On Sun, Jul 19, 2009 at 9:04 AM, William Stein<wst...@gmail.com> wrote:
>
>
> Please do not make the above change. It would be very inconsistent
> with what happens for symbolic variables:
>
> sage: var('x,y,z,w')
> sage: f = 1.0*x^2 - 1.0*y
> sage: f.variables()
> (x, y)
I'm not sure symbolic variables are consistent to start with:
sage: SR(1.0)
1.00000000000000
sage: SR(1.0*x)
x
sage: SR(2.0*x)
2.00000000000000*x
sage: SR(1.0*x+1.0)
x + 1.00000000000000
This does not look promising. Printing should be consistent across
similar elements of the same parent, and it's not.
I would argue that, strictly speaking, the variable 'x' is not an
element of the polynomial ring R[x]. The latter is defined as finite
formal sums of the form
a0 + a1*x + ... + an*x^n
So x is not in R[x], but R(1)*x is. x is a formal variable/symbol,
while R(1)*x is a polynomial.
What I'm trying to get at is this: we can't have our cake and eat it
too. If we agree that 1.0*x should be printed as 1.0000000000*x, and
we want f.variables() to return x as an element of the polynomial
ring, then it will be printed as 1.00000000000*x.
If we make f.variables() return the formal variable x somehow, then we
can always do R(x) to get the polynomial.
I'm not saying that I think I have the correct solution to this, I'm
just pointing out that symbolic expressions are printed almost as
inconsistently as multivariate polynomials (and differently to
univariate polynomials) so they might not be the right model to
follow.
Best,
Alex
--
Alex Ghitza -- Lecturer in Mathematics -- The University of Melbourne
-- Australia -- http://www.ms.unimelb.edu.au/~aghitza/
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