Decomposing an ideal using Macaulay2
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I give Macaulay2 the ideal $I=(y^2, x) in Q[x , y]$ and then I put decompose I. The result is $(x , y)$ but I do not understand why. Does it mean that $I = (x , y)$? but that is not true, because we can not create $y$ in $I$.
ideals macaulay2
edited Dec 9 '18 at 9:36
Rodrigo de Azevedo
13k41958
asked Sep 26 '16 at 18:04
M. SaM. Sa
495
$endgroup$
add a comment |
$begingroup$
I give Macaulay2 the ideal $I=(y^2, x) in Q[x , y]$ and then I put decompose I. The result is $(x , y)$ but I do not understand why. Does it mean that $I = (x , y)$? but that is not true, because we can not create $y$ in $I$.
ideals macaulay2
edited Dec 9 '18 at 9:36
Rodrigo de Azevedo
13k41958
asked Sep 26 '16 at 18:04
M. SaM. Sa
495
$endgroup$
add a comment |
$begingroup$
I give Macaulay2 the ideal $I=(y^2, x) in Q[x , y]$ and then I put decompose I. The result is $(x , y)$ but I do not understand why. Does it mean that $I = (x , y)$? but that is not true, because we can not create $y$ in $I$.
ideals macaulay2
edited Dec 9 '18 at 9:36
Rodrigo de Azevedo
13k41958
asked Sep 26 '16 at 18:04
M. SaM. Sa
495
$endgroup$
I give Macaulay2 the ideal $I=(y^2, x) in Q[x , y]$ and then I put decompose I. The result is $(x , y)$ but I do not understand why. Does it mean that $I = (x , y)$? but that is not true, because we can not create $y$ in $I$.
ideals macaulay2
ideals macaulay2
edited Dec 9 '18 at 9:36
Rodrigo de Azevedo
13k41958
asked Sep 26 '16 at 18:04
M. SaM. Sa
495
edited Dec 9 '18 at 9:36
Rodrigo de Azevedo
13k41958
asked Sep 26 '16 at 18:04
M. SaM. Sa
495
edited Dec 9 '18 at 9:36
Rodrigo de Azevedo
13k41958
edited Dec 9 '18 at 9:36
Rodrigo de Azevedo
13k41958
edited Dec 9 '18 at 9:36
Rodrigo de Azevedo
13k41958
13k41958
asked Sep 26 '16 at 18:04
M. SaM. Sa
495
asked Sep 26 '16 at 18:04
M. SaM. Sa
495
asked Sep 26 '16 at 18:04
M. SaM. Sa
495
495
add a comment |
add a comment |
1 Answer
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From the documentation:
decomposeis a synonym forminimalPrimes.
This function computes the minimal associated primes of the ideal
Iusing characteristic sets. Geometrically, it decomposes the algebraic set defined byI.
So $(x,y)$ is the minimal associated prime of $I = (y^2,x)$. (It's just the radical of $I$, since $I$ is a primary ideal.)
answered Sep 26 '16 at 18:25
arkeetarkeet
5,175923
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
From the documentation:
decomposeis a synonym forminimalPrimes.
This function computes the minimal associated primes of the ideal
Iusing characteristic sets. Geometrically, it decomposes the algebraic set defined byI.
So $(x,y)$ is the minimal associated prime of $I = (y^2,x)$. (It's just the radical of $I$, since $I$ is a primary ideal.)
answered Sep 26 '16 at 18:25
arkeetarkeet
5,175923
$endgroup$
add a comment |
$begingroup$
From the documentation:
decomposeis a synonym forminimalPrimes.
This function computes the minimal associated primes of the ideal
Iusing characteristic sets. Geometrically, it decomposes the algebraic set defined byI.
So $(x,y)$ is the minimal associated prime of $I = (y^2,x)$. (It's just the radical of $I$, since $I$ is a primary ideal.)
answered Sep 26 '16 at 18:25
arkeetarkeet
5,175923
$endgroup$
add a comment |
$begingroup$
From the documentation:
decomposeis a synonym forminimalPrimes.
This function computes the minimal associated primes of the ideal
Iusing characteristic sets. Geometrically, it decomposes the algebraic set defined byI.
So $(x,y)$ is the minimal associated prime of $I = (y^2,x)$. (It's just the radical of $I$, since $I$ is a primary ideal.)
answered Sep 26 '16 at 18:25
arkeetarkeet
5,175923
$endgroup$
From the documentation:
decomposeis a synonym forminimalPrimes.
This function computes the minimal associated primes of the ideal
Iusing characteristic sets. Geometrically, it decomposes the algebraic set defined byI.
So $(x,y)$ is the minimal associated prime of $I = (y^2,x)$. (It's just the radical of $I$, since $I$ is a primary ideal.)
answered Sep 26 '16 at 18:25
arkeetarkeet
5,175923
answered Sep 26 '16 at 18:25
arkeetarkeet
5,175923
answered Sep 26 '16 at 18:25
arkeetarkeet
5,175923
answered Sep 26 '16 at 18:25
arkeetarkeet
5,175923
5,175923
add a comment |
add a comment |
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