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Re: [Axiom-developer] about Expression Integer
From: |
Francois Maltey |
Subject: |
Re: [Axiom-developer] about Expression Integer |
Date: |
22 Feb 2006 19:11:12 +0100 |
User-agent: |
Gnus/5.09 (Gnus v5.9.0) Emacs/21.4 |
"Bill Page" writes :
> > > Could you please define in what sense "Otherwise we don't
> > > get a polynomial, obviously."? To me this is not obvious -
> > > it is wrong.
> >
> > Why should this be wrong?
> >
> > Here's a definition for polynomial from wikipedia:
> >
> > In mathematics, a polynomial is an expression in which constants
> > and variables are combined using (only) addition, subtraction,
> > and multiplication. Thus, 7x^2+4x-5 is a polynomial; 2/x is not.
I have the same point of view than Martin,
everything is done in DMP in order to have a polynomial ring,
DMP isn't only a << collect >> command which factorise x and so.
> I think this definition is less general it needs to be and
> difficult to apply in the context of Axiom.
If we change DMP assumption, it's no more ring.
> We need to know what are "constants" and what are "variables"
So the same variable is forbiden in the constant ring.
I find it's a bug to allow DMP ([X,Z], DMP ([X,Y], INT))
> > I recall that in the Algebra course I attended, the polynomial
> > ring was defined as a ring (of coefficients) together with a
> > variable which is to be transcendent over that ring.
>
> That definition is much better. In the case we are discusing
> the ring of coefficients is the domain 'EXPR INT' which
> includes expressions of the form '1/x' and so it is correct
> to say that '2/x' is not in itself a polynomial but it can
> be a coefficient in a polynomial.
I don't think so,
a polynomial ring has variables which are not in the initial ring.
The DMP error (for derivative) isn't in the derivative function but
in the fact that axiom accepts 1/x has variable in DMP[x].
And 1/x isn't transcendent over that rign because y=1/x is solution of
xy-1=0 in this field.
Either we say to the user he _must_ be carreful with this,
(only in the EXPR INTEGER field?)
Either monomial command of DMP reject 1/x coefficient if x is a variable.
In France we say we can be << jesuite >> :
The real axiom accepts coefficients as 1/x in DMP ([x], EXPR INT)
because axiom EXPR INT isn't perfect, but it souldn't.
But I'm sure it's a mistake to change derivative.
> How would you use such a domain to solve the problem originally
> posed by Francois about expansion of trigonometric expressions
> that started this thread?
When we expand a trigonometric expression,
the question is a << linear one >> not a polynomial one.
We expand more often sin (4*x+5*y) than sin (x^2+x) ;
for sin (x^2+x) we use series.
Have a good day !
Francois
- Re: [Axiom-developer] about Expression Integer, (continued)
- Re: [Axiom-developer] about Expression Integer, Ralf Hemmecke, 2006/02/21
- RE: [Axiom-developer] about Expression Integer, Bill Page, 2006/02/21
- Re: [Axiom-developer] about Expression Integer, Ralf Hemmecke, 2006/02/21
- RE: [Axiom-developer] about Expression Integer, Bill Page, 2006/02/21
- Re: [Axiom-developer] about Expression Integer, Ralf Hemmecke, 2006/02/21
- RE: [Axiom-developer] about Expression Integer, Bill Page, 2006/02/21
- Re: [Axiom-developer] about Expression Integer, Martin Rubey, 2006/02/22
- RE: [Axiom-developer] about Expression Integer, Bill Page, 2006/02/23
- Re: [Axiom-developer] about Expression Integer, Martin Rubey, 2006/02/22
- RE: [Axiom-developer] about Expression Integer, Bill Page, 2006/02/22
- Re: [Axiom-developer] about Expression Integer,
Francois Maltey <=
- Re: [Axiom-developer] about Expression Integer, Martin Rubey, 2006/02/23
- RE: [Axiom-developer] about Expression Integer, Bill Page, 2006/02/23
- Re: [Axiom-developer] about Expression Integer, Ralf Hemmecke, 2006/02/24
- Re: [Axiom-developer] about Expression Integer, William Sit, 2006/02/24
- Re: [Axiom-developer] about Expression Integer, Ralf Hemmecke, 2006/02/20
- Re: [Axiom-developer] about Expression Integer, Gabriel Dos Reis, 2006/02/20
- Re: [Axiom-developer] about Expression Integer, Ralf Hemmecke, 2006/02/20
- RE: [Axiom-developer] about Expression Integer, Bill Page, 2006/02/20
- Re: [Axiom-developer] about Expression Integer, Gabriel Dos Reis, 2006/02/20
- Re: [Axiom-developer] about Expression Integer, Ralf Hemmecke, 2006/02/21