The leading coefficient of a resultant
Clash Royale CLAN TAG#URR8PPP
up vote
0
down vote
favorite
Let $k$ be a field and $f,gin k[x,y]$. Let $R(y)=Res_x(f,g)$ be the resultant of $f$ and $g$ considered as polynomials in x over the field $k(y)$. Can you give a nice formula for the leading coefficient of $R(y)$?
Since I am interested only in the leading coefficient of $R(y)$ I was wondering if one could replace $(f,g)$ with $(F,G)$, where F and G are actually "simpler" polynomials in such a way that $Res_x(f,g)=Res_x(F,G)$ (of course, a more explicit formula would be even better).
polynomials resultant
add a comment |Â
up vote
0
down vote
favorite
Let $k$ be a field and $f,gin k[x,y]$. Let $R(y)=Res_x(f,g)$ be the resultant of $f$ and $g$ considered as polynomials in x over the field $k(y)$. Can you give a nice formula for the leading coefficient of $R(y)$?
Since I am interested only in the leading coefficient of $R(y)$ I was wondering if one could replace $(f,g)$ with $(F,G)$, where F and G are actually "simpler" polynomials in such a way that $Res_x(f,g)=Res_x(F,G)$ (of course, a more explicit formula would be even better).
polynomials resultant
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let $k$ be a field and $f,gin k[x,y]$. Let $R(y)=Res_x(f,g)$ be the resultant of $f$ and $g$ considered as polynomials in x over the field $k(y)$. Can you give a nice formula for the leading coefficient of $R(y)$?
Since I am interested only in the leading coefficient of $R(y)$ I was wondering if one could replace $(f,g)$ with $(F,G)$, where F and G are actually "simpler" polynomials in such a way that $Res_x(f,g)=Res_x(F,G)$ (of course, a more explicit formula would be even better).
polynomials resultant
Let $k$ be a field and $f,gin k[x,y]$. Let $R(y)=Res_x(f,g)$ be the resultant of $f$ and $g$ considered as polynomials in x over the field $k(y)$. Can you give a nice formula for the leading coefficient of $R(y)$?
Since I am interested only in the leading coefficient of $R(y)$ I was wondering if one could replace $(f,g)$ with $(F,G)$, where F and G are actually "simpler" polynomials in such a way that $Res_x(f,g)=Res_x(F,G)$ (of course, a more explicit formula would be even better).
polynomials resultant
polynomials resultant
asked Sep 1 at 9:52
Reyx_0
703414
703414
add a comment |Â
add a comment |Â
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2901529%2fthe-leading-coefficient-of-a-resultant%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password