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adding BibTeX example in LaTeX-notes
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‎Notes/LaTeX-notes/bibTeX-example.bbl‎

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\begin{thebibliography}{1}
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\bibitem{sturmfels_algorithms_2008}
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Bernd Sturmfels.
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\newblock {\em Algorithms in invariant theory}.
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\newblock Texts \& monographs in symbolic computation. Springer-Verlag, Wien ;, 2nd ed. edition, 2008.
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\bibitem{derksen_polynomial_2000}
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Harm Derksen.
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\newblock Polynomial bounds for rings of invariants.
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\newblock {\em Proceedings of the American Mathematical Society}, 129(4):955--963, October 2000.
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\bibitem{gao_zero-sum_2006}
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Weidong Gao and Alfred Geroldinger.
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\newblock Zero-sum problems in finite abelian groups: {A} survey.
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\newblock {\em Expositiones Mathematicae}, 24(4):337--369, November 2006.
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\bibitem{sezer_sharpening_2002}
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Müfit Sezer.
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\newblock Sharpening the generalized {Noether} bound in the invariant theory of finite groups.
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\newblock {\em Journal of Algebra}, 254(2):252--263, August 2002.
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\bibitem{schmid_finite_1991}
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Barbara~J. Schmid.
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\newblock Finite groups and invariant theory.
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\newblock In {\em Topics in {Invariant} {Theory}}, pages 35--66, Berlin, Heidelberg, 1991. Springer Berlin Heidelberg.
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\end{thebibliography}

‎Notes/LaTeX-notes/bibTeX-example.blg‎

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This is BibTeX, Version 0.99d (TeX Live 2025)
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Capacity: max_strings=200000, hash_size=200000, hash_prime=170003
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The top-level auxiliary file: bibTeX-example.aux
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The style file: unsrt.bst
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Database file #1: sample.bib
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You've used 5 entries,
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and the built_in function-call counts, 1195 in all, are:
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= -- 125
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‎Notes/LaTeX-notes/bibTeX-example.pdf‎

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‎Notes/LaTeX-notes/bibTeX-example.tex‎

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\documentclass[a4paper,10pt]{article}
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\usepackage[utf8]{inputenc}
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\title{Bibliography management: BibTeX}
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\author{Share\LaTeX}
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\begin{document}
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\maketitle
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This document is an example of BibTeX using in bibliography management.\\
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Let's cite something! \cite{sturmfels_algorithms_2008}\\
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Let's cite another thing! \cite{derksen_polynomial_2000}\\
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Let's keep the citation train! \cite{gao_zero-sum_2006} \\
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And yet another one! \cite{sezer_sharpening_2002} \\
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This is so exciting! \cite{schmid_finite_1991}
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\medskip
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\bibliographystyle{unsrt}%Used BibTeX style is unsrt
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\bibliography{sample}
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\end{document}

