Degree of resultant of polynomials in $mathbb{Z}[Y][X]$
I am trying to write a program that computes the resultant of two polynomials with coefficients in $mathbb{Z}[Y]$. If I know the degree of the polynomial as a polynomial in $Y$ is $k$ say, I can evaluate at $k+1$ points by computing resultants over $mathbb{Z}$ which I can already do, but how do I know what the degree of the resultant over $mathbb{Z}[Y]$ is?
I can bound it by the product of the $Y$-degrees of the input polynomials. It seems to me like this bound shouldn't always be achieved.
Is there a way around this, either by not needing to know the exact degree, or by finding what the degree is easily?
linear-algebra polynomials
asked Dec 13 '18 at 10:20
Evgeny TEvgeny T
709414
add a comment |
I am trying to write a program that computes the resultant of two polynomials with coefficients in $mathbb{Z}[Y]$. If I know the degree of the polynomial as a polynomial in $Y$ is $k$ say, I can evaluate at $k+1$ points by computing resultants over $mathbb{Z}$ which I can already do, but how do I know what the degree of the resultant over $mathbb{Z}[Y]$ is?
I can bound it by the product of the $Y$-degrees of the input polynomials. It seems to me like this bound shouldn't always be achieved.
Is there a way around this, either by not needing to know the exact degree, or by finding what the degree is easily?
linear-algebra polynomials
asked Dec 13 '18 at 10:20
Evgeny TEvgeny T
709414
add a comment |
I am trying to write a program that computes the resultant of two polynomials with coefficients in $mathbb{Z}[Y]$. If I know the degree of the polynomial as a polynomial in $Y$ is $k$ say, I can evaluate at $k+1$ points by computing resultants over $mathbb{Z}$ which I can already do, but how do I know what the degree of the resultant over $mathbb{Z}[Y]$ is?
I can bound it by the product of the $Y$-degrees of the input polynomials. It seems to me like this bound shouldn't always be achieved.
Is there a way around this, either by not needing to know the exact degree, or by finding what the degree is easily?
linear-algebra polynomials
asked Dec 13 '18 at 10:20
Evgeny TEvgeny T
709414
I am trying to write a program that computes the resultant of two polynomials with coefficients in $mathbb{Z}[Y]$. If I know the degree of the polynomial as a polynomial in $Y$ is $k$ say, I can evaluate at $k+1$ points by computing resultants over $mathbb{Z}$ which I can already do, but how do I know what the degree of the resultant over $mathbb{Z}[Y]$ is?
I can bound it by the product of the $Y$-degrees of the input polynomials. It seems to me like this bound shouldn't always be achieved.
Is there a way around this, either by not needing to know the exact degree, or by finding what the degree is easily?
linear-algebra polynomials
linear-algebra polynomials
asked Dec 13 '18 at 10:20
Evgeny TEvgeny T
709414
asked Dec 13 '18 at 10:20
Evgeny TEvgeny T
709414
asked Dec 13 '18 at 10:20
Evgeny TEvgeny T
709414
asked Dec 13 '18 at 10:20
Evgeny TEvgeny T
709414
asked Dec 13 '18 at 10:20
Evgeny TEvgeny T
709414
709414
add a comment |
add a comment |
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