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## [Axiom-developer] [Fwd: Integrating UTS] Bug #10350

 From: William Sit Subject: [Axiom-developer] [Fwd: Integrating UTS] Bug #10350 Date: Sat, 02 Oct 2004 17:59:11 -0400

```Hi Martin:

I don't know if you automatically get comments to your bug posts. So I am
forwarding this (slightly edited from the posted version: I can't re-edit what I
posted) to you. I want also to add that EXPR INT is used within UTS rather than
FRAC POLY INT is probably because the coefficients of the Taylor series usually
involve factorials (I guess, hidden in Stream EXPR INT).

William

-------- Original Message --------

bug #10350 overview: integrating UTS

Neither of these is a bug. In the first one, Axiom coerced 1/x into FRAC POLY
INT correctly: the only / operation available in UTS is one induced from the
coefficient domain, which requires the denominator to be in the coefficient
domain, and the division is done termwise to the coefficients of the series. So
1/x ends up in FRAC POLY INT. Note that to obtain a Taylor series at x = 0 is
mathematically is wrong, since 1/x is not defined at x=0. Also the way to obtain
a Taylor series is taylor(func, x=a). If you do integrate(taylor(1/x,x=1),x),
that would cause no problems. Note that the domain of this command is UTS(EXPR
INT, x,1), so such towers are valid and necessary in Axiom. Note also there are
only two exported [coerce] in UTS and they do NOT apply to 1/x.  The x in UTS is
like the x in UP and is different from the x in FRAC POLY INT. The
representation is Stream Coef (no variable specified because it is univariate).

For the same reason, in the second command, 1/y is correctly coerced into FRAC
POLY INT. However, in UTS(*,x,*), the only integrations allowed are with respect
to x. If you want to do integration in FRAC POLY INT, then you should do so
without coercing 1/y into UTS.

So your examples do not illustrate the problem about mixed up variables. In
fact, they support use of towers like UTS(EXPR INT, x, a).

William
--
William Sit