first steps into defining functions

Author: thomasWeise

bibliography/bibliography.bib

@@ -33,6 +33,7 @@ @string { a_barham_paul
 @string { a_barret_daniel_j = "Daniel J. Barrett" }
 @string { a_baumgartner_gary = "Gary Baumgartner" }
 @string { a_beazley_david_m = "David M.\ Beazley" }
+@string { a_beguenane_rachid = "Rachid Beguenane" }
 @string { a_beigel_richard = "Richard Beigel" }
 @string { a_ben_david_shai = "Shai Ben{-}David" }
 @string { a_bentley_jon = "Jon Bentley" }
@@ -45,9 +46,11 @@ @string { a_bommarito_ethan
 @string { a_bommarito_michael = "Michael Bommarito" }
 @string { a_bose_cherokee = "Cherokee Boose" }
 @string { a_bott_ed = "Ed Bott" }
+@string { a_bottazzini_umberto = "Umberto Bottazzini" }
 @string { a_bradbury_james = "James Bradbury" }
 @string { a_brandl_georg = "Georg Brandl" }
 @string { a_brash_ron = "Ron Brash" }
+@string { a_brent_richard_p = "Richard P.\ Brent" }
 @string { a_brett_matthew = "Matthew Brett" }
 @string { a_bright_jonathan = "Jonathan Bright" }
 @string { a_brucher_matthieu = "Matthieu Brucher" }
@@ -56,6 +59,7 @@ @string { a_bruneau_pierrix
 @string { a_burovski_evgeni = "Evgeni Burovski" }
 @string { a_carey_cj = "CJ Carey" }
 @string { a_castro_oscar = "Oscar Castro" }
+@string { a_chabini_noureddine = "Noureddine Chabini" }
 @string { a_chanan_gregory = "Gregory Chanan" }
 @string { a_chen_boqi = "Boqi Chen" }
 @string { a_chen_jianmin = "Jianmin Chen" }
@@ -83,18 +87,22 @@ @string { a_devito_zachary
 @string { a_dimitrovic_slobodan = "Slobodan Dmitrovi{\'c}" }
 @string { a_dubourg_vincent = "Vincent Dubourg" }
 @string { a_duchesnay_edouard = "Edouard Duchesnay" }
+@string { a_dutka_jacques = "Jacques Dutka" }
 @string { a_editors_of_encyclopaedia_britannica = "The Editors of Encyclopaedia Britannica" }
 @string { a_eglen_stephen_j = "Stephen J.\ Eglen" }
+@string { a_euclid = "{{Euclid of Alexandria}~{(\ensuremath{E{\acute\upsilon}\kappa\lambda\varepsilon{\acute\iota}\delta\eta\varsigma})}}" }
 @string { a_euler_leonhard = "Leonhard Euler" }
 @string { a_fang_lu = "Lu Fang" }
 @string { a_feng_yu = "Yu Feng" }
 @string { a_fernandez_del_rio_jaime = "Jaime {Fern{\'a}ndez del R{\'i}o}" }
 @string { a_filaseta_michael = "Michael Filaseta" }
+@string { a_fitzpatrick_richard = "Richard Fitzpatrick" }
 @string { a_flannery_brian_p = "Brian P.\ Flannery" }
 @string { a_flight_robert_m = "Robert M.\ Flight" }
 @string { a_fox_emily_b = "Emily B.\ Fox" }
 @string { a_fowler_david = "David Fowler" }
 @string { a_fufezan_christian = "Christian Fufezan" }
+@string { a_fujita_toru = "Toru Fujita" }
 @string { a_garcia_alessandro = "Alessandro Garcia" }
 @string { a_garnett_roman = "Roman Garnett" }
 @string { a_gatto_laurent = "Laurent Gatto" }
@@ -118,6 +126,7 @@ @string { a_hance_jared
 @string { a_harris_charles_r = "Charles R.\ Harris" }
 @string { a_hausenblas_michael = "Michael Hausenblas" }
 @string { a_heap_danny = "Danny Heap" }
+@string { a_heiberg_johan_ludvig = "Johan Ludvig Heiberg" }
 @string { a_henriksen_ian = "Ian Henriksen" }
 @string { a_herbsleb_james_d = "James D.\ Herbsleb" }
 @string { a_hollasch_steve = "Steve Hollasch" }
@@ -128,6 +137,7 @@ @string { a_hunter_john_d
 @string { a_hunt_john = "John Hunt" }
 @string { a_irving_geoffrey = "Geoffrey Irving" }
 @string { a_isard_michael = "Michael Isard" }
+@string { a_ito_ysuaki = "Yasuaki Ito" }
 @string { a_jain_shantanu = "Shantanu Jain" }
 @string { a_joh_sangwoo = "Sangwoo Joh" }
 @string { a_johansson_robert = "Robert Johansson" }
@@ -168,6 +178,7 @@ @string { a_liu_yuxi
 @string { a_lotha_gloria = "Gloria Lotha" }
 @string { a_loy_marc = "Marc Loy" }
 @string { a_lun_anthony_w_c = "Anthony W.-C.\ Lun" }
+@string { a_luschny_peter = "Peter Luschny" }
 @string { a_mann_samuel = "Samuel Mann" }
 @string { a_marsh_charlie = "Charlie Marsh" }
 @string { a_massa_francisco = "Francisco Massa" }
@@ -184,6 +195,7 @@ @string { a_moore_sherry
 @string { a_morris_sidney_a = "Sidney A.\ Morris" }
 @string { a_murray_derek_gordon = "Derek Gordon Murray" }
 @string { a_naik_ganesh = "Ganesh Naik" }
+@string { a_nakano_koji = "Koji Nakano" }
 @string { a_negus_christopher = "Christopher Negus" }
 @string { a_nelson_andrew_r_j = "Andrew R.\ J.\ Nelson" }
 @string { a_newham_cameron = "Cameron Newham" }
@@ -307,15 +319,18 @@ @string { a_zinoviev_dimitry
 
