On 2014-02-27, etienne mann <[email protected]> wrote: > Hello, > > I agree but you can also divide by something which is not a Grobner basis, > like in my example. > So I wonder if this division is implemented on sage. yes, you can reduce w.r.t. any Sequence, it does not need to be a GB.
E.g. sage: x,y,z = QQ['x,y,z'].gens() sage: I = Sequence((x^5 + y^4 + z^3 - 1, x^3 + y^3 + z^2 - 1)) sage: (x^6*y^5).reduce(I) y^11 + 2*y^8*z^2 + y^5*z^4 - 2*y^8 - 2*y^5*z^2 + y^5 > The trick is that this division is not well-defined i.e. the reminder is > not unique...that's why it is not implemented. If you divide by a groebner > basis the reminder is unique :) > > all the best, > Etienne > > Le jeudi 27 février 2014 15:59:49 UTC+1, Dima Pasechnik a écrit : >> >> On 2014-02-27, etienne mann <[email protected] <javascript:>> wrote: >> > Hi, >> > >> > is there a command for the "division for multivariable polynomials" ? >> > >> > for example >> > f= x^2*y+x*y^2+x+y+1 >> > g1=x*y-1 >> > g2=y^2-1 >> > >> > we want to divide f by (g1,g2) with lexicographic order ? >> >> You can do f.reduce(B), for B a Groebner basis of (g1,g2). >> See e.g. >> >> http://www.math.ucla.edu/~jimc/mathnet_d/sage/reference/sage/rings/polynomial/multi_polynomial_ideal.html >> >> for an example. >> >> HTH, >> Dmitrii >> >> > -- You received this message because you are subscribed to the Google Groups "sage-support" 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-support. For more options, visit https://groups.google.com/groups/opt_out.
