/usr/share/axiom-20170501/src/algebra/GUESSUP.spad is in axiom-source 20170501-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 | )abbrev package GUESSUP GuessUnivariatePolynomial
++ References:
++ Rube06 Extended rate, more GFUN
++ Hebi10 Extended Rate, more GFUN
++ Description:
++ This package exports guessing of sequences of univariate rational functions
GuessUnivariatePolynomial(q) : SIG == CODE where
q : Symbol
UP ==> MyUnivariatePolynomial(q, Integer)
EXPRR ==> MyExpression(q, Integer)
F ==> Fraction UP
S ==> UP
NNI ==> NonNegativeInteger
LGOPT ==> List GuessOption
GUESSRESULT ==> List Record(function: EXPRR, order: NNI)
GUESSER ==> (List F, LGOPT) -> GUESSRESULT
SIG ==> with
guess : List F -> GUESSRESULT
++ \spad{guess l} applies recursively \spadfun{guessRec} and
++ \spadfun{guessADE} to the successive differences and quotients of
++ the list. Default options as described in
++ \spadtype{GuessOptionFunctions0} are used.
guess : (List F, LGOPT) -> GUESSRESULT
++ \spad{guess(l, options)} applies recursively \spadfun{guessRec}
++ and \spadfun{guessADE} to the successive differences and quotients
++ of the list. The given options are used.
guess : (List F, List GUESSER, List Symbol) -> GUESSRESULT
++ \spad{guess(l, guessers, ops)} applies recursively the given
++ guessers to the successive differences if ops contains the symbol
++ guessSum and quotients if ops contains the symbol guessProduct to
++ the list. Default options as described in
++ \spadtype{GuessOptionFunctions0} are used.
guess : (List F, List GUESSER, List Symbol, LGOPT) -> GUESSRESULT
++ \spad{guess(l, guessers, ops)} applies recursively the given
++ guessers to the successive differences if ops contains the symbol
++ \spad{guessSum} and quotients if ops contains the symbol
++ \spad{guessProduct} to the list. The given options are used.
guessExpRat : List F -> GUESSRESULT
++ \spad{guessExpRat l} tries to find a function of the form
++ n+->(a+b n)^n r(n), where r(n) is a rational function, that fits
++ l.
guessExpRat : (List F, LGOPT) -> GUESSRESULT
++ \spad{guessExpRat(l, options)} tries to find a function of the
++ form n+->(a+b n)^n r(n), where r(n) is a rational function, that
++ fits l.
guessBinRat : List F -> GUESSRESULT
++ \spad{guessBinRat(l, options)} tries to find a function of the
++ form n+->binomial(a+b n, n) r(n), where r(n) is a rational
++ function, that fits l.
guessBinRat : (List F, LGOPT) -> GUESSRESULT
++ \spad{guessBinRat(l, options)} tries to find a function of the
++ form n+->binomial(a+b n, n) r(n), where r(n) is a rational
++ function, that fits l.
-- if F has RetractableTo Symbol and S has RetractableTo Symbol then
guessExpRat : Symbol -> GUESSER
++ \spad{guessExpRat q} returns a guesser that tries to find a
++ function of the form n+->(a+b q^n)^n r(q^n), where r(q^n) is a
++ q-rational function, that fits l.
guessBinRat : Symbol -> GUESSER
++ \spad{guessBinRat q} returns a guesser that tries to find a
++ function of the form n+->qbinomial(a+b n, n) r(n), where r(q^n) is a
++ q-rational function, that fits l.
-------------------------------------------------------------------------------
guessHP : (LGOPT -> HPSPEC) -> GUESSER
++ \spad{guessHP f} constructs an operation that applies Hermite-Pade
++ approximation to the series generated by the given function f.
guessADE : List F -> GUESSRESULT
++ \spad{guessADE l} tries to find an algebraic differential equation
++ for a generating function whose first Taylor coefficients are
++ given by l, using the default options described in
++ \spadtype{GuessOptionFunctions0}.
guessADE : (List F, LGOPT) -> GUESSRESULT
++ \spad{guessADE(l, options)} tries to find an algebraic
++ differential equation for a generating function whose first Taylor
++ coefficients are given by l, using the given options.
guessAlg : List F -> GUESSRESULT
++ \spad{guessAlg l} tries to find an algebraic equation for a
++ generating function whose first Taylor coefficients are given by
++ l, using the default options described in
++ \spadtype{GuessOptionFunctions0}. It is equivalent to
++ \spadfun{guessADE}(l, maxDerivative == 0).
guessAlg : (List F, LGOPT) -> GUESSRESULT
++ \spad{guessAlg(l, options)} tries to find an algebraic equation
++ for a generating function whose first Taylor coefficients are
++ given by l, using the given options. It is equivalent to
++ \spadfun{guessADE}(l, options) with \spad{maxDerivative == 0}.