 %% locations
 @string { l_australia_hobart = "{{Hobart}, {TAS}, {Australia}}" }
+@string { l_canada_halifax = "{{Halifax}, {NS}, {Canada}}" }
 @string { l_canada_oakville = "{{Oakville}, {ON}, {Canada}}" }
 @string { l_canada_toronto = "{{Toronto}, {ON}, {Canada}}" }
 @string { l_canada_vancouver = "{{Vancouver}, {BC}, {Canada}}" }
 @string { l_china_beijing = "{{China}, {Beijing}}" }
 @string { l_france_toulouse = "{{Toulouse}, {France}}" }
+@string { l_germany_heidelberg = "{{Heidelberg}, {Baden-W{\"u}rttemberg}, {Germany}}" }
 @string { l_germany_leipzig = "{{Leipzig}, {Sachsen}, {Germany}}" }
 @string { l_germany_wadern = "{{Wadern}, {Saarland}, {Germany}}" }
 @string { l_iceland_reykjavik = "{{Reykjav{\'i}k}, {Iceland}}" }
 @string { l_india_noida = "{{Noida}, {Uttar Pradesh}, {India}}" }
+@string { l_japan_higashi_hiroshima = "{{Higashi-Hiroshima}, {Japan}}" }
 @string { l_netherlands_amsterdam = "{{Amsterdam}, {The~Netherlands}}" }
 @string { l_portugal_lisbon = "{{Lisbon}, {Portugal}}" }
 @string { l_qatar_doha = "{{Doha}, {Qatar}}" }
@@ -330,6 +345,7 @@ @string { l_uk_chichester
 @string { l_uk_london = "{{London}, {England}, {UK}}" }
 @string { l_uk_oxford = "{{Oxford}, {Oxfordshire}, {England}, {UK}}" }
 @string { l_uk_st_andrews = "{{St~Andrews}, {Scotland}, {UK}}" }
+@string { l_usa_austin = "{{Austin}, {TX}, {USA}}" }
 @string { l_usa_beaverton = "{{Beaverton}, {OR}, {USA}}" }
 @string { l_usa_berkeley = "{{Berkeley}, {CA}, {USA}}" }
 @string { l_use_boston = "{{Boston}, {MA}, {USA}}" }
@@ -340,6 +356,7 @@ @string { l_usa_centennial
 @string { l_usa_champaign = "{{Champaign}, {IL}, {USA}}" }
 @string { l_usa_cincinnati = "{{Cincinnati}, {OH}, {USA}}" }
 @string { l_usa_columbia = "{{Columbia}, {SC}, {USA}}" }
+@string { l_usa_highland_park = "{{Highland Park}, {NJ}, {USA}}" }
 @string { l_usa_hoboken = "{{Hoboken}, {NJ}, {USA}}" }
 @string { l_usa_ithaca = "{{Ithaca}, {NY}, {USA}}" }
 @string { l_usa_lake_buena_vista = "{{Lake Buena Vista}, {FL}, {USA}}" }
@@ -382,6 +399,7 @@ @string { p_cornell_university_library
 @string { p_elsevier = "{Elsevier~B.V.}" }
 @string { p_geeksforgeeks = "{GeeksforGeeks -- Sanchhaya Education Private Limited}" }
 @string { p_github = "{{GitHub} Inc}" }
+@string { p_hiroshima_university_dep_ie = "{Department of Information Engineering, Hiroshima University}" }
 @string { p_iec = "{International Electrotechnical Commission~{(IEC)}}" }
 @string { p_ieee = "{Institute of Electrical and Electronics Engineers~{(IEEE)}}" }
 @string { p_infinite_skills = "Infinite Skills Inc" }
@@ -393,8 +411,10 @@ @string { p_manning_publications
 @string { p_mcgraw_hill = "McGraw-Hill" }
 @string { p_mit_press = "{{MIT} Press}" }
 @string { p_neurips = "{The Neural Information Processing Systems Foundation~{(NeurIPS)}}" }
+@string { p_oeis_foundation = "The {OEIS} Foundation Inc." }
 @string { p_oracle = "{Oracle Corporation}" }
 @string { p_oreilly = "{{O'Reilly} Media, Inc.}" }
+@string { p_oxford_university_cl = "{Oxford University Computing Laboratory}" }
 @string { p_oxford_university_press = "{Oxford University Press}" }
 @string { p_packt = "{Packt Publishing Ltd}" }
