Changes http://wiki.axiom-developer.org/MantepseSpad/diff
--
??changed:
-This page was renamed to mantepse.spad.pamphlet. You can delete this one if no
longer needed.
-
+This is the first part of the code from [mantepse.spad.pamphlet].
+
+\begin{axiom}
+)lib RECOP FAMR2 FFFG FFFGF NEWTON
+\end{axiom}
+\begin{spad}
+)abbrev domain UFPS UnivariateFormalPowerSeries
+UnivariateFormalPowerSeries(Coef: Ring) ==
+ UnivariateTaylorSeries(Coef, 'x, 0$Coef)
+
+)abbrev package UFPS1 UnivariateFormalPowerSeriesFunctions
+UnivariateFormalPowerSeriesFunctions(Coef: Ring): Exports == Implementation
+ where
+
+ UFPS ==> UnivariateFormalPowerSeries Coef
+
+ Exports == with
+
+ hadamard: (UFPS, UFPS) -> UFPS
+
+ Implementation == add
+
+ hadamard(f, g) ==
+ series map(#1*#2, coefficients f, coefficients g)
+ $StreamFunctions3(Coef, Coef, Coef)
+
+)abbrev domain GOPT GuessOption
+++ Author: Martin Rubey
+++ Description: GuessOption is a domain whose elements are various options used
+++ by \spadtype{Guess}.
+GuessOption(): Exports == Implementation where
+
+ Exports == SetCategory with
+
+ maxDerivative: Integer -> %
+ ++ maxDerivative(d) specifies the maximum derivative in an algebraic
+ ++ differential equation. maxDerivative(-1) specifies that the maximum
+ ++ derivative can be arbitrary. This option is expressed in the form
+ ++ \spad{maxDerivative == d}.
+
+ maxShift: Integer -> %
+ ++ maxShift(d) specifies the maximum shift in a recurrence
+ ++ equation. maxShift(-1) specifies that the maximum shift can be
+ ++ arbitrary. This option is expressed in the form \spad{maxShift == d}.
+
+ maxPower: Integer -> %
+ ++ maxPower(d) specifies the maximum degree in an algebraic differential
+ ++ equation. For example, the degree of (f'')^3 f' is 4. maxPower(-1)
+ ++ specifies that the maximum exponent can be arbitrary. This option is
+ ++ expressed in the form \spad{maxPower == d}.
+
+ homogeneous: Boolean -> %
+ ++ homogeneous(d) specifies whether we allow only homogeneous algebraic
+ ++ differential equations. This option is expressed in the form
+ ++ \spad{homogeneous == d}.
+
+ maxLevel: Integer -> %
+ ++ maxLevel(d) specifies the maximum number of recursion levels operators
+ ++ guessProduct and guessSum will be applied. maxLevel(-1) specifies
+ ++ that all levels are tried. This option is expressed in the form
+ ++ \spad{maxLevel == d}.
+
+ maxDegree: Integer -> %
+ ++ maxDegree(d) specifies the maximum degree of the coefficient
+ ++ polynomial in an algebraic differential equation or a recursion with
+ ++ polynomial coefficients. maxDegree(-1) specifies that the maximum
+ ++ degree can be arbitrary. This option is expressed in the form
+ ++ \spad{maxDegree == d}.
+
+ allDegrees: Boolean -> %
+ ++ allDegrees(d) specifies whether all possibilities of the degree vector
+ ++ - taking into account maxDegree - should be tried. This is mainly
+ ++ interesting for rational interpolation. This option is expressed in
+ ++ the form \spad{allDegrees == d}.
+
+ safety: NonNegativeInteger -> %
+ ++ safety(d) specifies the number of values reserved for testing any
+ ++ solutions found. This option is expressed in the form \spad{safety ==
+ ++ d}.
+
+ one: Boolean -> %
+ ++ one(d) specifies whether we are happy with one solution. This option
+ ++ is expressed in the form \spad{one == d}.
+
+ debug: Boolean -> %
+ ++ debug(d) specifies whether we want additional output on the
+ ++ progress. This option is expressed in the form \spad{debug == d}.
+
+ functionName: Symbol -> %
+ ++ functionName(d) specifies the name of the function given by the
+ ++ algebraic differential equation or recurrence. This option is
+ ++ expressed in the form \spad{functionName == d}.
