improved glossary and bibliography

Author: thomasWeise

bibliography/bibliography.bib

@@ -84,6 +84,7 @@ @string { a_dubourg_vincent
 @string { a_duchesnay_edouard = "Edouard Duchesnay" }
 @string { a_editors_of_encyclopaedia_britannica = "The Editors of Encyclopaedia Britannica" }
 @string { a_eglen_stephen_j = "Stephen J.\ Eglen" }
+@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}" }
@@ -282,6 +283,8 @@ @string { a_wiebe_mark
 @string { a_wieser_eric = "Eric Wieser" }
 @string { a_wilson_joshua = "Joshua Wilson" }
 @string { a_wu_zhize = "Zhize Wu" }
+@string { a_wyman_bostwick_f = "Bostwick F.\ Wyman" }
+@string { a_wyman_myra_f = "Myra F.\ Wyman" }
 @string { a_xiong_peng = "Peng Xiong" }
 @string { a_yanev_martin = "Martin Yanev" }
 @string { a_yang_edward_z = "Edward Z.\ Yang" }
@@ -306,6 +309,7 @@ @string { l_germany_wadern
 @string { l_iceland_reykjavik = "{{Reykjav{\'i}k}, {Iceland}}" }
 @string { l_india_noida = "{{Noida}, {Uttar Pradesh}, {India}}" }
 @string { l_portugal_lisbon = "{{Lisbon}, {Portugal}}" }
+@string { l_russia_petropolis = "{{Petropolis} {(St.~Petersburg)}, {Russia}}" }
 @string { l_spain_leioa = "{{Leioa}, {Bizkaia}, {Spain}}" }
 @string { l_switzerland_cham = "{{Cham}, {Switzerland}}" }
 @string { l_switzerland_geneva = "{{Geneva}, {Switzerland}}" }
@@ -389,6 +393,7 @@ @string { p_springer_new_york
 @string { p_springer_science_and_business = "{Springer Science+Business Media}" }
 @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}" }
@@ -444,6 +449,7 @@ @string { pa_springer_new_york
 @string { pa_springer_science_and_business = l_usa_new_york }
 @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 }
@@ -483,6 +489,12 @@ @xdata{j_ca
  issn = {0001-0782},
 }
 
+@xdata{j_casp,
+ journal = {Commentarii Academiae Scientiarum Petropolitanae},
+ publisher = p_typis_academiae,
+ address = pa_typis_academiae
+}
+
 @xdata{j_csae,
  journal = {Computing in Science \& Engineering},
  issn = {1521-9615},
@@ -525,6 +537,13 @@ @xdata{j_mm
  issn = {0025-570X},
 }
 
+@xdata{j_mst,
+ journal = {Mathematical Systems Theory},
+ issn = {1432-4350},
+ publisher = p_springer_science_and_business,
+ address = pa_springer_science_and_business,
+}
+
 @xdata{j_n,
  journal = {Nature},
  issn = {0028-0836},
@@ -687,7 +706,7 @@ @book{APM1991AAAFI
 }
 
 @inbook{APM1991TOEAP,
- title = {Transcendence of~$e$ and~$\pi$},
+ title = {Transcendence of~\numberE\ and~\numberPi},
  crossref = {APM1991AAAFI},
  chapter = {9},
  pages = {115--161},
@@ -796,7 +815,7 @@ @techreport{BB2019AEAOTPPIP
  url = {https://arxiv.org/abs/1907.11073},
  urldate = {2024-08-17},
  doi = {10.48550/arXiv.1907.11073},
- note = {\mbox{arXiv:1907.11073v2} \mbox{[cs.SE]} \mbox{26~Jul~2019}}
+ addendum = {\mbox{arXiv:1907.11073v2} \mbox{[cs.SE]} \mbox{26~Jul~2019}}
 }
 
 @book{BHK2006CNFCMEARFCS,
@@ -929,6 +948,33 @@ @book{DBvR2024ITN
  isbn = {9781836208631},
 }
 
