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Add bibliographical info from mathscinet and run bibtool
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joschmitt committed Nov 15, 2024
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108 changes: 60 additions & 48 deletions docs/oscar_references.bib
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Original file line number Diff line number Diff line change
Expand Up @@ -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},
Expand Down Expand Up @@ -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},
Expand Down Expand Up @@ -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},
Expand Down Expand Up @@ -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},
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8 changes: 4 additions & 4 deletions experimental/HasseSchmidt/src/HasseSchmidt.jl
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Expand Up @@ -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'
###

################################################################################
Expand All @@ -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
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