User talk:D.Lazard

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Safe Primes, in RSA

Ok, let's try to discuss here: https://en.wikipedia.org/wiki/Talk:RSA_(cryptosystem)#Safe_Primes,_in_RSA_Key_Generation No "reliable sources" are needed here. Here you just need to think with your own head. This is math. In any case, I do not owe you anything, and I do not demand anything from you.

Coordinate Systems and Analytic Geometry

Moved to Talk:Cartesian coordinate system

– Nothing personal in this discussion

Parker vector applications

Are you knowledgeable or have internet access to knowledge about the usefulness of the Parker vector, especially for Galois groups? If so, can you add it to the article? thanks.Rich (talk) 01:17, 22 August 2024 (UTC)[reply]

I never heard from Parker vectors before your post. As the Wikipedia article is a stub, I did a Scholar Google search on "Parker vector" (with quotes for avoiding articles where the two words appear in different sentences). This gives very few (less than 10 articles) that seem relevant to expand the stub, and none seem related to Galois theory. On the contrary, the Parker vector seems to be one of the numerous invariants of finite permutation groups. Moreover one of the article says explicitly that the Parker vector does not suffices alone for characterizing a permutation group.

Also, the Wikipedia article asserts without source that "the Parker vector can assist in the recognition of Galois groups". This seems dubious and appears as a hope of some authors rather than an encyclopedic fact. In any case, no method is provided for computing the Parker vector of the Galois group of a polynomial, without computing the Galois group. D.Lazard (talk) 08:25, 22 August 2024 (UTC)[reply]

Thanks for your research...the portion of an article by Daniele Gewurz that I was able to access indicated the Parker vector was defined by Richard Parker. Do you know if that is the mathematician Richard A. Parker from the UK who died in January?Rich (talk) 12:42, 22 August 2024 (UTC)[reply]

This article mention Richard A. Parker as the inventor of Parker vectors. Since Richard A. Parker was a specialist of finite groups, he is certainly the same person. D.Lazard (talk) 16:38, 22 August 2024 (UTC)[reply]

okay, thanks for everything!Rich (talk) 21:53, 22 August 2024 (UTC)[reply]

Informal definition of indeterminate

@D.Lazard, Due to the condition of the indeterminate (variable) article, I figured it would be nice to have an area where we can discuss with one another a (somewhat informal) definition of "indeterminate" so that we can have a common ground when editing the article. Given that the term is somewhat ill-defined in literature, I suggest that for this conversation we do not rely too much on exact sources.

I can start. I have a few issues with the definition as it currently stands "This is just a symbol used in a formal way"

(1) Doesn't mean anything, as just about every symbol in math can be described this way. For instance, the symbol '+' is used in a formal way, does that make it an indeterminate? Obviously not.

(2) As an informal statement, it is unenlightening, and would only leave a reader unfamiliar with the subject more confused.

(3) It cannot be easily formalized, as the most obvious meaning "A variable that represents nothing" does not satisfy the algebraic requirements of such an item, namely, equality of polynomials. Since any equation involving an indeterminate by this definition would vacuously form an identity, thus 3-2X = 4 is true. Since all resolutions of X (none) make this true; or more clearly, there does not exist a resolution of X which makes the equation false.

Do you have other proposals for the definition? Farkle Griffen (talk) 19:32, 26 August 2024 (UTC)[reply]

Again, this is not the role of Wikipedia to propose definitions. Wikipedia, as every encyclopedia, must only report the common knowledge. So the discussion on a definition of an "indeterminate" has no place in Wikipedia. The only relevant question is whether the definition of the article is the same as the most common definition and whether significant variants of the definition are correctly reported. The discussion you suggest should be placed in a mathematical forum, which Wikipedia is not. D.Lazard (talk) 19:57, 26 August 2024 (UTC)[reply]

The issue is that the introduction is not the most common definition, in fact, it seems there is no reasonable "most common definition" since very few authors in algebra make an attempt to define it.

But that is not the point of this discussion. While the topic is "Informal definition of indeterminate", the point of this discussion is to find common ground in reference to the article. If things continue as they have been, it seems we will not reach a satisfying conclusion.

If you would like to change the exact topic we can. The goal is to understand your side so we can ease the tension and actually work on improving the article. Farkle Griffen (talk) 20:20, 26 August 2024 (UTC)[reply]