/usr/share/axiom-20170501/src/algebra/D01AQFA.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 | )abbrev domain D01AQFA d01aqfAnnaType
++ 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{d01aqfAnnaType} is a domain of
++ \axiomType{NumericalIntegrationCategory}
++ for the NAG routine D01AQF, a general numerical integration routine which
++ can solve an integral of the form
++ /home/bjd/Axiom/anna/hypertex/bitmaps/d01aqf.xbm
++ The function \axiomFun{measure} measures the usefulness of the routine
++ D01AQF for the given problem. The function \axiomFun{numericalIntegration}
++ performs the integration by using \axiomType{NagIntegrationPackage}.
d01aqfAnnaType() : 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()$Result
Den := denominator(args.fn)
(Den = 1) =>
[0.0,"d01aqf: A suitable weight function has not been found", ext]
listOfZeros:LDF := problemPoints(args.fn,args.var,args.range)
numberOfZeros := (#(listOfZeros))$LDF
zero?(numberOfZeros) =>
[0.0,"d01aqf: A suitable weight function has not been found", ext]
numberOfZeros = 1 =>
s:SDF := singularitiesOf(args)
more?(s,1)$SDF =>
[0.0,"d01aqf: Too many singularities have been found", ext]
cFloat:Float := (convert(first(listOfZeros)$LDF)@Float)$DF
cString:ST := (convert(cFloat)@ST)$Float
lany:Any := coerce(listOfZeros)$AnyFunctions1(LDF)
ex:Record(key:S,entry:Any) := [d01aqfextra@S,lany]
ext := insert!(ex,ext)$Result
[getMeasure(R,d01aqf@S)$RT, "Recommended is d01aqf with the "
"hilbertian weight function of 1/(x-c) where c = " cString, ext]
[0.0,"d01aqf: More than one factor has been found and so does not "
"have a suitable weight function",ext]
numericalIntegration(args:NIA,hints:Result) ==
Args := copy args
ca:Any := coerce(search((d01aqfextra@S),hints)$Result)@Any
c:DF := first(retract(ca)$AnyFunctions1(LDF))$LDF
ci:FI := df2fi(c)$ExpertSystemToolsPackage
Var:EFI := Args.var :: EFI
Gx:EFI := (Var-(ci::EFI))*(edf2efi(Args.fn)$ExpertSystemToolsPackage)
ArgsFn := map(x+->convert(x)$FI,Gx)$EF2(FI,Float)
b:Float:=getButtonValue("d01aqf","functionEvaluations")$AttributeButtons
fEvals:INT := wholePart exp(1.1513*(1.0/(2.0*(1.0-b))))
iw:INT := 75*fEvals
f : Union(fn:FileName,fp:Asp1(G)) := [retract(ArgsFn)$Asp1(G)]
d01aqf(getlo(Args.range),gethi(Args.range),c,_
Args.abserr,Args.relerr,4*iw,iw,-1,f)
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