Talk:Numerical algebraic geometry

Things to add

We should add articles on the following concepts:

• Self-conjugacy of a component of an algebraic variety.

Article title

The article title "Numerical algebraic geometry" is confusing, as suggesting that the article is about a subarea of mathematics. This is wrong, as this article is about a single method (homotopy continuation, and its applications). In fact, homotopy continuation is only one of the methods of computational algebraic geometry, as well as Gröbner bases, cylindrical algebraic decomposition, Canny's roadmap algorithm, Regular chains, ... As far as I know, every problem that can be solved with homotopy continuation may also be solved by one of these methods. In general homotopy continuation is faster, but less robust (possibility of errors not detected by the software). Thus, it is wrong to present homotopy continuation as an area of mathematics.

For these reasons, I'll modify the lead, and move the article to Homotopy continuation, leaving the present title as a redirect (this is needed, because of the name of Sommese's book). D.Lazard (talk) 16:16, 8 January 2017 (UTC)

I am reverting the page back. There are frequently formal gatherings and academic publications on numerical algebraic geometry, and there are mathematicians who refer to themselves as numerical algebraic geometers. This is indeed a field of mathematics. In fact, a group of 15 experts is sitting in a room right now, discussing and authoring this page.

Homotopy continuation is the fundamental method, but by no means the only method, of numerical algebraic geometry. They are not synonymous. As we describe this young field in Wikipedia, we will create a page for homotopy continuation, and many others in the coming weeks, months, and years. Please be patient and understanding. Ofloveandhate (talk) 20:09, 8 January 2017 (UTC)

Let me underscore this reversion. Numerical algebraic geometry is becoming an important tool in the applications of algebraic geometry and as a subject in its own right. Please let that community develop pages to inform others about it. Thank you, Frank Sottile (talk) 00:18, 9 January 2017 (UTC)

Section "Theorem Star"

While I think the notation is curious enough to be mentioned in an article, I do not see how it fits with the topic of this article (that is, homotopy continuation). Maybe it should be moved to another page? (I do not know yet which page would be relevant). Saung Tadashi (talk) 19:29, 25 July 2018 (UTC)

@Saung Tadashi: I see no evidence that "Theorem Star" is an established notation. Even the cited authors don't claim there is any such term: they just say that they have used a star to designate computer-assisted proofs. I think this section has no value, and I will delete it. RockMagnetist(talk) 18:14, 27 April 2020 (UTC)

@RockMagnetist: Agreed. Thanks for the answer. Saung Tadashi (talk) 21:01, 27 April 2020 (UTC)