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1. • CommentRowNumber1.
   • CommentAuthornLab edit announcer
   • CommentTimeJun 5th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexstarting discussion page here Anonymous <a href="https://ncatlab.org/nlab/revision/diff/rational+function/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/rational+function/12">v12</a>, <a href="https://ncatlab.org/nlab/show/rational+function">current</a>

   starting discussion page here

   Anonymous

   diff, v12, current

2. • CommentRowNumber2.
   • CommentAuthorGuest
   • CommentTimeJun 5th 2022
   • PermaLink
   Author: Guest
   Format: MarkdownItexThis article needs to be split, because there is a significant difference between rational functions in the function algebra of a field, vs what is described as "rational fractions" in this article, the field of fractions of a polynomial ring. The second are usually called "rational expressions" in typical school algebra; [[Frank Quinn]] calls the second object "polynomial fractions" in [Proof Projects for Teachers](https://personal.math.vt.edu/fquinn/education/pfs4teachers0.pdf). In particular, rational expressions form a field of fractions. However, rational functions over a field do not form a field of fractions, due to issues involving the definition of [[partial functions]] and division by zero.

   This article needs to be split, because there is a significant difference between rational functions in the function algebra of a field, vs what is described as “rational fractions” in this article, the field of fractions of a polynomial ring. The second are usually called “rational expressions” in typical school algebra; Frank Quinn calls the second object “polynomial fractions” in Proof Projects for Teachers. In particular, rational expressions form a field of fractions. However, rational functions over a field do not form a field of fractions, due to issues involving the definition of partial functions and division by zero.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJun 5th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexSounds good, please do split, if you have the energy.

   Sounds good, please do split, if you have the energy.

4. • CommentRowNumber4.
   • CommentAuthornLab edit announcer
   • CommentTimeJun 5th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexremoving the first definition and keeping the second, going to create new article with the first definition Anonymous <a href="https://ncatlab.org/nlab/revision/diff/rational+function/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/rational+function/12">v12</a>, <a href="https://ncatlab.org/nlab/show/rational+function">current</a>

   removing the first definition and keeping the second, going to create new article with the first definition

   Anonymous

   diff, v12, current

5. • CommentRowNumber5.
   • CommentAuthornLab edit announcer
   • CommentTimeJun 5th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexon the contrary it seems that "rational function" is also used for rational expressions/polynomial fractions in arithmetic geometry, which should also deserve its own page separate from rational functions as actually partial functions. Anonymous <a href="https://ncatlab.org/nlab/revision/diff/rational+function/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/rational+function/12">v12</a>, <a href="https://ncatlab.org/nlab/show/rational+function">current</a>

   on the contrary it seems that “rational function” is also used for rational expressions/polynomial fractions in arithmetic geometry, which should also deserve its own page separate from rational functions as actually partial functions.

   Anonymous

   diff, v12, current

6. • CommentRowNumber6.
   • CommentAuthorDmitri Pavlov
   • CommentTimeJun 5th 2022
   • (edited Jun 6th 2022)
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexThe new definition seems to claim that $1/(x^p-x)$ in the field $\mathbf{Z}/p$ is not a rational function. This contradicts the standard terminology: <https://stacks.math.columbia.edu/tag/01RT>. It also contradicts the Wikipedia article, which talks about the field of fractions of $k[X]$. I suggest reverting to the old definition.

   The new definition seems to claim that $1/(x^p-x)$ in the field $\mathbf{Z}/p$ is not a rational function.

   This contradicts the standard terminology: https://stacks.math.columbia.edu/tag/01RT. It also contradicts the Wikipedia article, which talks about the field of fractions of $k[X]$.

   I suggest reverting to the old definition.

7. • CommentRowNumber7.
   • CommentAuthornLab edit announcer
   • CommentTimeJun 5th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexfixed definition and linked to [[division]] Anonymous <a href="https://ncatlab.org/nlab/revision/diff/rational+function/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/rational+function/12">v12</a>, <a href="https://ncatlab.org/nlab/show/rational+function">current</a>

   fixed definition and linked to division

   Anonymous

   diff, v12, current