Hi All,
I want to compute the Grobner basis of a system of polynomial equations
in K[x_1,x_2,x_3] receiving * arbitrary *coefficients from
K=GF(2^d). I hope to understand the behaviour of the grobner basis of the
ideal defined by polynomials with 3 arbitrary distinct tuples of
ceofficients.
So I have 3 polynomial equatons in 3 variables,
P1(x1,x2,x3) with its coeffficent tuple value 1
P2(x1,x2,x3) with its coeffficent tuple value 2
P3(x1,x2,x3) with its coeffficent tuple value 3
P1,P2,P3 differ from the fact that the coefficients they recieve are
from 3 distinct tuples.
I wish to find the Grobner basis of this system to understand
*when the variety V={x1,x2,x3 | P1=P2=P3=0 at x} is finite for arbitrary
distinct coefficient tuples that define the above system.*
However, I don't know how I can find the grobner basis for arbitrary
symbolic coefficients in SAGE. I wonder if this is possible and how to do
this ?
Best,
Kyzer
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