1) I think that applying Polynomial division by commands like sage: f(x)=x^3+5*x^2-3*x+1 sage: g(x)=x+1 sage: f.maxima_methods().divide(g) [x^2 + 4*x - 7, 8]
are not very intuitive. This should be done by specific methods/operators for polynomials, and this can only be done by a specific class for polynomials. 2) As mentioned direct call of algorithms (e.g. compute gcd, Gröbner basis etc.) 3) More symbolic manipulation possibilities for specific for symbolic polynomials. 4) faster and numerical more stable evaluation methods On Tuesday, December 17, 2013 5:23:20 PM UTC+1, Simon King wrote: > > Hi, > > On 2013-12-17, maldun <[email protected] <javascript:>> 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 > > > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
