Hi,
On 2013-12-17, maldun <dom...@gmx.net> wrote:
> On ticket http://trac.sagemath.org/ticket/9706 for the orthogonal
> Polynomials Jeroen Demeyer came up with the the idea of a
> SymbolicPolynomial class. I think that's a great idea, because, if well
> designed, such a class has much potential to give very much comfort to the
> handling of sage. Because many algorithms that deal with Polynomials have
> to be called from external programs and libraries.
I don't see the point here.
On the sage-support list, one quite often sees questions that boil down to
the misunderstanding that a symbolic polynomial
sage: var('x')
x
sage: x^2+1
x^2 + 1
sage: type(x^2+1)
<type 'sage.symbolic.expression.Expression'>
and a symbolic polynomial function
sage: f(x) = x^2+1
sage: f
x |--> x^2 + 1
sage: type(f)
<type 'sage.symbolic.expression.Expression'>
and an element of a polynomial ring
sage: P.<x> = GF(5)[]
sage: x^2+1
x^2 + 1
sage: type(x^2+1)
<type 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint'>
have the same range of applications. Very often, the posters on
sage-support were using symbolic expressions but should rather be using
polynomials, for efficiency.
So, what exactly would be the purpose of a SymbolicPolynomial class? And
why do you think that the existence of such a class could give much
comfort to the handling of sage (even when you restrict this statements
to users such as myself, who use multivariate polynomials on a daily basis,
in the sense of computing Gröbner bases and test for membership in polynomial
ideals)?
Best regards,
Simon
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