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Does Macaulay2 compute contractions of ideals under ring homomorphisms. Specifically, if $R\subseteq S$ is a ring extension (say polynomial rings over $\mathbb{Q}$ which can be specified in M2) and $I$ is an ideal in $S$ given by generators, is there a command to compute $I\cap R$?

EDIT: The eliminate command is supposed to do what I want, except when I use it the output is an ideal in the original ring.

Rodrigo de Azevedo
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Amd
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2 Answers2

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More generally there is also the function preimage which takes $f$ a function from $R$ to $S$ and $I$ an ideal in $S$ and outputs $I^c$ in $R$ http://www.math.uiuc.edu/Macaulay2/doc/Macaulay2-1.6/share/doc/Macaulay2/Macaulay2Doc/html/_preimage.html

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You could set f=map(S/I,R) and obtain the intersection as ker(f).

Marc Olschok
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    Marc, if intend to continue to contribute regularly to this site, it would be nice if you registered your account (it takes only a minute to do that). This way it would be easier for the software to recognize you (and it's the third time I ask the moderators to merge your older account into a newly created one). – t.b. Jan 07 '12 at 17:29
  • actually I want to register (I meanwhile have an OPen ID), but cannot find the link for this. I also registerd with the same name but a newer account. – Marc Olschok Jan 09 '12 at 20:47
  • The account you used for writing your last comment is registered. If you want to add other registration information like Open ID, then you should go to your user profile here (this page is accessible by clicking on your name at the top middle at the top of each page). Adding registration information can be done here (this page can be reached by clicking "my logins" on the user profile page). – t.b. Jan 09 '12 at 20:55