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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**, *Ralf Hemmecke*, `2006/08/20`