I forget to add few more equations to system ie. {x^4-x,y^4-y,z^4-z}
in reason to have solution in GF(4) and zero dimensional ideal, so I
answered my question.
But, I have another issue.
When I use quotient ring Q, J.groebner_basis() does not return
completely reduced basis.
Also, with quotient ring Q, J.variety() returns ValueError: Could not
detect ring.Code: K.<alpha>=GF(4) R.<a,b,c>=PolynomialRing(K,3,order='lex') Q.<x,y,z>=R.quotient(sage.rings.ideal.FieldIdeal(R)) R.inject_variables() Q.inject_variables() F=[a^3+a+c,b+c,a^4-a,b^4-b,c^4-c] G=[x^3+x+z,y+z] I=Ideal(F) J=Ideal(G) print I.groebner_basis() print J.groebner_basis() Defining a, b, c Defining x, y, z [a^2 + a + c^2 + c, a*c + c^2 + c, b + c, c^3 + c^2 + c] [x^2 + x*z + x, x*z + z^2 + z, y + z, z^3 + z^2 + z] J.variety() Traceback (click to the left of this block for traceback) ... ValueError: Could not detect ring. On Oct 26, 5:58 pm, Dušan Orlović <duleorlo...@gmail.com> wrote: > Hi all, > I have a question how to solve system in GF(4) using Grobner basis and > elimination (I want to find just one solution). > The system (which is already in reduced form) is: > > x^3+x+z > y+z > > If we put z=1 then first equation x^3+x+1 has no root in GF(4). If z=0 we > have solution y=0, x=0. > Is there an algorithm that can determine right values of z instead of trying > all values? > Thanks, -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
