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last edited 8 months ago by beccari |
Edit detail for SandBox.GuessingSequence revision 3 of 598
added:
From Thomas Sun Jan 27 03:05:54 -0800 2008
From: Thomas
Date: Sun, 27 Jan 2008 03:05:54 -0800
Subject:
Message-ID: <20080127030554-0800@axiom-wiki.newsynthesis.org>
\begin{axiom}
guess([1,1,6,54,660,10260,194040,4326840,111177360,3234848400,105135861600], [guessRat], [guessSum, guessProduct], maxLevel==2)
\end{axiom}
This page makes test uses of the guessing package by Martin Rubey. Feel free to add new sequences or change the sequences to ones you like to try.
We need to load these packages:
axiom)lib RECOP FAMR2 FFFG FFFGF NEWTON UFPS UFPS1 GOPT GOPT0 GUESS GUESSINT GUESSP GUESSF1 GUESSF )library cannot find the file FFFGF. RecurrenceOperator is now explicitly exposed in frame initial RecurrenceOperator will be automatically loaded when needed from /var/zope2/var/LatexWiki/RECOP.NRLIB/code FiniteAbelianMonoidRingFunctions2 is now explicitly exposed in frame initial FiniteAbelianMonoidRingFunctions2 will be automatically loaded when needed from /var/zope2/var/LatexWiki/FAMR2.NRLIB/code FractionFreeFastGaussian is now explicitly exposed in frame initial FractionFreeFastGaussian will be automatically loaded when needed from /var/zope2/var/LatexWiki/FFFG.NRLIB/code NewtonInterpolation is now explicitly exposed in frame initial NewtonInterpolation will be automatically loaded when needed from /var/zope2/var/LatexWiki/NEWTON.NRLIB/code UnivariateFormalPowerSeries is now explicitly exposed in frame initial UnivariateFormalPowerSeries will be automatically loaded when needed from /var/zope2/var/LatexWiki/UFPS.NRLIB/code UnivariateFormalPowerSeriesFunctions is now explicitly exposed in frame initial UnivariateFormalPowerSeriesFunctions will be automatically loaded when needed from /var/zope2/var/LatexWiki/UFPS1.NRLIB/code GuessOption is now explicitly exposed in frame initial GuessOption will be automatically loaded when needed from /var/zope2/var/LatexWiki/GOPT.NRLIB/code GuessOptionFunctions0 is now explicitly exposed in frame initial GuessOptionFunctions0 will be automatically loaded when needed from /var/zope2/var/LatexWiki/GOPT0.NRLIB/code Guess is now explicitly exposed in frame initial Guess will be automatically loaded when needed from /var/zope2/var/LatexWiki/GUESS.NRLIB/code GuessInteger is now explicitly exposed in frame initial GuessInteger will be automatically loaded when needed from /var/zope2/var/LatexWiki/GUESSINT.NRLIB/code GuessPolynomial is now explicitly exposed in frame initial GuessPolynomial will be automatically loaded when needed from /var/zope2/var/LatexWiki/GUESSP.NRLIB/code GuessFiniteFunctions is now explicitly exposed in frame initial GuessFiniteFunctions will be automatically loaded when needed from /var/zope2/var/LatexWiki/GUESSF1.NRLIB/code GuessFinite is now explicitly exposed in frame initial GuessFinite will be automatically loaded when needed from /var/zope2/var/LatexWiki/GUESSF.NRLIB/code
See GuessingFormulasForSequences? for some explanations.
axiomguess([1, 4, 11, 35, 98, 294, 832, 2401, 6774, 19137, 53466, 148994, 412233], [guessRat], [guessSum, guessProduct], maxLevel==2)
 | (1) |
Type: List Record(function: Expression Integer,order: NonNegativeInteger?)
The answer being an empty list tells us, that there is no
rational function of total degree less than 13, that generates
these numbers. Furthermore, for 
being such a rational
function, there is no formula of the form 
or
, nor 
,
nor replacing the products by sums. In fact, if you look at
Sloane's encyclopedia, you will find a good reason for that: I'd
by very surprised to find such a simple formula for such a family
of objects...
axiomguessExpRat [(1+x)^x for x in 0..3]
 | (2) |
Type: List Record(function: Expression Integer,order: NonNegativeInteger?)