 @string { p_pearson_education = "Pearson Education, Inc." }
@@ -407,13 +427,15 @@ @string { p_springer
 @string { p_springer_nature_limited = "{Springer Nature Limited}" }
 @string { p_springer_new_york = "{Springer New York}" }
 @string { p_springer_science_and_business = "{Springer Science+Business Media}" }
+@string { p_springer_verlag = "{Springer-Verlag {GmbH} Germany}" }
 @string { p_taylor_and_francis = "{Taylor and Francis Ltd.}" }
 @string { p_teubner_b_g = "{B.\ G.\ Teubner}" }
 @string { p_typis_academiae = "{Typis Academiae}" }
 @string { p_unicode_consortium = "{The Unicode Consortium}" }
 @string { p_universidad_del_pais_vasco = "{{Universidad del Pa{\'i}s Vasco} / {Euskal Herriko Unibertsitatea}}" }
 @string { p_university_of_south_carolina = "{University of South Carolina}" }
 @string { p_university_of_st_andrews_somas = "{{University of St~Andrews}, {School of Mathematics and Statistics}}" }
+@string { p_university_of_texas_austin = "{The University of Texas at Austin}" }
 @string { p_university_of_toronto_cs = "{{Department of Computer Science}, {University of Toronto}}" }
 @string { p_university_of_washington = "{University of Washington}" }
 @string { p_usas = "{United States of America Standards Institute~{(USAS)}}" }
@@ -442,6 +464,7 @@ @string { pa_crc_press
 @string { pa_elsevier = l_netherlands_amsterdam }
 @string { pa_geeksforgeeks = l_india_noida}
 @string { pa_github = l_usa_san_francisco }
+@string { pa_hiroshima_university_dep_ie = l_japan_higashi_hiroshima }
 @string { pa_iso_iec = l_switzerland_geneva }
 @string { pa_ieee = l_usa_piscataway }
 @string { pa_ieee_ny = l_usa_new_york }
@@ -453,8 +476,10 @@ @string { pa_manning_publications
 @string { pa_mcgraw_hill = l_usa_new_york }
 @string { pa_mit_press = l_usa_cambridge }
 @string { pa_neurips = l_usa_san_diego }
+@string { pa_oeis_foundation = l_usa_highland_park }
 @string { pa_oracle = l_usa_redwood_shores }
 @string { pa_oreilly = l_usa_sebastopol }
+@string { pa_oxford_university_cl = l_uk_oxford }
 @string { pa_oxford_university_press = l_uk_oxford }
 @string { pa_packt = l_uk_birmingham }
 @string { pa_pearson_education = l_usa_hoboken }
@@ -467,13 +492,15 @@ @string { pa_springer_cham
 @string { pa_springer_nature_limited = l_uk_london }
 @string { pa_springer_new_york = l_usa_new_york }
 @string { pa_springer_science_and_business = l_usa_new_york }
+@string { pa_springer_verlag = l_germany_heidelberg }
 @string { pa_taylor_and_francis = l_uk_london }
 @string { pa_teubner_b_g = l_germany_leipzig }
 @string { pa_typis_academiae = l_russia_petropolis }
 @string { pa_unicode_consortium = l_usa_south_san_francisco }
 @string { pa_universidad_del_pais_vasco = l_spain_leioa }
 @string { pa_university_of_south_carolina = l_usa_columbia }
 @string { pa_university_of_st_andrews_somas = l_uk_st_andrews }
+@string { pa_university_of_texas_austin = l_usa_austin }
 @string { pa_university_of_toronto_cs = l_canada_toronto }
 @string { pa_university_of_washington = l_usa_seattle }
 @string { pa_usas = l_usa_new_york }
@@ -502,6 +529,13 @@ @xdata{j_acs
  issn = {0360-0300},
 }
 