‎Notes/LaTeX-notes/sample.bib‎

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@book{sturmfels_algorithms_2008,
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address = {Wien ;},
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edition = {2nd ed.},
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series = {Texts \& monographs in symbolic computation},
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title = {Algorithms in invariant theory},
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isbn = {978-3-211-77417-5},
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abstract = {J. Kung and G.-C. Rota, in their 1984 paper, write: “Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics”. The book of Sturmfels is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner bases method is the main tool by which the central problems in invariant theory become amenable to algorithmic solutions. Students will find the book an easy introduction to this “classical and new” area of mathematics. Researchers in mathematics, symbolic computation, and computer science will get access to a wealth of research ideas, hints for applications, outlines and details of algorithms, worked out examples, and research problems.},
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language = {eng},
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publisher = {Springer-Verlag},
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author = {Sturmfels, Bernd},
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year = {2008},
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doi = {10.1007/978-3-211-77417-5},
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keywords = {Algorithms, Electronic books, Geometry, Projective, Invariants},
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file = {PDF:/Users/gordienovak/Zotero/storage/EBYK5E57/Sturmfels - 2008 - Algorithms in invariant theory.pdf:application/pdf},
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}
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@article{derksen_polynomial_2000,
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title = {Polynomial bounds for rings of invariants},
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volume = {129},
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issn = {0002-9939, 1088-6826},
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url = {http://www.ams.org/proc/2001-129-04/S0002-9939-00-05698-7/},
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doi = {10.1090/S0002-9939-00-05698-7},
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abstract = {Hilbert proved that invariant rings are finitely generated for linearly reductive groups acting rationally on a finite dimensional vector space. Popov gave an explicit upper bound for the smallest integer d such that the invariants of degree ≤ d generate the invariant ring. This bound has factorial growth. In this paper we will give a bound which depends only polynomially on the input data.},
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language = {en},
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number = {4},
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urldate = {2021-07-15},
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journal = {Proceedings of the American Mathematical Society},
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author = {Derksen, Harm},
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month = oct,
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year = {2000},
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pages = {955--963},
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file = {Derksen - 2000 - Polynomial bounds for rings of invariants.pdf:/Users/gordienovak/Zotero/storage/7XR9VQMM/Derksen - 2000 - Polynomial bounds for rings of invariants.pdf:application/pdf},
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}
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@article{gao_zero-sum_2006,
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title = {Zero-sum problems in finite abelian groups: {A} survey},
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volume = {24},
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issn = {0723-0869},
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shorttitle = {Zero-sum problems in finite abelian groups},
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url = {https://www.sciencedirect.com/science/article/pii/S0723086906000351},
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doi = {10.1016/j.exmath.2006.07.002},
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abstract = {We give an overview of zero-sum theory in finite abelian groups, a subfield of additive group theory and combinatorial number theory. In doing so we concentrate on the algebraic part of the theory and on the development since the appearance of the survey article by Y. Caro in 1996.},
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language = {en},
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number = {4},
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urldate = {2021-04-22},
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journal = {Expositiones Mathematicae},
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author = {Gao, Weidong and Geroldinger, Alfred},
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month = nov,
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year = {2006},
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keywords = {Finite abelian groups, Zero-sum sequences},
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pages = {337--369},
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file = {ScienceDirect Full Text PDF:/Users/gordienovak/Zotero/storage/7SX42NR3/Gao and Geroldinger - 2006 - Zero-sum problems in finite abelian groups A surv.pdf:application/pdf;ScienceDirect Snapshot:/Users/gordienovak/Zotero/storage/4977JDVI/S0723086906000351.html:text/html},
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}
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@article{sezer_sharpening_2002,
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title = {Sharpening the generalized {Noether} bound in the invariant theory of finite groups},
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volume = {254},
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issn = {0021-8693},
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url = {https://www.sciencedirect.com/science/article/pii/S0021869302000182},
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doi = {10.1016/S0021-8693(02)00018-2},
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abstract = {We consider linear representations of a finite group G on a finite dimensional vector space over a field F in which {\textbar}G{\textbar} is invertible. By a theorem due to E. Noether in char 0, and to Fleischmann and Fogarty in general, the ring of invariants is generated by homogeneous elements of degree at most {\textbar}G{\textbar}. Schmid, Domokos, and Hegedu\&\#x030B;s sharpened Noether's bound when G is not cyclic and char F=0. We prove that the sharpened bound holds over general fields: If G is not cyclic and {\textbar}G{\textbar} is invertible in F, then the ring of invariants is generated by elements of degree at most 34·{\textbar}G{\textbar} if {\textbar}G{\textbar} is even, and at most 58·{\textbar}G{\textbar} if {\textbar}G{\textbar} is odd.},
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language = {en},
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number = {2},
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urldate = {2021-04-29},
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journal = {Journal of Algebra},
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author = {Sezer, Müfit},
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month = aug,
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year = {2002},
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pages = {252--263},
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file = {ScienceDirect Full Text PDF:/Users/gordienovak/Zotero/storage/75VRF52E/Sezer - 2002 - Sharpening the generalized Noether bound in the in.pdf:application/pdf;ScienceDirect Snapshot:/Users/gordienovak/Zotero/storage/AARDRD52/S0021869302000182.html:text/html},
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}
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@inproceedings{schmid_finite_1991,
