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I have the following question about Macaulay2. How to find all integral elements over a subring?

What I mean is the following. Suppose $A$ is a subring of $B$. How can I find the following set?

$$L=\{x\in B : x \text{ is integral over }A\}$$

Here $B$ is a quotient of polynomial ring over rational numbers (e.g., $\mathbb Q[x,y]/(xy+x-1))$ and $A$ is a subring of $B$. I am also not sure how to declare a subring $A$ inside another ring.

Thank you for your help!

Rodrigo de Azevedo
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Ben
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  • First you say that $A$ is a subring of $B$, then you say that $A$ is a quotient ring and $B$ is a subring. I am confused. – Alex M. Sep 13 '15 at 18:13
  • I mean A is a quotient ring e.g. $\mathbb{Q}[x,y,z]/(xyz-1)$ and $B$ is a subring of $A$ e.g. $\mathbb{Q}[x]$ inside $\mathbb{Q}[x,y,z]/(xyz-1)$.Is it clear now? – Ben Sep 13 '15 at 22:42
  • In this case, how can $A$ be a subring of $B$, as you write in paragraph 2? – Alex M. Sep 14 '15 at 09:33
  • Oh sorry.I mean A is a subring of B.I carelessly switched the role of A and B.I have edited the question now.Thabk you. – Ben Sep 14 '15 at 16:56

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