+@xdata{j_afhoes,
+ journal = {Archive for History of Exact Sciences},
+ issn = {0003-9519},
+ publisher = p_springer_verlag,
+ address = pa_springer_verlag
+}
+
 @xdata{j_ca,
  journal = {Communications of the {ACM}~({CACM})},
  publisher = p_acm,
@@ -529,6 +563,14 @@ @xdata{j_hm
  address = pa_elsevier
 }
 
+@xdata{j_ijnc,
+ journal = {International Journal of Networking and Computing~{(IJNC)}},
+ issn = {2185-2839},
+ url = {http://www.ijnc.org},
+ publisher = p_hiroshima_university_dep_ie,
+ address = pa_hiroshima_university_dep_ie
+}
+
 @xdata{j_ijoc,
  journal = {{INFORMS} Journal on Computing},
  issn = {1091-9856},
@@ -783,6 +825,18 @@ @book{B1999PP
  isbn = {978-0201657883}
 }
 
+@techreport{B1999FAOTBEA,
+ author = a_brent_richard_p,
+ title = {Further Analysis of the Binary {Euclidean} Algorithm},
+ xdata = {rep_arxiv_corr},
+ number = {abs/1303.2772},
+ date = {1999-11/2013-03-12},
+ url = {https://arxiv.org/abs/1303.2772},
+ urldate = {2024-09-28},
+ doi = {10.48550/arXiv.1303.2772},
+ addendum = {\mbox{arXiv:1303.2772v1} \mbox{[cs.DS]} \mbox{12~Mar~2013}. Report number~\mbox{PRG~TR-7-99} of } # pa_oxford_university_cl # {:~} # p_oxford_university_cl # {, } # nov # {~1999, see \url{https://maths-people.anu.edu.au/~brent/pd/rpb183tr.pdf}},
+}
+
 @article{B2012DPWP,
  author = a_beazley_david_m,
  title = {Data Processing with \pandas},
@@ -894,6 +948,14 @@ @article{C2002LFLHADWTDM
  urldate = {2024-08-09},
 }
 
+@inproceedings{CB2022FBDOTFF,
+ author = a_chabini_noureddine # and # a_beguenane_rachid,
+ title = {{FPGA}-Based Designs of the Factorial Function},
+ crossref = {PROC2022CCECE},
+ pages = {16--20},
+ doi = {10.1109/CCECE49351.2022.9918302},
+}
+
 @article{CBST2024LOHPPTDDSAMLA,
  author = a_castro_oscar # and # a_bruneau_pierrix # and # a_sottet_jean_sebastien # and # a_torregrossa_dario,
  title = {Landscape of High-Performance \python\ to Develop Data Science and Machine Learning Applications},
@@ -955,6 +1017,18 @@ @book{CR2003LH
  urldate = {2024-08-10}
 }
 
