> ("solve" seems to be very much an overkill and it is not that
> transparent in what it does...)Definitely! And I won't even believe the output... > I want to solve polynomial equations and in order to do so, I do > something like: > > sage: R.<x,y> = PolynomialRing(QQ, order='lex') > sage: I = R.ideal([x*y-1, x^2-y^2]) > sage: I.groebner_basis() > [x - y^3, y^4 - 1] > > What is the Sage command to do this operation, i.e., backwards > substituting to find a solution? One possibility (I do not think there is a ready made function) sage: sage: R.<x,y> = PolynomialRing(QQ, order='lex') sage: sage: I = R.ideal([x*y-1, x^2-y^2]) sage: sage: I.groebner_basis() [x - y^3, y^4 - 1] sage: f1, f2 = I.groebner_basis() sage: Ry.<y> = PolynomialRing(QQ) sage: Rx.<x> = PolynomialRing(QQbar) sage: roots_y = Ry(f2).roots(QQbar) sage: print roots_y [(-1, 1), (1, 1), (-1*I, 1), (1*I, 1)] sage: for r,_ in roots_y: ....: for s,_ in Rx(f1.subs(y=r)).roots(QQbar): ....: print (s,r) (-1, -1) (1, 1) (1*I, -1*I) (-1*I, 1*I) Vincent -- 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 sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