+@article{E1737DFCD,
+ author = a_euler_leonhard,
+ title = {De Fractionibus Continuis Dissertation},
+ date = {1737/1744},
+ xdata = {j_casp},
+ volume = {9},
+ pages = {98--137},
+ url = {https://scholarlycommons.pacific.edu/cgi/viewcontent.cgi?article=1070},
+ urldate = {2024-09-24},
+ addendum = {See \cite{E1985AEOCF} for a translation.}
+}
+
+@article{E1985AEOCF,
+ author = a_euler_leonhard,
+ translator = a_wyman_myra_f # and # a_wyman_bostwick_f,
+ title = {An Essay on Continued Fractions},
+ xdata = {j_mst},
+ volume = {18},
+ pages = {295--328},
+ number = {1},
+ date = {1985-12},
+ doi = {10.1007/BF01699475},
+ url = {https://www.researchgate.net/publication/301720080},
+ urldate = {2024-09-24},
+ addendum = {Translation of of \cite{E1737DFCD}.},
+}
+
 @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},
@@ -941,7 +987,7 @@ @incollection{EOEBSRGML2024LY
 @inbook{F2011TTOEAP,
  author = a_filaseta_michael,
  booktitle = {Math~785: Transcendental Number Theory},
- title = {The Transcendence of~$e$ and~$\pi$},
+ title = {The Transcendence of~\numberE\ and~\numberPi},
  chapter = {6},
  date = {2011-21},
  publisher = p_university_of_south_carolina,
@@ -1200,7 +1246,7 @@ @book{M2022RAEFPLACFWIR
 
 @article{N1939TTOP,
  author = a_niven_ivan,
- title = {The Transcendence of~$\pi$},
+ title = {The Transcendence of~\numberPi},
  xdata = {j_tamm},
  volume = {46},
  number = {8},
@@ -1515,7 +1561,7 @@ @book{PTVF2007NRTAOSC
  title = {Numerical Recipes: The Art of Scientific Computing},
  edition = {3},
  date = {2007/2011},
- note = {Version~3.04},
+ addendum = {Version~3.04},
  publisher = p_cambridge_uni_press_ass,
  address = pa_cambridge_uni_press_ass,
  isbn = {978-0-521-88068-8},
@@ -1538,7 +1584,7 @@ @book{R1994PNACMFF
  title = {Prime Numbers and Computer Methods for Factorization},
  xdata = {ser_pm},
  doi = {10.1007/978-1-4612-0251-6},
- imprint = pa_birkhauser_boston # {:~} # p_birkhauser_boston,
+ addendum = pa_birkhauser_boston # {:~} # p_birkhauser_boston,
  isbn = {978-0-8176-3743-9},
  date = {1994-10-01/2012-09-30},
  edition = {2}
@@ -1713,7 +1759,7 @@ @article{VGOHRCBPWBvdWBWMMNJKLCPFMVLPCHQHARPvMS2020SFAFSCIP
  doi = {10.1038/s41592-019-0686-2},
  url = {http://arxiv.org/abs/1907.10121},
  urldate = {2024-06-26},
- note = {See also \mbox{arXiv:1907.10121v1} \mbox{[cs.MS]} \mbox{23 Jul 2019}.}
+ addendum = {See also \mbox{arXiv:1907.10121v1} \mbox{[cs.MS]} \mbox{23 Jul 2019}.}
 }
 
 @book{VHN2023HOADWP,
@@ -1796,5 +1842,5 @@ @techreport{Z2024DESIEWS
  url = {https://arxiv.org/abs/2405.01562},
  urldate = {2024-06-27},
  doi = {10.48550/ARXIV.2405.01562},
- note = {\mbox{arXiv:2405.01562v1} \mbox{[cs.MS]} \mbox{3 Apr 2024}}
+ addendum = {\mbox{arXiv:2405.01562v1} \mbox{[cs.MS]} \mbox{3 Apr 2024}}
 }

notation/math.sty

@@ -9,25 +9,25 @@ It holds that~$\naturalNumbersZ\subset\integerNumbers$%
 }%
 \newSymbol{naturalNumbersO}{\ensuremath{\mathSpace{N}_1}}{N1}{%
 the set of the natural numbers \emph{excluding}~0, i.e., 1, 2, 3, 4, and so on. %
-It holds that~$\naturalNumbersO\subset\integerNumbers$}%
-%
+It holds that~$\naturalNumbersO\subset\integerNumbers$%
+}%
 \newSymbol{integerNumbers}{\ensuremath{\mathSpace{Z}}}{Z}{%
 the set of the integers numbers including positive and negative numbers and~0, i.e., {\dots}, -3, -2, -1, 0, 1, 2, 3, {\dots}, and so on. %
-It holds that~$\integerNumbers\subset\realNumbers$.}%
-%
+It holds that~$\integerNumbers\subset\realNumbers$%
+}%
 \newSymbol{realNumbers}{\mathSpace{R}}{R}{the set of the real numbers}%
-%
 \newSymbol{realNumbersP}{\ensuremath{\mathSpace{R}^+}}{R+}{%
 the set of the positive real numbers, i.e., $\mathSpace{R}^+=\{x\in\realNumbers:x>0\}$}%
 %
-\protected\gdef\intRange#1#2{\ensuremath{#1\pgls{intSetDots}#2}}%
+\protected\gdef\intRange#1#2{\ensuremath{#1\gls{intSetDots}#2}}%
 \newglossaryentry{intSetDots}{%
 type={symbols},
-name={..},%
+name={$i..j$},%
+text={..},%
 sort={..},%
 description={\sloppy%
-The set \mbox{$i..j$} with $i\leq j$ containts all integer numbers in the inclusive range from~$i$ to~$j$. %
-For example, \mbox{$5..9$}~is equivalent to~\mbox{$\{5, 6, 7, 8, 9\}$}.}%
+with $i,j\in\integerNumbers$ and $i\leq j$ is the set that contains all integer numbers in the inclusive range from~$i$ to~$j$. %
+For example, \mbox{$5..9$}~is equivalent to~\mbox{$\{5, 6, 7, 8, 9\}$}}%
 }%
 %
 %
@@ -37,3 +37,12 @@ For example, \mbox{$5..9$}~is equivalent to~\mbox{$\{5, 6, 7, 8, 9\}$}.}%
 \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}%
 %
+\newSymbol{numberPi}{\ensuremath{\pi}}{$\pi$}{%
+is the ratio of the circumference~$U$ of a circle and its diameter~$d$, i.e., $\pi=U/d$. %
+$\pi\in\realNumbers$ is an irrational and transcendental number~\cite{N1939TTOP,APM1991TOEAP,F2011TTOEAP}, which is approximately~$\pi\approx3.141\decSep592\decSep653\decSep589\decSep793\decSep238\decSep462\decSep643$. %
+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. %
+$e\in\realNumbers$ 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}}%

