Mixing
Resultants to find common root in $mathbb Z[x_1,dots,x_n]$
$begingroup$
If we have $n$ non-homogeneous polynomials in $mathbb Z[x_1,dots,x_n]$ which pairwise have no non-trivial gcd and with a common root in $mathbb Z^n$ then is it possible to use elimination theory to extract the common root?
What tools should we use from resultants and grobner basis and is there a non-trivial illustrative example in $4$ variables?
algebraic-geometry polynomials ring-theory roots resultant
asked Jan 6 at 3:20
BroutBrout
2,1571428
$endgroup$
add a comment |
$begingroup$
If we have $n$ non-homogeneous polynomials in $mathbb Z[x_1,dots,x_n]$ which pairwise have no non-trivial gcd and with a common root in $mathbb Z^n$ then is it possible to use elimination theory to extract the common root?
What tools should we use from resultants and grobner basis and is there a non-trivial illustrative example in $4$ variables?
algebraic-geometry polynomials ring-theory roots resultant
asked Jan 6 at 3:20
BroutBrout
2,1571428
$endgroup$
add a comment |
$begingroup$
If we have $n$ non-homogeneous polynomials in $mathbb Z[x_1,dots,x_n]$ which pairwise have no non-trivial gcd and with a common root in $mathbb Z^n$ then is it possible to use elimination theory to extract the common root?
What tools should we use from resultants and grobner basis and is there a non-trivial illustrative example in $4$ variables?
algebraic-geometry polynomials ring-theory roots resultant
asked Jan 6 at 3:20
BroutBrout
2,1571428
$endgroup$
If we have $n$ non-homogeneous polynomials in $mathbb Z[x_1,dots,x_n]$ which pairwise have no non-trivial gcd and with a common root in $mathbb Z^n$ then is it possible to use elimination theory to extract the common root?
What tools should we use from resultants and grobner basis and is there a non-trivial illustrative example in $4$ variables?
algebraic-geometry polynomials ring-theory roots resultant
algebraic-geometry polynomials ring-theory roots resultant
asked Jan 6 at 3:20
BroutBrout
2,1571428
asked Jan 6 at 3:20
BroutBrout
2,1571428
asked Jan 6 at 3:20
BroutBrout
2,1571428
asked Jan 6 at 3:20
BroutBrout
2,1571428
asked Jan 6 at 3:20
BroutBrout
2,1571428
2,1571428
add a comment |
add a comment |
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