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1. starting discussion page here

Anonymous

• CommentRowNumber2.
• CommentAuthorGuest
• CommentTimeJun 5th 2022

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.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJun 5th 2022

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

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

Anonymous

3. 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

• CommentRowNumber6.
• CommentAuthorDmitri Pavlov
• CommentTimeJun 5th 2022
• (edited Jun 6th 2022)

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.

4. fixed definition and linked to division

Anonymous