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address = {Berlin, Heidelberg},
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title = {Finite groups and invariant theory},
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isbn = {978-3-540-47592-7},
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booktitle = {Topics in {Invariant} {Theory}},
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publisher = {Springer Berlin Heidelberg},
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author = {Schmid, Barbara J.},
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year = {1991},
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pages = {35--66},
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file = {PDF:/Users/gordienovak/Zotero/storage/HLUCJ6X2/Schmid - 1991 - Finite groups and invariant theory.pdf:application/pdf},
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}
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@article{wehlau_noether_nodate,
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title = {{THE} {NOETHER} {NUMBER} {IN} {INVARIANT} {THEORY}},
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abstract = {Let F be any field. Let G be any reductive linear algebraic group and consider a finite dimensional rational representation V of G. Then the F-algebra F[V ]G of polynomial invariants for G acting on V is finitely generated. The Noether Number β(G, V ) is the highest degree of an element of a minimal homogeneous generating set for F[V ]G. We survey what is known about Noether Numbers, in particular describing various upper and lower bounds for them. Both finite and infinite groups and both characteristic 0 and positive characteristic are considered.},
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language = {en},
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author = {Wehlau, David L},
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pages = {24},
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file = {Wehlau - THE NOETHER NUMBER IN INVARIANT THEORY.pdf:/Users/gordienovak/Zotero/storage/MT9BX9MM/Wehlau - THE NOETHER NUMBER IN INVARIANT THEORY.pdf:application/pdf},
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}
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@article{stanley_invariants_1979,
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title = {Invariants of finite groups and their applications to combinatorics},
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volume = {1},
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issn = {0273-0979},
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url = {http://www.ams.org/journal-getitem?pii=S0273-0979-1979-14597-X},
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doi = {10.1090/S0273-0979-1979-14597-X},
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language = {en},
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number = {3},
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urldate = {2019-08-06},
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journal = {Bulletin of the American Mathematical Society},
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author = {Stanley, Richard P.},
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month = may,
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year = {1979},
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pages = {475--512},
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file = {Stanley - 1979 - Invariants of finite groups and their applications.pdf:/Users/gordienovak/Zotero/storage/TGW8BZ75/Stanley - 1979 - Invariants of finite groups and their applications.pdf:application/pdf},
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}
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@misc{derksen_hilbert_2005,
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title = {Hilbert series of subspace arrangements},
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url = {http://arxiv.org/abs/math/0510584},
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abstract = {The vanishing ideal I of a subspace arrangement is an intersection of linear ideals. We give a formula for the Hilbert polynomial of I if the subspaces meet transversally. We also give a formula for the Hilbert series of a product J of the linear ideals without any assumptions on the subspace arrangement. It turns out that the Hilbert series of J is a combinatorial invariant of the subspace arrangement: it only depends on the intersection lattice and the dimension function. The graded Betti numbers of J are determined by the Hilbert series, so they are combinatorial invariants as well. The results can be applied to Generalized Principal Component Analysis (GPCA), a tool that is useful for computer vision and image processing.},
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urldate = {2022-10-27},
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publisher = {arXiv},
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author = {Derksen, Harm},
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month = oct,
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year = {2005},
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note = {arXiv:math/0510584},
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keywords = {05B35, 13D02, 13D40, Mathematics - Combinatorics, Mathematics - Commutative Algebra},
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annote = {Comment: 14 pages},
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file = {arXiv Fulltext PDF:/Users/gordienovak/Zotero/storage/KRIFPMVV/Derksen - 2005 - Hilbert series of subspace arrangements.pdf:application/pdf;arXiv.org Snapshot:/Users/gordienovak/Zotero/storage/HAAQKF7G/0510584.html:text/html},
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}
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@article{derksen_computation_1999,
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title = {Computation of {Invariants} for {Reductive} {Groups}},
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volume = {141},
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issn = {00018708},
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url = {https://linkinghub.elsevier.com/retrieve/pii/S000187089891787X},
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doi = {10.1006/aima.1998.1787},
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language = {en},
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number = {2},
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urldate = {2020-08-13},
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journal = {Advances in Mathematics},
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author = {Derksen, Harm},
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month = feb,
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year = {1999},
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pages = {366--384},
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file = {Derksen - 1999 - Computation of Invariants for Reductive Groups.pdf:/Users/gordienovak/Zotero/storage/7AP62HEP/Derksen - 1999 - Computation of Invariants for Reductive Groups.pdf:application/pdf},
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}
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@article{kraft_classical_nodate,
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title = {{CLASSICAL} {INVARIANT} {THEORY}},
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language = {en},
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author = {Kraft, Hanspeter and Procesi, Claudio},
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pages = {128},
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file = {Kraft and Procesi - CLASSICAL INVARIANT THEORY.pdf:/Users/gordienovak/Zotero/storage/728546BP/Kraft and Procesi - CLASSICAL INVARIANT THEORY.pdf:application/pdf},
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}
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@article{derksen_introduction_nodate,
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title = {An {Introduction} to {Invariant} {Theory}},
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language = {en},
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author = {Derksen, Harm},
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pages = {88},
