2 2 , +--R 3f(x) - 8f(x) + x + 2x + 5= 0,f(0)= 1(0)!,f (0)= 1(1)! +--R +--R , +--R ,, ,,, (iv) +--R f (0)= 2(2)!,f (0)= 6(3)!,f (0)= 24(4)! +--R +--R , +--R order= 0] +--R ] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 81 + +--S 82 of 102 +guessRec([s l for l in 0..8], Somos==6, homogeneous==4) +--R +--R There are no library operations named Somos +--R Use HyperDoc Browse or issue +--R )what op Somos +--R to learn if there is any operation containing " Somos " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Somos +--R with argument type(s) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 82 + +--S 83 of 102 +guessRec([s l for l in 0..8], Somos==true, homogeneous==4, maxShift==3) +--R +--R There are no library operations named Somos +--R Use HyperDoc Browse or issue +--R )what op Somos +--R to learn if there is any operation containing " Somos " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Somos +--R with argument type(s) +--R Boolean +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 83 + +--S 84 of 102 +guessRec([s l for l in 0..8], Somos==true, homogeneous==true, _ + maxPower==4, maxShift==3) +--R +--R There are no library operations named Somos +--R Use HyperDoc Browse or issue +--R )what op Somos +--R to learn if there is any operation containing " Somos " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Somos +--R with argument type(s) +--R Boolean +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 84 + +)clear all + +)clear values s + +--S 85 of 102 +s 0 == 1 +--R +--R Type: Void +--E 85 + +--S 86 of 102 +s 1 == 2 +--R +--R Type: Void +--E 86 + +--S 87 of 102 +s n == s(n-1)^2*s(n-2) +--R +--R Type: Void +--E 87 + +--S 88 of 102 +guessRec([s l for l in 0..5], Somos==true, maxShift==2, maxPower==3) +--R +--R Compiling function s with type Integer -> PositiveInteger +--R Compiling function s as a recurrence relation. +--R There are no library operations named Somos +--R Use HyperDoc Browse or issue +--R )what op Somos +--R to learn if there is any operation containing " Somos " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Somos +--R with argument type(s) +--R Boolean +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 88 + +--S 89 of 102 +guessRec([0, 1, 0, 0, 0, 2, 0, 7, 0, 0, 0, 15, 0, 0, 0], one==false) +--R +--R +--R (4) +--R [ +--R [ +--R function = +--R BRACKET +--R f(n): +--R 4 3 2 +--R 65f(n)f(n + 2) - 7f(n) + 161f(n) - 889f(n) + 735f(n)= 0 +--R , +--R f(0)= 0,f(1)= 1 +--R , +--R order= 0] +--R , +--R +--R 4 2 +--R [function= [f(n): 20f(n) + (- 941n + 5741)f(n) + (647n - 5467)f(n)= 0], +--R order= 0] +--R , +--R +--R [ +--R function = +--R BRACKET +--R f(n): +--R 2 3 2 +--R (79n - 948n + 2133)f(n + 2) + 28f(n) - 1008f(n) +--R + +--R (784n + 196)f(n) +--R = +--R 0 +--R , +--R f(0)= 0,f(1)= 1 +--R , +--R order= 0] +--R , +--R +--R 3 2 +--R [function= [f(n): 40f(n) + (- 79n + 219)f(n) + (93n - 273)f(n)= 0], +--R order= 0] +--R , +--R 2 2 +--R [function= [f(n): (11n - 31)f(n) + (- 20n + 103n - 63)f(n)= 0],order= 0], +--R 2 3 2 +--R [function= [f(n): 240f(n) + (11n - 233n + 997n - 1015)f(n)= 0],order= 0]] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 89 + +)clear all + +--S 90 of 102 +guessExpRat([0,3,32,375,5184]) +--R +--R +--R n +--R (1) [[function= n (n + 2) ,order= 0]] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 90 + +)clear all + +--S 91 of 102 +guessBinRat([1,1,k+1,(3*k*k+5*k+2)/2,(8*k^3+18*k*k+13*k+3)/3]) +--R +--R +--R (k + 1)n (k + 1)n + 1 +--R ( ) ( ) +--R n n +--R (1) [[function= ----------,order= 0],[function= --------------,order= 0]] +--R k n + 1 (k + 1)n + 1 +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 91 + +--S 92 of 102 +guessBinRat([binomial(3+7*k, k)/(k+3) for k in 0..6]::List PF 3001) +--R +--R +--R >> Error detected within library code: +--R (1 . failed) cannot be coerced to mode (Integer) +--R +--R