See http://www.sagemath.org/doc/reference/polynomial_rings/sage/rings/polynomial/multi_polynomial_ideal.html#sage.rings.polynomial.multi_polynomial_ideal.MPolynomialIdeal_singular_repr.elimination_ideal
On Tuesday, April 2, 2013 2:45:46 PM UTC+1, Neda wrote: > > so Is there any way for writing Elimination theory in sage? > > Let I c k [ x1,...,xn] be an ideal and let G be a groebner basis of I > with respect to lex order wherex1> x2 > ... >xn , then for every 0< l <n > , the set Gl =G k[xl+1,...,xn ] is the groebner basis of the l-th > elimination ideal. > > > On Tuesday, April 2, 2013 1:47:59 PM UTC+4:30, Volker Braun wrote: >> >> Your question is not about elimination theory. >> >> Your lex order groebner basis is the solution. g4 determines z. Then g3 >> and g2 determine y. Then g1 determines x. >> >> >> >> On Tuesday, April 2, 2013 9:34:00 AM UTC+1, Neda wrote: >>> >>> Hello >>> Could you pleas tell me how can I solve the system of equations x^2 + y >>> + z - 1 =0 x+ y^2 + z - 1 =0 x + y + z^ 2 - 1 =0 over C[x,y] with a given >>> ideal I =< x^2 +y+z-1,x+y^2+z-1,x+y+z^2-1 > and Groebner basis g1=x+y+z^2-1 >>> g2= y^2-y-z^2+z >>> g3=2*y*z^2 +z^4 -z^2 >>> g4=z6-4*z^4+4*z^3-z^2 >>> with *Elimination* *theory* in sage? I know how to solve it but I can't >>> solve it in sage. >> >> -- 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?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