text/main/basics/collections/summary/summary.tex

@@ -3,7 +3,7 @@
 If you have managed to fight your way through the book until this point, then you can already do quite a few things.
 You can use the computer like a fancy calculator by evaluating numerical expressions, which you learned in
 \cref{sec:simplyDataTypesAndOperations}.
-By utilizing variables as discussed in \cref{sec:variables}, you can realize some simple algorithms like approximating~$\pi$.
+By utilizing variables as discussed in \cref{sec:variables}, you can realize some simple algorithms like approximating~\numberPi.
 In this section, you learned about compound datastructures that can store multiple values.
 You learned about mutable and immutable sequences of values, namely lists and tuples.
 You also learned that \python\ offers you the mathematical notion of sets as well as dictionaries, which are key-value mappings.

text/main/basics/simpleDataTypesAndOperations/float/float.tex

@@ -8,7 +8,7 @@
 \begin{sloppypar}%
 In an ideal world, we would have a similar feature also for real numbers.
 However, such a thing cannot be practically implemented.
-You will certainly remember the numbers $\pi\approx3.141\decSep592\decSep653\decSep590\dots$ and $e\approx2.718\decSep281\decSep828\decSep459\dots$ from highschool maths.
+You will certainly remember the numbers $\numberPi\approx3.141\decSep592\decSep653\decSep590\dots$ and $e\approx2.718\decSep281\decSep828\decSep459\dots$ from highschool maths.
 They are transcendental~\cite{N1939TTOP,APM1991TOEAP,F2011TTOEAP}, i.e., their fractional digits never end and nobody has yet detected an orderly pattern in them.
 Since these numbers are \inQuotes{infinitely long,} we would require infinitely much memory to store them \emph{if} we wanted to represent them \emph{exactly}.
 So we don't and neither does \python.
@@ -112,24 +112,24 @@
 We always need to keep this in mind.%
 \end{sloppypar}%
 %
-Let us recall our initial example of the transcendental irrational numbers~$\pi$ and~$e$.
+Let us recall our initial example of the transcendental irrational numbers~\numberPi\ and~\numberE.
 Certainly, these are very important constants that would be used in many computations.
 We can make them accessible in our code by importing them from the \pythonilIdx{math} module.\footnote{%
 We will learn about these mechanism in detail later on.}
 This can be done by typing \pythonil{from math import pi, e}\pythonIdx{import}\pythonIdx{from}\pythonIdx{math}.
 When we then type \pythonilIdx{pi} and \pythonilIdx{e}, we can get to see their value in floating point representations: \pythonil{3.141592653589793} and \pythonil{2.718281828459045}, respectively.
 Again, these are not the exact values, but they are as close as we can get in this format.
 
-Of course, $\pi$ and~$e$ alone are not that much useful.
+Of course, \numberPi\ and~\numberE\ alone are not that much useful.
 If you reach back into your highschool days again, you will remember many interesting functions that are related to them.
 Let us import a few of them, again from the \pythonilIdx{math} module, via \pythonil{from math import sin, cos, tan, log}\pythonIdx{sin}\pythonIdx{cos}\pythonIdx{tan}\pythonIdx{log}.
 I think you can guess what these functions do.
 
