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Re: [Axiom-math] Curious behavior of Taylor series
From: |
William Sit |
Subject: |
Re: [Axiom-math] Curious behavior of Taylor series |
Date: |
Wed, 30 Aug 2006 06:25:02 -0400 |
"Igor Khavkine" <address@hidden> writes:
OK, but the following definitely looks like a bug.
(279) -> monx := monomial(1,1)$UTS(EXPR INT,x,0)
(279) x
Type:
UnivariateTaylorSeries(Expression Integer,x,0)
(281) -> sqrt(monx*monx)
(281) ->
(281) 1
Type:
In the Windows version, I get the correct answer. So this
bug is newly introduced.
AXIOM Computer Algebra System
Version of Tuesday November 30, 2004 at
21:11:14
-----------------------------------------------------------------------------
Issue )copyright to view copyright notices.
Issue )summary for a summary of useful system
commands.
Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
(1) -> )set mess auto off
(1) -> monx := monomial(1,1)$UTS(EXPR INT,x,0)
(1) x
Type:
UnivariateTaylorSeries(Expression Integer,x,0)
(2) -> sqrt(monx*monx)
(2) x
Type:
UnivariateTaylorSeries(Expression Integer,x,0)
(3) -> x
(3) x
Type: Variable x
Note in particular (3), which illustrates that Axiom
treats undefined identifiers as symbols (or variables).
Even though x has been used in (1) and (2), it is still
undefined! The reason is the way UTS (or any univariate
domain) is constructed in Axiom: since it is univariate,
Axiom designers decided that it is not necessary to
associate the main variable to an identifier. The x that
appears in the output (and input) is external to the UTS
computing environment and a pure notation in I/O for the
convenience of the user. Internally, the main variable is
represented by a place holder (and denoted by the local
identifier ?). One reason for this set up is to allow
coefficient domains to include Symbol (that is, all
identifiers) and since ? is only a local identifier, it
will not get mixed up with anything in the coefficient
domain. This explains why in your example, x*y gives x*x
(which is really x*?). It is important to know that the
line
y:=taylor x
does NOT define x, only y. You cannot use x to mean the
main variable until you define it. So you can do this:
(1) -> y:=taylor x
(1) x
Type:
UnivariateTaylorSeries(Expression Integer,x,0)
(2) -> x:UTS(EXPR INT,x,0):='x
(2) x
Type:
UnivariateTaylorSeries(Expression Integer,x,0)
(3) -> x*y
2
(3) x
Type:
UnivariateTaylorSeries(Expression Integer,x,0)
William
- Re: [Axiom-math] Curious behavior of Taylor series, (continued)
- Re: [Axiom-math] Curious behavior of Taylor series, Ralf Hemmecke, 2006/08/21
- Re: [Axiom-math] Curious behavior of Taylor series, Jay Belanger, 2006/08/21
- Re: [Axiom-math] Curious behavior of Taylor series, Ralf Hemmecke, 2006/08/21
- Re: [Axiom-math] Curious behavior of Taylor series, Jay Belanger, 2006/08/22
- Re: [Axiom-math] Curious behavior of Taylor series, Ralf Hemmecke, 2006/08/22
Re: [Axiom-math] Curious behavior of Taylor series, Igor Khavkine, 2006/08/21
Re: [Axiom-math] Curious behavior of Taylor series,
William Sit <=
Re: [Axiom-math] Curious behavior of Taylor series, Ralf Hemmecke, 2006/08/20