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[Axiom-developer] Re: partfrac, expand, combine, rewrite and simplify.
From: |
Dylan Thurston |
Subject: |
[Axiom-developer] Re: partfrac, expand, combine, rewrite and simplify. |
Date: |
Tue, 7 Oct 2003 15:12:01 -0400 |
User-agent: |
Mutt/1.5.4i |
On Tue, Oct 07, 2003 at 12:56:51PM -0400, Tim Daly wrote:
> (5) -> aa:UP(x,FRAC INT):=2*x^3
>
> 3
> (5) 2x
> Type: UnivariatePolynomial(x,Fraction Integer)
> (6) -> bb:UP(x,FRAC INT):=1-x^2
>
> 2
> (6) - x + 1
> Type: UnivariatePolynomial(x,Fraction Integer)
>
> And the call succeeds:
>
> (7) -> partialFraction(aa,bb)
>
> 1 1
> (7) - 2x - ----- - -----
> x - 1 x + 1
> Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
>
> So partialFraction can create the correct call signature. I suspect the
> interpreter created some intermediate type that it couldn't coerce to
> the required target type. I agree that it should have been able to
> give the factored output but did not.
Note that there is some behaviour which seems to definitely be a bug. To
continue your example:
(32) -> partialFraction(aa,bb)
1 1
(32) - 2x - ----- - -----
x - 1 x + 1
Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
(33) -> partialFraction(2*x^3,bb)
1 1
(33) - 2x - ----- - -----
x - 1 x + 1
Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
These are fine, but:
(34) -> partialFraction(aa,1-x^2)
2x
(34) - 2x - ------
2
x - 1
Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
This must be a bug, since the output is not actually a PartialFraction!
(I'm curious if this happens with the NAG version.)
The fact that partialFraction(2*x^3,1-x^2) doesn't work is more of a
wishlist item, since it doesn't give a wrong answer. Note that
explicitly making the coefficients fractional works:
(3) -> partialFraction(x^3/2, (x^2-1)/2)
1 1
- -
2 2
(3) x + ----- + -----
x - 1 x + 1
Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
But we can see the same bug I mentioned above if only the numerator has
a fraction:
(4) -> partialFraction(x^3/2, x^2-1)
1
- x
1 2
(4) - x + ------
2 2
x - 1
Type: PartialFraction UnivariatePolynomial(x,Fraction Integer)
> If you really want to see the struggles the interpreter is going thru try:
>
> )lisp (setq |$monitorNewWorld| t)
>
> and you can see the interpreter trying to find the correct signature
> using various coercions.
Thanks! It looks pretty painful, though: I tried to follow it, but failed.
Peace,
Dylan
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Description: Digital signature
- [Axiom-developer] Re: partfrac, expand, combine, rewrite and simplify., Tim Daly, 2003/10/07
- Re: [Axiom-developer] Re: partfrac, expand, combine, rewrite and simplify., Dylan Thurston, 2003/10/07
- [Axiom-developer] Re: partfrac, expand, combine, rewrite and simplify., Tim Daly, 2003/10/07
- [Axiom-developer] Re: partfrac, expand, combine, rewrite and simplify.,
Dylan Thurston <=
- [Axiom-developer] factor bug (actually a tex bug), Tim Daly, 2003/10/07
- Message not available