+@article{D1991TEHOTFF,
+ author = a_dutka_jacques,
+ title = {The Early History of the Factorial Function},
+ xdata = {j_afhoes},
+ date = {1991-09},
+ volume = {43},
+ number = {3},
+ pages = {225--249},
+ doi = {10.1007/BF00389433},
+ addendum = {Communicated by~} # a_bottazzini_umberto
+}
+
 @book{D2024MCFABAFITTCPL,
  author = a_dimitrovic_slobodan,
  title = {Modern~\Pgls{C} for Absolute Beginners: A Friendly Introduction to the \Pgls{C}~Programming Language},
@@ -1012,6 +1086,26 @@ @article{E1985AEOCF
  addendum = {Translation of~\cite{E1737DFCD}.},
 }
 
+@book{EHF2008EEOGTGOJLH11FEEEELIEILHIATBG11EAPWMETBFR,
+ title = {Euclid's Elements of Geometry~(\ensuremath{\Sigma\tau{o}\iota\chi\varepsilon{\tilde{\iota}}\alpha}). The Greek Text of J.L.~Heiberg~(1883-1885) from Euclidis Elementa, Edidit et Latine Interpretatus est I.L.~Heiberg in Aedibus } #  p_teubner_b_g # {i, 1883-1885. Edited, and provided with a modern English translation, by } # a_fitzpatrick_richard,
+ author = a_euclid,
+ translator = a_heiberg_johan_ludvig,
+ editor = a_fitzpatrick_richard,
+ edition = {revised and corrected},
+ date = {2008},
+ isbn = {978-0-6151-7984-1},
+ publisher = p_university_of_texas_austin,
+ address = pa_university_of_texas_austin,
+ url = {https://farside.ph.utexas.edu/Books/Euclid/Elements.pdf},
+ urldate = {2024-09-30},
+}
+
+@inbook{EHF2008ENT,
+ crossref = {EHF2008EEOGTGOJLH11FEEEELIEILHIATBG11EAPWMETBFR},
+ title = {Elementary Number Theory},
+ chapter = {Book~7},
+}
+
 @incollection{EOEBSRGML2024LY,
  author = a_editors_of_encyclopaedia_britannica # and # a_setia_veenu # and # a_rodriguez_emily # and # a_gaur_aakanksha # and # a_matthias_meg # and # a_lotha_gloria,
  title = {Leap Year},
@@ -1323,6 +1417,16 @@ @inbook{H2024POICBS
  urldate = {2024-09-26},
 }
 
+@book{L2015ANKOFF,
+ author = a_luschny_peter,
+ title = {A New Kind of Factorial Function},
+ date = {2015-10-04},
+ publisher = p_oeis_foundation,
+ address = pa_oeis_foundation,
+ url = {https://oeis.org/A000142/a000142.pdf},
+ urldate = {2024-09-29},
+}
+
 @article{N1939TTOP,
  author = a_niven_ivan,
  title = {The Transcendence of~\numberPi},
@@ -1523,6 +1627,15 @@ @proceedings{PROC2022ASE
  isbn = {978-1-4503-9475-8},
 }
 
+@proceedings{PROC2022CCECE,
+ title = {{IEEE} Canadian Conference on Electrical and Computer Engineering~{(CCECE'22)}, } # sep # {~18--20, 2022, } # l_canada_halifax,
+ publisher = p_ieee,
+ address = pa_ieee,
+ date = {2022},
+ doi = {10.1109/CCECE49351.2022},
+ isbn = {978-1-6654-8432-9},
+}
+
 @proceedings{PROC2023ECOOP,
  title = {37th European Conference on Object-Oriented Programming~{(ECOOP'23)}, } # jul # {~17-21, 2023, } # l_usa_seattle,
  editor = a_ali_karim # and # a_salvaneschi_guido,
@@ -1828,6 +1941,18 @@ @book{T2024BGAGVCPMATFTND
  execute = {\sloppy}
 }
 
