From b9a03bd43c9a32e2d0e43193d89eff0dc09aae9c Mon Sep 17 00:00:00 2001 From: Johannes Schmitt Date: Fri, 15 Nov 2024 14:21:26 +0100 Subject: [PATCH] Add bibliographical info from mathscinet and run `bibtool` --- docs/oscar_references.bib | 108 ++++++++++-------- experimental/HasseSchmidt/src/HasseSchmidt.jl | 8 +- 2 files changed, 64 insertions(+), 52 deletions(-) diff --git a/docs/oscar_references.bib b/docs/oscar_references.bib index a4c79e0cc3f..2203c3521f7 100644 --- a/docs/oscar_references.bib +++ b/docs/oscar_references.bib @@ -625,6 +625,18 @@ @Article{Cor21 doi = {10.1007/s00029-021-00679-6} } +@Book{Cut04, + author = {Cutkosky, Steven Dale}, + title = {Resolution of singularities}, + mrnumber = {2058431}, + series = {Graduate Studies in Mathematics}, + volume = {63}, + publisher = {American Mathematical Society, Providence, RI}, + pages = {viii+186}, + year = {2004}, + doi = {10.1090/gsm/063} +} + @InCollection{DE02, author = {Decker, Wolfram and Eisenbud, David}, title = {Sheaf algorithms using the exterior algebra}, @@ -1005,6 +1017,19 @@ @InProceedings{FLINT numpages = {4} } +@Article{FRS21, + author = {Frühbis-Krüger, Anne and Ristau, Lukas and Schober, Bernd}, + title = {Embedded desingularization for arithmetic surfaces---toward a parallel implementation}, + mrnumber = {4273121}, + journal = {Math. Comp.}, + fjournal = {Mathematics of Computation}, + volume = {90}, + number = {330}, + pages = {1957--1997}, + year = {2021}, + doi = {10.1090/mcom/3624} +} + @Article{FY04, author = {Feichtner, Eva Maria and Yuzvinsky, Sergey}, title = {Chow rings of toric varieties defined by atomic lattices}, @@ -1067,54 +1092,6 @@ @Book{Ful98 doi = {10.1007/978-1-4612-1700-8} } -@Article{FKRS21, - author = {Fruehbis-Krueger, Anne and Ristau, Lukas and Schober, Bernd}, - title = {Embedded desingularization for arithmetic surfaces -- toward a parallel implementation}, - pages = {32}, - year = {2021}, - doi = {10.1090/mcom/3624} -} - -@Article{Hasse1937, - author = {Hasse, H.}, - title = {Noch eine Begründung der Theorie der höheren Differentialquotienten in einem algebraischen Funktionenkörper einer Unbestimmten. (Nach einer brieflichen Mitteilung von F.K. Schmidt in Jena).}, - journal = {Journal für die reine und angewandte Mathematik}, - pages = {215-223}, - year = {1937}, - url = {http://eudml.org/doc/150015} -} - -@Book{Cut04, - author = {Cutkosky, S.D.}, - title = {Resolution of Singularities}, - isbn = {9780821872383}, - series = {Graduate studies in mathematics}, - publisher = {American Mathematical Soc.}, - url = {https://books.google.de/books?id=OkAppJ7dXsgC} -} - -@Article{Haze11, - author = {Hazewinkel, Michiel}, - title = {Hasse-Schmidt Derivations and the Hopf Algebra of Non-Commutative Symmetric Functions}, - journal = {Axioms}, - volume = {1}, - year = {2012}, - number = {2}, - pages = {149--154}, - issn = {2075-1680}, - doi = {10.3390/axioms1020149} -} - -@Misc{Haze11, - title = {Hasse-Schmidt derivations and the Hopf algebra of noncommutative symmetric functions}, - author = {Michiel Hazewinkel}, - year = {2011}, - eprint = {1110.6108}, - archivePrefix = {arXiv}, - primaryClass = {math.RA}, - url = {https://arxiv.org/abs/1110.6108} -} - @Article{GH12, author = {Grimm, Thomas W. and Hayashi, Hirotaka}, title = {F-theory fluxes, chirality and Chern-Simons theories}, @@ -1395,6 +1372,41 @@ @Book{Har77 doi = {10.1007/978-1-4757-3849-0} } +@Article{Has37, + author = {Hasse, H.}, + title = {Noch eine Begründung der Theorie der höheren Differentialquotienten in einem algebraischen + Funktionenkörper einer Unbestimmten. (Nach einer brieflichen Mitteilung von F. K. + Schmidt in Jena)}, + mrnumber = {1581557}, + journal = {J. Reine Angew. Math.}, + fjournal = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]}, + volume = {177}, + pages = {215--237}, + year = {1937}, + doi = {10.1515/crll.1937.177.215} +} + +@Misc{Haz11, + author = {Michiel Hazewinkel}, + title = {Hasse-Schmidt derivations and the Hopf algebra of noncommutative symmetric functions}, + year = {2011}, + url = {https://arxiv.org/abs/1110.6108}, + eprint = {1110.6108}, + archiveprefix = {arXiv}, + primaryclass = {math.RA} +} + +@Article{Haz12, + author = {Hazewinkel, Michiel}, + title = {Hasse-Schmidt Derivations and the Hopf Algebra of Non-Commutative Symmetric Functions}, + journal = {Axioms}, + volume = {1}, + number = {2}, + pages = {149--154}, + year = {2012}, + doi = {10.3390/axioms1020149} +} + @Article{Hul22, author = {Hulpke, Alexander}, title = {The perfect groups of order up to two million}, diff --git a/experimental/HasseSchmidt/src/HasseSchmidt.jl b/experimental/HasseSchmidt/src/HasseSchmidt.jl index f882424b140..e1297df2aec 100644 --- a/experimental/HasseSchmidt/src/HasseSchmidt.jl +++ b/experimental/HasseSchmidt/src/HasseSchmidt.jl @@ -2,12 +2,12 @@ export hasse_derivatives ### We consider Hasse-Schmidt derivatives of polynomials as seen in ### -### [FKRS21](@cite) Fruehbis-Krueger, Ristau, Schober: 'Embedded desingularization for arithmetic surfaces -- toward a parallel implementation' +### [FRS21](@cite) Fruehbis-Krueger, Ristau, Schober: 'Embedded desingularization for arithmetic surfaces -- toward a parallel implementation' ### ### This is a special case of a more general definition of a Hasse-Schmidt derivative. These more general and rigorous definitions can be found in the following sources: ### ### [Cut04](@cite) Cutkosky: 'Resolution of Singularities' -### [Haze11](@cite) Michiel Hazewinkel: 'Hasse-Schmidt derivations and the Hopf algebra of noncommutative symmetric functions' +### [Haz12](@cite) Michiel Hazewinkel: 'Hasse-Schmidt derivations and the Hopf algebra of noncommutative symmetric functions' ### ################################################################################ @@ -18,8 +18,8 @@ export hasse_derivatives Return a list of Hasse-Schmidt derivatives of `f`, each with a multiindex `[a_1, ..., a_n]`, where `a_i` describes the number of times `f` was derived w.r.t. the `i`-th variable. -Hasse-Schmidt derivatives as seen in [FKRS21](@cite). -For more general and rigorous definition see [Cut04](@cite) or [Haze11](@cite). +Hasse-Schmidt derivatives as seen in [FRS21](@cite). +For more general and rigorous definition see [Cut04](@cite) or [Haz12](@cite). # Examples ```jldoctest