guessHolo : List F -> GUESSRESULT
++ \spad{guessHolo l} tries to find an ordinary linear differential
++ equation for a generating function whose first Taylor coefficients
++ are given by l, using the default options described in
++ \spadtype{GuessOptionFunctions0}. It is equivalent to
++ \spadfun{guessADE}\spad{(l, maxPower == 1)}.
guessHolo : (List F, LGOPT) -> GUESSRESULT
++ \spad{guessHolo(l, options)} tries to find an ordinary linear
++ differential equation for a generating function whose first Taylor
++ coefficients are given by l, using the given options. It is
++ equivalent to \spadfun{guessADE}\spad{(l, options)} with
++ \spad{maxPower == 1}.
guessPade : (List F, LGOPT) -> GUESSRESULT
++ \spad{guessPade(l, options)} tries to find a rational function
++ whose first Taylor coefficients are given by l, using the given
++ options. It is equivalent to \spadfun{guessADE}\spad{(l,
++ maxDerivative == 0, maxPower == 1, allDegrees == true)}.
guessPade : List F -> GUESSRESULT
++ \spad{guessPade(l, options)} tries to find a rational function
++ whose first Taylor coefficients are given by l, using the default
++ options described in \spadtype{GuessOptionFunctions0}. It is
++ equivalent to \spadfun{guessADE}\spad{(l, options)} with
++ \spad{maxDerivative == 0, maxPower == 1, allDegrees == true}.
guessRec : List F -> GUESSRESULT
++ \spad{guessRec l} tries to find an ordinary difference equation
++ whose first values are given by l, using the default options
++ described in \spadtype{GuessOptionFunctions0}.
guessRec : (List F, LGOPT) -> GUESSRESULT
++ \spad{guessRec(l, options)} tries to find an ordinary difference
++ equation whose first values are given by l, using the given
++ options.
guessPRec : (List F, LGOPT) -> GUESSRESULT
++ \spad{guessPRec(l, options)} tries to find a linear recurrence
++ with polynomial coefficients whose first values are given by l,
++ using the given options. It is equivalent to
++ \spadfun{guessRec}\spad{(l, options)} with \spad{maxPower == 1}.
guessPRec : List F -> GUESSRESULT
++ \spad{guessPRec l} tries to find a linear recurrence with
++ polynomial coefficients whose first values are given by l, using
++ the default options described in
++ \spadtype{GuessOptionFunctions0}. It is equivalent to
++ \spadfun{guessRec}\spad{(l, maxPower == 1)}.
guessRat : (List F, LGOPT) -> GUESSRESULT
++ \spad{guessRat(l, options)} tries to find a rational function
++ whose first values are given by l, using the given options. It is
++ equivalent to \spadfun{guessRec}\spad{(l, maxShift == 0, maxPower
++ == 1, allDegrees == true)}.
guessRat : List F -> GUESSRESULT
++ \spad{guessRat l} tries to find a rational function whose first
++ values are given by l, using the default options described in
++ \spadtype{GuessOptionFunctions0}. It is equivalent to
++ \spadfun{guessRec}\spad{(l, maxShift == 0, maxPower == 1,
++ allDegrees == true)}.
diffHP : LGOPT -> HPSPEC
++ \spad{diffHP options} returns a specification for Hermite-Pade
++ approximation with the differential operator
shiftHP : LGOPT -> HPSPEC
++ \spad{shiftHP options} returns a specification for Hermite-Pade
++ approximation with the shift operator
-- if F has RetractableTo Symbol and S has RetractableTo Symbol then
shiftHP : Symbol -> (LGOPT -> HPSPEC)
++ \spad{shiftHP options} returns a specification for
++ Hermite-Pade approximation with the $q$-shift operator
diffHP : Symbol -> (LGOPT -> HPSPEC)
++ \spad{diffHP options} returns a specification for Hermite-Pade
++ approximation with the $q$-dilation operator
guessRec : Symbol -> GUESSER
++ \spad{guessRec q} returns a guesser that finds an ordinary
++ q-difference equation whose first values are given by l, using
++ the given options.
guessPRec : Symbol -> GUESSER
++ \spad{guessPRec q} returns a guesser that tries to find
++ a linear q-recurrence with polynomial coefficients whose first
++ values are given by l, using the given options. It is
++ equivalent to \spadfun{guessRec}\spad{(q)} with
++ \spad{maxPower == 1}.
guessRat : Symbol -> GUESSER
++ \spad{guessRat q} returns a guesser that tries to find a
++ q-rational function whose first values are given by l, using
++ the given options. It is equivalent to \spadfun{guessRec} with
++ \spad{(l, maxShift == 0, maxPower == 1, allDegrees == true)}.
guessADE : Symbol -> GUESSER
++ \spad{guessADE q} returns a guesser that tries to find an
++ algebraic differential equation for a generating function whose
++ first Taylor coefficients are given by l, using the given
++ options.
-------------------------------------------------------------------------------
CODE ==> Guess(Fraction UP, UP, MyExpression(q, Integer), Fraction UP,
id$MappingPackage1(Fraction UP),
coerce$MyExpression(q, Integer))
|