User:D.Lazard

Wikipedia:Babel

en-2This user can contribute with an intermediate level of English.

frCet utilisateur a pour langue maternelle le français.

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Main contributions

This list, aimed to summarize my main contributions to Wikipedia, was started on September 2017, 8. As I am editing since may 2010, it will take some time before it will be reasonably complete. For some time, I'll add old entries only when I'll come back to them for any reason.

Article	Date	Diff	Edit summary	Comments
System of polynomial equations	May 2010		Article created	My initial contributions still represents 75% of the article
Hilbert series and Hilbert polynomial	December 2011		Moved and largely expanded	Emphasis on Hilbert series Simple presentation of dimension and degree theory
Algebraic geometry	December 2011 to January 2012		Rewriting lead + clarifying and expanding basic notions (classical algebraic geometry) + adding computational geometry and real algebraic geometry	Previous version gave a undue weight to scheme theory and generalizations
Dimension of an algebraic variety	December 2011 to January 2014	[1]	12 equivalent definitions, distinguishing affine and projective cases, real dimension, methods of computation	Previously, only the definition as the degree of transcendence of the function field (6 lines of text in the whole article)
Polynomial greatest common divisor	April 2012 to September 2012		Moving + Adding modern methods	The previous version described the state of the art before the computer era
Algebra	February 2013		Clarifying the definition (various meanings)	Previously, confusion with the old meaning of "theory of equations" + old fashioned distinction between algebra and abstract algebra
Resultant	September 2012 to November 2016		Largely expanding. Adding homogeneous resultant, Macaulay's resultant, U-resultant	Size multiplied by 5
Algebraic curve	October 2012		Adding the classical elementary study	This was completely lacking in WP
Factorization of polynomials	September 2014		Introduction of the modern methods and their general strategy
Finite field	September 2014		Modern presentation	Previous version was focused on operation tables
0.999...	August 2017		Lead for defining the subject to the article Creating section "Elementary proof"	Motivate for clarifying an endless discussion on the talk page
Surface (mathematics)	April 2016 and May 2016		Writing this article from scratch	Was a redirect to a dab page
Hilbert's syzygy theorem	July 2016 to November 2016	[2]	From short stub to B-class
Decimal	August 2017		Emphasis on finite decimals	Motivated by a discussion on Talk:0.999...
Gaussian integer	September 2017		Expanding, less technical and linking to related articles
Primary decomposition	September 2017		Adding various examples	The article deserve to be restructured
Computational complexity	September 8, 2017		Creating as a broad-concept article	Was a dab, not convenient, as none of the links covers the concept for a non-specialist, who does not care of the distinction between complexity theory, analysis of algorithms and their practical implications
Computational complexity	December 2017		Expanding to C-class
Euclidean division			Moving from "Division algorithm"	This term was unknown in WP
Gröbner basis			Adding section "Properties and use"+ More accurate wording	Still deserves a better description of the theory
Symbolic computation			Moved to Computer algebra	Not finished
Hypersurface	November 2017		Splitting the manifold and the variety case + expanding the algebraic case
Zeros and poles	January 15, 2018		New article resulting of the merge of Zero (complex analysis) and Pole (complex analysis)	Expanding it and emphasizing on the symmetry between zeros and poles
Linear differential equation	February 6, 2018	[3]	Was a mess. Complete rewrite	Added a section on holonomic functions
Matrix multiplication	February 2018	[4]	Major revision	C-class -> B-class
Factorization	March 2018	[5]	Few true additions, except distinguishing factorization of polynomials and factorization of expressions	Was written in a confusing style that pretended to be elementary
Multi-homogeneous Bézout theorem	March 27, 2018	[6]	Creating stub and redirects from Multi-projective variety and Multi-homogeneous polynomial	Linked to from projective variety and Homogeneous polynomial
Vandermonde matrix	March 2018	[7]	Providing 3 proofs + cleaning up
Surface	April 6, 2016 and March 3, 2018		I did not really edited, but started the two move discussions that have led to this article	First discussion and second discussion
Function (mathematics)	April 2018	[8]	Complete rewrite
Homomorphism	January 2017	[9]	Clarifying the relationships epimorphism–surjection, and monomorphism–injection	Also restructuring and expanding
Vector (mathematics and physics)	September 2017	[10]	From a WP:SIA (indiscriminate list of items) to a WP:Broad-concept article
Basis (linear algebra)	October 2018	[11]	Complete rewriting of the main sections of the article	The incitation was a remark in the talk page that the section "change of basis" was a mess
Sturm's theorem	November 2018	[12]	Restructuring, adding context, removing out-of-scope section "history"
Budan's theorem	November 2018	[13]	Major rewrite
Vincent's theorem	December 2018	[14]	Redirected to a section in Real-root isolation	Had multiple issues: wP:COI, , WP:NPOV
Real-root isolation	December 2018	[15]	New article	Update and expands both Vincent's theorem and Root-finding algorithm#Roots of polynomials
Root-finding algorithm	December 2018	[16]	Rewrite and update § Roots of polynomials	Includes {{main|Real-root isolation}}
Curvature	October 2019	[17]	Rewrite the part on curves	Motivated by bad tentative by a crank for fixing true weaknesses of this article
Curve	May 2019	[18]	Clarification of the difference between classes of curves, and giving them their correct weight per WP:NPOV
Euclidean space	September 2019	[19]	Previous version was a mess	Aimed for clarifying common misconceptions occurring in many Wikipedia articles, such that "a Euclidean space is a vector space"
Cubic function	September 2019	[20]	Splitting out Cubic Equation and adding cubic interpolation
Cubic equation	September 2019	[21]	Splitted out from Cubic function	Widely rewritten for an encyclopedic tone

To do

Article	Date	Edit summary	Comments
Root-finding algorithm	September 2017	Rewriting section on polynomials	WP:TECHNICAL and WP:NPOV

Group theory

Your removal of the new section was premature. The mathematical point that I was making concerns the existence of infinite groups in the 3-dimensions of the physical world. These groups have useful applications even to very simple systems like the 3-atom molecules that were illustrated. Please remember that interest in the subject matter of this article will not be confined to specialist mathematicians. Petergans (talk) 21:48, 16 March 2022 (UTC)

To editor Petergans: There are many infinite groups that can be understood by almost everybody. Among the simplest examples are the integers, the translations, the plane rotations with a fixed center, and the rigid motions. Your examples are cryptic, except maybe for experts in chemistry. Your section is also unsourced. So, as it is, your section is not convenient for Wikipedia. Moreover, even rewritten completely, it is definively misplaced as a subsection of "Finite groups". Rewritten as a section "Applications in chimestry", and correctly sourced, its inclusion could be discussed. However, as infinite groups are used in almost all sciences, I do not see any reason for such an emphasis on chimestry. D.Lazard (talk) 23:20, 16 March 2022 (UTC)