-From highschool, you may remember that~$\sin{\frac{\pi}{4}}=\frac{\sqrt{2}}{2}$ and thus~$\sin^2{\frac{\pi}{4}}=0.5$.
+From highschool, you may remember that~$\sin{\frac{\numberPi}{4}}=\frac{\sqrt{2}}{2}$ and thus~$\sin^2{\frac{\numberPi}{4}}=0.5$.
 Let us compute this in \python\ by doing \pythonil{sin(0.25 * pi) ** 2}\pythonIdx{sin}.
 Surprisingly, we get \pythonil{0.4999999999999999} instead of \pythonil{0.5}.
 The reason is again the limited precision of \pythonilIdx{float}, which cannot represent~$\frac{\sqrt{2}}{2}$ exactly.
-Similarly, $\cos{\frac{\pi}{3}}=\frac{1}{2}$ but \pythonil{cos(pi / 3)}\pythonIdx{cos} yields \pythonil{0.5000000000000001} and $\tan{\frac{\pi}{4}}$ expressed as \pythonil{tan(pi / 4)}\pythonIdx{tan} returns \pythonil{0.9999999999999999} instead of~$1$.
+Similarly, $\cos{\frac{\numberPi}{3}}=\frac{1}{2}$ but \pythonil{cos(pi / 3)}\pythonIdx{cos} yields \pythonil{0.5000000000000001} and $\tan{\frac{\numberPi}{4}}$ expressed as \pythonil{tan(pi / 4)}\pythonIdx{tan} returns \pythonil{0.9999999999999999} instead of~$1$.
 Then again, these values are incredibly close to the exact results.
 They are off by \emph{less than~$10^{-15}$} so for all practical concerns, they are close enough.
 Sometimes, we even get the accurate result, e.g., when computing $\ln(e^{10})$ by evaluating \pythonil{log(e ** 10)}\pythonIdx{log}, which results in~\pythonil{10.0}.
@@ -371,8 +371,8 @@
 As another example, let us again import the natural logarithm function \pythonilIdx{log} and the Euler's constant~\pythonilIdx{e} from the \pythonilIdx{math} module by doing \pythonil{from math import e, log}\pythonIdx{from}\pythonIdx{math}\pythonIdx{import}.
 We now can compute the natural logrithm from the largest possible \pythonilIdx{float} via \pythonil{log(1.7976931348623157e+308)}.
 We get \pythonil{709.782712893384}.
-Raising~$e$ to this power by doing \pythonil{e ** 709.782712893384} leads to the slightly smaller number~\pythonil{1.7976931348622053e+308} due to the limited precision of the \pythonilIdx{float} type.
-However, if we try to raise~$e$ to a slightly larger power, and, for example, try to do \pythonil{e ** 709.782712893385}, we again face an \pythonilIdx{OverflowError}.
+Raising~\numberE\ to this power by doing \pythonil{e ** 709.782712893384} leads to the slightly smaller number~\pythonil{1.7976931348622053e+308} due to the limited precision of the \pythonilIdx{float} type.
+However, if we try to raise~\numberE\ to a slightly larger power, and, for example, try to do \pythonil{e ** 709.782712893385}, we again face an \pythonilIdx{OverflowError}.
 
 We can also try to divide~1 by the largest \pythonilIdx{float} and do \pythonil{1 / 1.7976931348623157e+308}\pythonIdx{/}.
 The result is the very small number \pythonil{5.562684646268003e-309}.
@@ -443,7 +443,7 @@
 Very large integer numbers are, however, something of a corner case {\dots} they do not happen often.
 
 Real numbers in~\realNumbers\ are a whole different beast.
-They include irrational numbers like~$\sqrt{2}$ and transcendental numbers like~$\pi$.
+They include irrational numbers like~$\sqrt{2}$ and transcendental numbers like~\numberPi.
 These numbers are needed \emph{often} and they have infinitely many fractional digits.
 Thus, there is no way to exactly represent them in computer memory exactly.
 Another problem is that we may need both very large numbers like~$10^{300}$ and very small numbery like~$10^{-300}$.

text/main/basics/simpleDataTypesAndOperations/str/str.tex

@@ -222,7 +222,7 @@
 %
 \begin{sloppypar}%
 We can also access constants and variables from within the \pgls{fstring}.
-Let us again import the constant~$\pi$ from the \pythonilIdx{math} module by doing \pythonil{from math import pi}\pythonIdx{from}\pythonIdx{math}\pythonIdx{import}\pythonIdx{pi}.
+Let us again import the constant~\numberPi\ from the \pythonilIdx{math} module by doing \pythonil{from math import pi}\pythonIdx{from}\pythonIdx{math}\pythonIdx{import}\pythonIdx{pi}.
 We can print it as string by typing \pythonil{f"pi is approximately \{pi\}."} into the \python\ console.
 The result is the string \pythonil{"pi is approximately 3.141592653589793."}%
 \end{sloppypar}%