/usr/share/axiom-20170501/src/algebra/D01AKFA.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.
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++ Author: Brian Dupee
++ Date Created: March 1994
++ Date Last Updated: December 1997
++ References:
++ Dupe95 Using Computer Algebra to Choose and Apply Numerical Routines
++ Dewa92 Using Computer Algebra to Select Numerical Algorithms
++ Description:
++ \axiomType{d01akfAnnaType} is a domain of
++ \axiomType{NumericalIntegrationCategory}
++ for the NAG routine D01AKF, a numerical integration routine which is
++ is suitable for oscillating, non-singular functions. The function
++ \axiomFun{measure} measures the usefulness of the routine D01AKF
++ for the given problem. The function \axiomFun{numericalIntegration}
++ performs the integration by using \axiomType{NagIntegrationPackage}.
d01akfAnnaType() : SIG == CODE where
EF2 ==> ExpressionFunctions2
EDF ==> Expression DoubleFloat
LDF ==> List DoubleFloat
SDF ==> Stream DoubleFloat
DF ==> DoubleFloat
FI ==> Fraction Integer
EFI ==> Expression Fraction Integer
SOCDF ==> Segment OrderedCompletion DoubleFloat
NIA ==> Record(var:Symbol,fn:EDF,range:SOCDF,abserr:DF,relerr:DF)
MDNIA ==> Record(fn:EDF,range:List SOCDF,abserr:DF,relerr:DF)
INT ==> Integer
BOP ==> BasicOperator
S ==> Symbol
ST ==> String
LST ==> List String
RT ==> RoutinesTable
SIG ==> NumericalIntegrationCategory
CODE ==> Result add
Rep:=Result
import Rep, d01AgentsPackage, NagIntegrationPackage
measure(R:RT,args:NIA) ==
ext:Result := empty()$Result
pp:SDF := singularitiesOf(args)
not (empty?(pp)$SDF) =>
[0.0,"d01akf: There is a possible problem at the following point(s): "
commaSeparate(sdf2lst(pp)) ,ext]
o:Float := functionIsOscillatory(args)
one := 1.0
m:Float := (getMeasure(R,d01akf@S)$RT)*(one-one/(one+sqrt(o)))**2
m > 0.8 => [m,"d01akf: The expression shows much oscillation",ext]
m > 0.6 => [m,"d01akf: The expression shows some oscillation",ext]
m > 0.5 => [m,"d01akf: The expression shows little oscillation",ext]
[m,"d01akf: The expression shows little or no oscillation",ext]
numericalIntegration(args:NIA,hints:Result) ==
ArgsFn := map(x+->convert(x)$DF,args.fn)$EF2(DF,Float)
b:Float :=getButtonValue("d01akf","functionEvaluations")$AttributeButtons
fEvals:INT := wholePart exp(1.1513*(1.0/(2.0*(1.0-b))))
iw:INT := 75*fEvals
f : Union(fn:FileName,fp:Asp1(F)) := [retract(ArgsFn)$Asp1(F)]
d01akf(getlo(args.range),gethi(args.range),args.abserr,_
args.relerr,4*iw,iw,-1,f)
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