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file = {Derksen - An Introduction to Invariant Theory.pdf:/Users/gordienovak/Zotero/storage/TAE3TV25/Derksen - An Introduction to Invariant Theory.pdf:application/pdf},
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}
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@misc{derksen_computational_2017,
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series = {1},
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title = {Computational {Invariant} {Theory}},
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isbn = {3-540-43476-3},
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urldate = {2025-06-09},
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journal = {Encyclopaedia of Mathematical Sciences},
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publisher = {Springer-Verlag Berlin Heidelberg New York},
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author = {Derksen, Harm and Kemper, Gregor},
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month = mar,
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year = {2017},
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pages = {278},
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file = {PDF:/Users/gordienovak/Zotero/storage/Y5FF3GFE/Derksen and Kemper - 2017 - Computational Invariant Theory.pdf:application/pdf},
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}
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@book{neusel_invariant_2007,
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address = {Providence, Rhode Island},
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title = {Invariant {Theory}},
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volume = {36},
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isbn = {978-0-8218-4132-7},
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abstract = {This book presents the characteristic zero invariant theory of finite groups acting linearly on polynomial algebras. The author assumes basic knowledge of groups and rings, and introduces more advanced methods from commutative algebra along the way. The theory is illustrated by numerous examples and applications to physics, engineering, numerical analysis, combinatorics, coding theory, and graph theory. A wide selection of exercises and suggestions for further reading makes the book appropriate for an advanced undergraduate or first-year graduate level course.},
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language = {English},
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urldate = {2025-06-09},
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publisher = {American Mathematical Society},
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author = {Neusel, Mary},
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month = apr,
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year = {2007},
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file = {PDF:/Users/gordienovak/Zotero/storage/NXCVNKSV/Neusel - 2007 - Invariant Theory.pdf:application/pdf},
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}
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@book{hong_mathematical_2014,
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address = {Berlin, Heidelberg},
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series = {Lecture {Notes} in {Computer} {Science}},
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title = {Mathematical {Software} – {ICMS} 2014: 4th {International} {Congress}, {Seoul}, {South} {Korea}, {August} 5-9, 2014. {Proceedings}},
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volume = {8592},
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copyright = {http://www.springer.com/tdm},
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isbn = {978-3-662-44198-5 978-3-662-44199-2},
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shorttitle = {Mathematical {Software} – {ICMS} 2014},
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url = {http://link.springer.com/10.1007/978-3-662-44199-2},
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language = {en},
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urldate = {2025-06-10},
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publisher = {Springer Berlin Heidelberg},
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editor = {Hong, Hoon and Yap, Chee},
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year = {2014},
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doi = {10.1007/978-3-662-44199-2},
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file = {PDF:/Users/gordienovak/Zotero/storage/FPN22K9Z/Hong and Yap - 2014 - Mathematical Software – ICMS 2014 4th International Congress, Seoul, South Korea, August 5-9, 2014..pdf:application/pdf},
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}
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@misc{noauthor_sciencedirect_nodate,
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title = {{ScienceDirect} {Full} {Text} {PDF} {\textbar} {Zero}-sum problems in finite abelian groups: {A} survey {\textbar} {My} {Library} {\textbar} {Zotero}},
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url = {https://www.zotero.org/fragandi/collections/I8CUVBTT/items/H9FVJQJ4/attachment/PCM8VZGB/reader},
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urldate = {2025-06-11},
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file = {ScienceDirect Full Text PDF | Zero-sum problems in finite abelian groups\: A survey | My Library | Zotero:/Users/gordienovak/Zotero/storage/XS4WZC99/reader.html:text/html},
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}
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@misc{noauthor_sciencedirect_nodate-1,
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title = {{ScienceDirect} {Full} {Text} {PDF} {\textbar} {Sharpening} the generalized {Noether} bound in the invariant theory of finite groups {\textbar} {My} {Library} {\textbar} {Zotero}},
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url = {https://www.zotero.org/fragandi/collections/I8CUVBTT/items/U34LHDU3/attachment/NHMQA9MB/reader},
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urldate = {2025-06-11},
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file = {ScienceDirect Full Text PDF | Sharpening the generalized Noether bound in the invariant theory of finite groups | My Library | Zotero:/Users/gordienovak/Zotero/storage/XC3M6T8L/reader.html:text/html},
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}
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@misc{noauthor_dolgachevpdf_nodate,
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title = {Dolgachev.pdf {\textbar} {My} {Library} {\textbar} {Zotero}},
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url = {https://www.zotero.org/fragandi/collections/HMUG9UF9/items/ER5JM6QM/reader},
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urldate = {2025-06-11},
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file = {Dolgachev.pdf | My Library | Zotero:/Users/gordienovak/Zotero/storage/Y9DLRV3V/reader.html:text/html},
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}
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@misc{noauthor_derksen_nodate,
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title = {Derksen - 2000 - {Polynomial} bounds for rings of invariants.pdf {\textbar} {Polynomial} bounds for rings of invariants {\textbar} {My} {Library} {\textbar} {Zotero}},
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url = {https://www.zotero.org/fragandi/collections/DTH4AM8K/items/DP5A9L5L/attachment/9UWV34CI/reader},
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urldate = {2025-06-11},
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file = {Derksen - 2000 - Polynomial bounds for rings of invariants.pdf | Polynomial bounds for rings of invariants | My Library | Zotero:/Users/gordienovak/Zotero/storage/W9T32SGN/reader.html:text/html},
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}
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@book{noauthor_ideals_nodate,
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title = {Ideals, {Varieties}, {Ect}.},
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file = {PDF:/Users/gordienovak/Zotero/storage/ETZLSWLI/Ideals, Varieties, Ect..pdf:application/pdf},
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}

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