Continuing to read the file... +--R +--E 92 + +)clear all + +--S 93 of 102 +guess([1,1,2,7,42,429,7436,218348], [guessRat], [guessProduct]) +--R +--R +--R p - 1 2 +--R n - 1 8 27p + 54p + 24 +--R ++-++ ++-++ 7 7 +--R (1) [[function= | | | | -----------------,order= 0]] +--R | | | | 2 +--R p = 0 p = 0 16p + 32p + 12 +--R 8 7 7 7 +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 93 + +--S 94 of 102 +guess([0,1,3,9,33], [guessRat], [guessSum, guessProduct]) +--R +--R +--R s - 1 +--R n - 1 5 +--R --+ ++-++ +--R (2) [[function= > | | p + 2,order= 0]] +--R --+ | | 4 +--R s = 0 p = 0 +--R 5 4 +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 94 + +--S 95 of 102 +guess([product(1+factorial k, k=0..n-1) for n in 0..6], _ + [guessPRec], [guessProduct]) +--R +--R +--R (3) +--R [ +--R n - 1 +--R ++-++ +--R [function= | | [f(p ): f(p + 1) + (- p - 1)f(p ) + p = 0,f(0)= 2], +--R | | 7 7 7 7 7 +--R p = 0 +--R 7 +--R order= 0] +--R ] +--R Type: List Record(function: Expression Integer,order: NonNegativeInteger) +--E 95 + +--S 96 of 102 +guessPRec([1,2,3,4,5], Somos==3) +--R +--R There are no library operations named Somos +--R Use HyperDoc Browse or issue +--R )what op Somos +--R to learn if there is any operation containing " Somos " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Somos +--R with argument type(s) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 96 + +--S 97 of 102 +guessPRec([1,2,3,4,5], Somos==true) +--R +--R There are no library operations named Somos +--R Use HyperDoc Browse or issue +--R )what op Somos +--R to learn if there is any operation containing " Somos " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Somos +--R with argument type(s) +--R Boolean +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 97 + +--S 98 of 102 +guessRec([1,2,3,4], Somos==true, maxShift==4, homogeneous==1) +--R +--R There are no library operations named Somos +--R Use HyperDoc Browse or issue +--R )what op Somos +--R to learn if there is any operation containing " Somos " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Somos +--R with argument type(s) +--R Boolean +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 98 + +--S 99 of 102 +guessRec([1,2,3,4], Somos==5, maxShift==4, homogeneous==1) +--R +--R There are no library operations named Somos +--R Use HyperDoc Browse or issue +--R )what op Somos +--R to learn if there is any operation containing " Somos " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Somos +--R with argument type(s) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 99 + +)clear all + +--S 100 of 102 +guessADE(append([n/1 for n in 0..6],[1]),homogeneous==4,maxDegree==2) +--R +--R There are 2 exposed and 0 unexposed library operations named +--R homogeneous having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op homogeneous +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R homogeneous with argument type(s) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 100 + +--S 101 of 102 +guessADE(append([n/1 for n in 0..6],[1]),homogeneous==4,maxDegree==2,_ + checkExtraValues==false) +--R +--R There are 2 exposed and 0 unexposed library operations named +--R homogeneous having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op homogeneous +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R homogeneous with argument type(s) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 101 + +--S 102 of 102 +guessADE(append([n/1 for n in 0..6],[1]),homogeneous==4,maxDegree==2, _ + check=='MonteCarlo) +--R +--R There are 2 exposed and 0 unexposed library operations named +--R homogeneous having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op homogeneous +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R homogeneous with argument type(s) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 102 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} +