Extracting common roots of polynomials The Next CEO of Stack OverflowIrreducible homogeneous polynomials of arbitrary degreeThe implications of the insolvability of certain polynomialsSolving polynomials in $mathbbQ[X]$ exactlyHomogeneous polynomials propertyFind polynomial whose root is sum of roots of other polynomialsCan every polynomial with algebraic coeffitients be transformed into a polymonial with integer coefficients and at least some of the same roots?Faster multiplication of two polynomials over a fieldHow to extract square roots of polynomials in several variables?How can one efficiently determine whether a given parallelepiped contains an integer vector?Resultants to find common root in $mathbb Z[x_1,dots,x_n]$
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Extracting common roots of polynomials
The Next CEO of Stack OverflowIrreducible homogeneous polynomials of arbitrary degreeThe implications of the insolvability of certain polynomialsSolving polynomials in $mathbbQ[X]$ exactlyHomogeneous polynomials propertyFind polynomial whose root is sum of roots of other polynomialsCan every polynomial with algebraic coeffitients be transformed into a polymonial with integer coefficients and at least some of the same roots?Faster multiplication of two polynomials over a fieldHow to extract square roots of polynomials in several variables?How can one efficiently determine whether a given parallelepiped contains an integer vector?Resultants to find common root in $mathbb Z[x_1,dots,x_n]$
$begingroup$
If we have $2n$ (maximum possible) algebraically independent degree $2$ homogeneous system of polynomials with $mathbb Z$ coefficients in $2n$ variables with exactly one integer root (up to sign) can we find the root in faster than brute force elimination theory?
That is is there a $O(poly(nL))$ time algorithm where $L$ is the number of bits in encoding of all polynomial coefficients?
number-theory algebraic-geometry polynomials roots computational-complexity
asked Mar 19 at 11:41
BroutBrout
2,6061431
$endgroup$
add a comment |
$begingroup$
If we have $2n$ (maximum possible) algebraically independent degree $2$ homogeneous system of polynomials with $mathbb Z$ coefficients in $2n$ variables with exactly one integer root (up to sign) can we find the root in faster than brute force elimination theory?
That is is there a $O(poly(nL))$ time algorithm where $L$ is the number of bits in encoding of all polynomial coefficients?
number-theory algebraic-geometry polynomials roots computational-complexity
asked Mar 19 at 11:41
BroutBrout
2,6061431
$endgroup$
add a comment |
$begingroup$
If we have $2n$ (maximum possible) algebraically independent degree $2$ homogeneous system of polynomials with $mathbb Z$ coefficients in $2n$ variables with exactly one integer root (up to sign) can we find the root in faster than brute force elimination theory?
That is is there a $O(poly(nL))$ time algorithm where $L$ is the number of bits in encoding of all polynomial coefficients?
number-theory algebraic-geometry polynomials roots computational-complexity
asked Mar 19 at 11:41
BroutBrout
2,6061431
$endgroup$
If we have $2n$ (maximum possible) algebraically independent degree $2$ homogeneous system of polynomials with $mathbb Z$ coefficients in $2n$ variables with exactly one integer root (up to sign) can we find the root in faster than brute force elimination theory?
That is is there a $O(poly(nL))$ time algorithm where $L$ is the number of bits in encoding of all polynomial coefficients?
number-theory algebraic-geometry polynomials roots computational-complexity
number-theory algebraic-geometry polynomials roots computational-complexity
asked Mar 19 at 11:41
BroutBrout
2,6061431
asked Mar 19 at 11:41
BroutBrout
2,6061431
asked Mar 19 at 11:41
BroutBrout
2,6061431
asked Mar 19 at 11:41
BroutBrout
2,6061431
asked Mar 19 at 11:41
BroutBrout
2,6061431
2,6061431
add a comment |
add a comment |
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