A workaround is necessary, because of bug #128
axioml := [1, 1, 1+q, 1+q+q^2, 1+q+q^2+q^3+q^4, 1+q+q^2+q^3+2*q^4+q^5+q^6, 1+q+q^2+q^3+2*q^4+2*q^5+2*q^6+q^7+q^8+q^9, (1+q^4+q^6)*(1+q+q^2+q^3+q^4+q^5+q^6), (1+q^4)*(1+q+q^2+q^3+q^4+q^5+2*q^6+2*q^7+2*q^8+2*q^9+q^10+q^11+q^12)]
 | (3) |
Type: List Polynomial Integer
axiomguessPRec(q)(l, []).1
 | (4) |
Type: Record(function: Expression Integer,order: NonNegativeInteger?)
Here are some that are tried:
axiomlistA := [1,1,2,5,14,42,132];
Type: List PositiveInteger?
axiomlistB := [1,2,6,21,80, 322];
Type: List PositiveInteger?
axiomguess(listA, [guessRat], [guessSum, guessProduct])
 | (5) |
Type: List Record(function: Expression Integer,order: NonNegativeInteger?)
axiomguess(listB, [guessRat], [guessSum, guessProduct])
 | (6) |
Type: List Record(function: Expression Integer,order: NonNegativeInteger?)
axiomli := [-86, -975, -100, -1728, -31213]; guess(li, [guessRat], [guessSum, guessProduct])
 | (7) |
Type: List Record(function: Expression Integer,order: NonNegativeInteger?)
axiomguessPRec [1,2,3,4,5,6]
 | (8) |
Type: List Record(function: Expression Integer,order: NonNegativeInteger?)
... --Thomas, Sun, 27 Jan 2008 03:04:15 -0800 reply
axiom)lib RECOP FAMR2 FFFG FFFGF NEWTON UFPS UFPS1 GOPT GOPT0 GUESS GUESSINT GUESSP GUESSF1 GUESSF )library cannot find the file GUESS. RecurrenceOperator is now explicitly exposed in frame initial RecurrenceOperator will be automatically loaded when needed from /var/zope2/var/LatexWiki/RECOP.NRLIB/code FiniteAbelianMonoidRingFunctions2 is now explicitly exposed in frame initial FiniteAbelianMonoidRingFunctions2 will be automatically loaded when needed from /var/zope2/var/LatexWiki/FAMR2.NRLIB/code FractionFreeFastGaussian is now explicitly exposed in frame initial FractionFreeFastGaussian will be automatically loaded when needed from /var/zope2/var/LatexWiki/FFFG.NRLIB/code FractionFreeFastGaussianFractions is now explicitly exposed in frame initial FractionFreeFastGaussianFractions will be automatically loaded when needed from /var/zope2/var/LatexWiki/FFFGF.NRLIB/code NewtonInterpolation is now explicitly exposed in frame initial NewtonInterpolation will be automatically loaded when needed from /var/zope2/var/LatexWiki/NEWTON.NRLIB/code UnivariateFormalPowerSeries is now explicitly exposed in frame initial UnivariateFormalPowerSeries will be automatically loaded when needed from /var/zope2/var/LatexWiki/UFPS.NRLIB/code UnivariateFormalPowerSeriesFunctions is now explicitly exposed in frame initial UnivariateFormalPowerSeriesFunctions will be automatically loaded when needed from /var/zope2/var/LatexWiki/UFPS1.NRLIB/code GuessOption is now explicitly exposed in frame initial GuessOption will be automatically loaded when needed from /var/zope2/var/LatexWiki/GOPT.NRLIB/code GuessOptionFunctions0 is now explicitly exposed in frame initial GuessOptionFunctions0 will be automatically loaded when needed from /var/zope2/var/LatexWiki/GOPT0.NRLIB/code GuessInteger is now explicitly exposed in frame initial GuessInteger will be automatically loaded when needed from /var/zope2/var/LatexWiki/GUESSINT.NRLIB/code GuessPolynomial is now explicitly exposed in frame initial GuessPolynomial will be automatically loaded when needed from /var/zope2/var/LatexWiki/GUESSP.NRLIB/code GuessFiniteFunctions is now explicitly exposed in frame initial GuessFiniteFunctions will be automatically loaded when needed from /var/zope2/var/LatexWiki/GUESSF1.NRLIB/code GuessFinite is now explicitly exposed in frame initial GuessFinite will be automatically loaded when needed from /var/zope2/var/LatexWiki/GUESSF.NRLIB/code