+
+ variableName: Symbol -> %
+ ++ variableName(d) specifies the variable used in by the algebraic
+ ++ differential equation. This option is expressed in the form
+ ++ \spad{variableName == d}.
+
+ indexName: Symbol -> %
+ ++ indexName(d) specifies the index variable used for the formulas. This
+ ++ option is expressed in the form \spad{indexName == d}.
+
+ displayAsGF: Boolean -> %
+ ++ displayAsGF(d) specifies whether the result is a generating function
+ ++ or a recurrence. This option should not be set by the user, but rather
+ ++ by the HP-specification.
+
+ option : (List %, Symbol) -> Union(Any, "failed")
+ ++ option() is not to be used at the top level;
+ ++ option determines internally which drawing options are indicated in
+ ++ a draw command.
+
+ option?: (List %, Symbol) -> Boolean
+ ++ option?() is not to be used at the top level;
+ ++ option? internally returns true for drawing options which are
+ ++ indicated in a draw command, or false for those which are not.
+
+ checkOptions: List % -> Void
+ ++ checkOptions checks whether an option is given twice
+
+ Implementation ==> add
+ import AnyFunctions1(Boolean)
+ import AnyFunctions1(Symbol)
+ import AnyFunctions1(Integer)
+ import AnyFunctions1(NonNegativeInteger)
+
+ Rep := Record(keyword: Symbol, value: Any)
+
+ maxLevel d == ["maxLevel"::Symbol, d::Any]
+ maxDerivative d == ["maxDerivative"::Symbol, d::Any]
+ maxShift d == maxDerivative d
+ maxDegree d == ["maxDegree"::Symbol, d::Any]
+ allDegrees d == ["allDegrees"::Symbol, d::Any]
+ maxPower d == ["maxPower"::Symbol, d::Any]
+ safety d == ["safety"::Symbol, d::Any]
+ homogeneous d == ["homogeneous"::Symbol, d::Any]
+ debug d == ["debug"::Symbol, d::Any]
+ one d == ["one"::Symbol, d::Any]
+ functionName d == ["functionName"::Symbol, d::Any]
+ variableName d == ["variableName"::Symbol, d::Any]
+ indexName d == ["indexName"::Symbol, d::Any]
+ displayAsGF d == ["displayAsGF"::Symbol, d::Any]
+
+ coerce(x:%):OutputForm == x.keyword::OutputForm = x.value::OutputForm
+ x:% = y:% == x.keyword = y.keyword and x.value = y.value
+
+ option?(l, s) ==
+ for x in l repeat
+ x.keyword = s => return true
+ false
+
+ option(l, s) ==
+ for x in l repeat
+ x.keyword = s => return(x.value)
+ "failed"
+
+ checkOptions l ==
+ if not empty? l then
+ if find((first l).keyword = #1.keyword, rest l) case "failed"
+ then checkOptions rest l
+ else error "GuessOption: Option specified twice"
+
+)abbrev package GOPT0 GuessOptionFunctions0
+++ Author: Martin Rubey
+++ Description: GuessOptionFunctions0 provides operations that extract the
+++ values of options for \spadtype{Guess}.
+GuessOptionFunctions0(): Exports == Implementation where
+
+ LGOPT ==> List GuessOption
+
+ Exports == SetCategory with
+
+ maxLevel: LGOPT -> Integer
+ ++ maxLevel returns the specified maxLevel or -1 as default.
+
+ maxPower: LGOPT -> Integer
+ ++ maxPower returns the specified maxPower or -1 as default.
+
+ maxDerivative: LGOPT -> Integer
+ ++ maxDerivative returns the specified maxDerivative or -1 as default.
+
+ maxShift: LGOPT -> Integer
+ ++ maxShift returns the specified maxShift or -1 as default.
+
+ maxDegree: LGOPT -> Integer
+ ++ maxDegree returns the specified maxDegree or -1 as default.
+
+ allDegrees: LGOPT -> Boolean
+ ++ allDegrees returns whether all possibilities of the degree vector
+ ++ should be tried, the default being false.
+
+ safety: LGOPT -> NonNegativeInteger
+ ++ safety returns the specified safety or 1 as default.
+
+ one: LGOPT -> Boolean
+ ++ one returns whether we need only one solution, default being true.
+
+ homogeneous: LGOPT -> Boolean
+ ++ homogeneous returns whether we allow only homogeneous algebraic
+[104 more lines...]
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