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#308 Runtime error on integration ←	↑	→ #31 Hyperdoc segfault

#309 partial fraction with unknown constants

Edit detail for #309 partial fraction with unknown constants revision 1 of 3

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Editor: Time: 2007/11/17 22:24:33 GMT-8
Note: Maybe it's enough to expose PartialFractionPackage

changed:
-
This example is from Ulrich Schwardmann: Computeralgebra-Systeme, Addison-Wesley, 1995, p127f.
It tries to compute a partial fraction of a fraction with unknown constants.
The result is not the expected partial fraction decomposition, and does not seem to have any other senseful
interpretation (it is q/x).

Following is a verification of the partial fraction that macsyma computes.

\begin{axiom}
q:=(x+a)/(x*(x**3+(b+c)*x**2+b*c*x))
partialFraction(q,x)

(c-a)/((c^3-b*c**2)*(x+c))-(b-a)/((b**2*c-b**3)*(x+b))+((b-a)*c-a*b)/(b**2*c**2*x)+a/(b*c*x**2) - q

\end{axiom}


From kratt6 Tue Aug 8 08:42:30 -0500 2006
From: kratt6
Date: Tue, 08 Aug 2006 08:42:30 -0500
Subject: workaround
Message-ID: <20060808084230-0500@wiki.axiom-developer.org>

it seems that it is better to use 'partialFraction\$PartialFraction'. I did it as follows:

\begin{axiom}
SUP FRAC POLY INT has EUCDOM
den := univariate((x*(x**3+(b+c)*x**2+b*c*x)),x)::SUP FRAC POLY INT
num := univariate(x+a,x)::SUP FRAC POLY INT
partialFraction(num, factor den)$PartialFraction SUP FRAC POLY INT
\end{axiom}

Does this suggest that the bug is in 'PartialFractionPackage'?

From kratt6 Sat Aug 12 05:09:42 -0500 2006
From: kratt6
Date: Sat, 12 Aug 2006 05:09:42 -0500
Subject: Axiom chooses the "wrong" signature
Message-ID: <20060812050942-0500@wiki.axiom-developer.org>

The reason for the behaviour described above is quite simple to explain - unfortunately...

There are two operations 'partialFraction' with two arguments::

    partialFraction: (R, FRR) -> %
      ++ partialFraction(numer,denom) is the main function for
      ++ constructing partial fractions. The second argument is the
      ++ denominator and should be factored.

from the exposed domain 'PartialFraction' and::

      partialFraction: (FPR, Symbol) -> Any
         ++ partialFraction(rf, var) returns the partial fraction decomposition
         ++ of the rational function rf with respect to the variable var.

from the unexposed package 'PartialFractionPackage'. Of course, the interpreter chooses the exposed domain, which produced the surprising result.

This shows that overloading should be done very carefully. I think we should rename the operations in 'PartialFractionPackage'.

Martin

Martin

From ChristianSievers Tue Aug 15 10:48:13 -0500 2006
From: Christian Sievers
Date: Tue, 15 Aug 2006 10:48:13 -0500
Subject: Maybe it's enough to expose PartialFractionPackage
Message-ID: <20060815104813-0500@wiki.axiom-developer.org>

(Sorry for not first testing a simpler example...)

I came to the same result this weekend.
It seems to me from first tests that it would suffice to just also expose PartialFractionPackage.
However I don't know axiom good enough to see if there are any unwanted side effects.

\begin{axiom}
)expose PFRPAC
partialFraction((x+a)/(x*(x**3+(b+c)*x**2+b*c*x)),x)
partialFraction(1,10)
\end{axiom}

This example is from Ulrich Schwardmann: Computeralgebra-Systeme, Addison-Wesley, 1995, p127f. It tries to compute a partial fraction of a fraction with unknown constants. The result is not the expected partial fraction decomposition, and does not seem to have any other senseful interpretation (it is q/x).

Following is a verification of the partial fraction that macsyma computes.

axiom
q:=(x+a)/(x*(x**3+(b+c)*x**2+b*c*x))

(1)

Type: Fraction Polynomial Integer

axiom
partialFraction(q,x)

(2)

Type: PartialFraction? Fraction Polynomial Integer

axiom
(c-a)/((c^3-b*c**2)*(x+c))-(b-a)/((b**2*c-b**3)*(x+b))+((b-a)*c-a*b)/(b**2*c**2*x)+a/(b*c*x**2) - q

(3)

Type: Fraction Polynomial Integer

workaround --kratt6, Tue, 08 Aug 2006 08:42:30 -0500 reply

it seems that it is better to use partialFraction$PartialFraction. I did it as follows:

axiom
SUP FRAC POLY INT has EUCDOM

(4)

Type: Boolean

axiom
den := univariate((x*(x**3+(b+c)*x**2+b*c*x)),x)::SUP FRAC POLY INT

(5)

Type: SparseUnivariatePolynomial? Fraction Polynomial Integer

axiom
num := univariate(x+a,x)::SUP FRAC POLY INT

(6)

Type: SparseUnivariatePolynomial? Fraction Polynomial Integer

axiom
partialFraction(num, factor den)$PartialFraction SUP FRAC POLY INT

(7)

Type: PartialFraction? SparseUnivariatePolynomial? Fraction Polynomial Integer

Does this suggest that the bug is in PartialFractionPackage?

Axiom chooses the "wrong" signature --kratt6, Sat, 12 Aug 2006 05:09:42 -0500 reply

The reason for the behaviour described above is quite simple to explain - unfortunately...

There are two operations partialFraction with two arguments:

    partialFraction: (R, FRR) -> %
      ++ partialFraction(numer,denom) is the main function for
      ++ constructing partial fractions. The second argument is the
      ++ denominator and should be factored.

from the exposed domain PartialFraction and:

      partialFraction: (FPR, Symbol) -> Any
         ++ partialFraction(rf, var) returns the partial fraction decomposition
         ++ of the rational function rf with respect to the variable var.

from the unexposed package PartialFractionPackage. Of course, the interpreter chooses the exposed domain, which produced the surprising result.

This shows that overloading should be done very carefully. I think we should rename the operations in PartialFractionPackage.

Martin

Maybe it's enough to expose PartialFractionPackage? --Christian Sievers, Tue, 15 Aug 2006 10:48:13 -0500 reply

(Sorry for not first testing a simpler example...)

I came to the same result this weekend. It seems to me from first tests that it would suffice to just also expose PartialFractionPackage?. However I don't know axiom good enough to see if there are any unwanted side effects.

axiom)expose PFRPAC
   PartialFractionPackage is now explicitly exposed in frame initial 
partialFraction((x+a)/(x*(x**3+(b+c)*x**2+b*c*x)),x)

(8)

Type: PartialFraction? UnivariatePolynomial?(x,Fraction Polynomial Integer)

axiom
partialFraction(1,10)

(9)

Type: PartialFraction? Integer