+@article{TKY2016BEOEAOTCEG,
+ author = a_fujita_toru # and # a_nakano_koji # and # a_ito_ysuaki,
+ title = {Bulk Execution of {Euclidean} Algorithms on the {CUDA}-Enabled~{GPU}},
+ xdata = {j_ijnc},
+ volume = {6},
+ number = {1},
+ pages = {42--63},
+ date = {2016-01},
+ url = {http://www.ijnc.org/index.php/ijnc/article/download/117/119},
+ urldate = {2024-09-28},
+}
+
 @techreport{TSSL1995CICSNSE,
  title = {Chinese Internal Code Specification, National Standard Extended~{(GBK)}},
  type = {Technical Supervision Standard Letter},

notation/math.sty

@@ -1,6 +1,8 @@
-%%%
+\RequirePackage{cleveref}%%%
 %%% Mathematical Notation
 %%%
+\protected\gdef\decSep{\hspace*{0.175em}}%
+%
 \protected\gdef\mathSpace#1{\ensuremath{\mathbb{#1}}}%
 %
 \newSymbol{naturalNumbersZ}{\ensuremath{\mathSpace{N}_0}}{N0}{%
@@ -31,8 +33,6 @@ For example, \mbox{$5..9$}~is equivalent to~\mbox{$\{5, 6, 7, 8, 9\}$}}%
 }%
 %
 %
-\protected\gdef\decSep{\hspace*{0.175em}}%
-%
 \newFunc{bigO}{\ensuremath{\mathcal{O}}}{O(g(x))}{g(x)}{%
 \mbox{If $f(x)={\mathcal{O}}(g(x))$,} then there exist positive numbers~$x_0\in\realNumbersP$ and~$c\in\realNumbersP$ such that~\mbox{$f(x)\leq c*g(x)\forall x\geq x_0$}~\cite{B1894DAZDVPB,L1909HDLVDVDP}. %
 In other words, ${\mathcal{O}}(g(x))$~describes an upper bound for function growth}%
@@ -43,6 +43,18 @@ $\pi\in\realNumbers$ is an irrational and transcendental number~\cite{N1939TTOP,
 In \python, it is provided by the \pythonilIdx{math} module as constant \pythonilIdx{pi} with value~\pythonilIdx{3.141592653589793}}%
 %
 \newSymbol{numberE}{\ensuremath{e}}{e}{%
-is Euler's number~\cite{E1737DFCD,E1985AEOCF}, the base of the natural logarithm. %
+is Euler's number~\cite{E1737DFCD}, the base of the natural logarithm. %
 $e\in\realNumbers$ is an irrational and transcendental number~\cite{APM1991TOEAP,F2011TTOEAP}, which is approximately~$e\approx2.718\decSep281\decSep828\decSep459\decSep045\decSep235\decSep360$. %
 In \python, it is provided by the \pythonilIdx{math} module as constant \pythonilIdx{e} with value~\pythonilIdx{2.718281828459045}}%
+%
+\protected\gdef\factorial#1{\ensuremath{#1\gls{factorialMark}}}%
+\newglossaryentry{factorialMark}{%
+type={symbols},
+name={$i!$},%
+text={!},%
+sort={!},%
+description={\sloppy%
+The factorial~$a!$ of a natural number~$a\in\naturalNumbersO$ is the product of all positive natural numbers less than or equal to~$a$, i.e., $a!=1*2*3*4*\dots*(a-1)*a$~\cite{D1991TEHOTFF,CB2022FBDOTFF,L2015ANKOFF}. %
+See also \cref{eq:factorial} and \cref{lst:functions:def_factorial}%
+}}%
+%

requirements.txt

@@ -6,7 +6,7 @@
 # You can find it at https://thomasweise.github.io/latexgit_py,
 # https://github.com/thomasWeise/latexgit_py, or at
 # https://pypi.org/project/latexgit.
-latexgit == 0.8.18
+latexgit == 0.8.22
 
 # minify_html is needed to minify html output.
 minify_html == 0.15.0