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Jiahao Chen Fill out Cauchy references
over 8 years ago
Commit id: b6ee0bd66431f6fb61d0f5489a2cecba130ad4ad
deletions | additions
diff --git a/bibliography/biblio.bib b/bibliography/biblio.bib
index dc3a9c7..95b6dc6 100644
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+++ b/bibliography/biblio.bib
...
url = {https://books.google.com/books?id=cHGrfrQVq1oC}
}
@article{Cauchy1847,
author = {Augustin Cauchy},
title = {M\'emoire sur les lieux analytiques},
year = 1847,
pages = {885--887},
journal = {Comptes rendus hebdomadaires des séances de l'Académie des sciences},
volume = 24,
}
@article{Hamilton1847,
author = {William Rowan Hamilton},
title = {On Symbolical Geometry},
...
@article{Cauchy1853,
author = {Augustin Cauchy},
title = {Sur les clefs alg\'ebriques},
journal = {Comptes rendus hebdomadaires des séances de l'Académie des sciences},
pages = {70--76, 129--136},
url = {http://gallica.bnf.fr/ark:/12148/bpt6k90192k/f18.item.zoom},
year = 1853
}
@article{Cayley1855,
diff --git a/section_history.tex b/section_history.tex
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\S. 12 introduces the term ``scalar product'' for the case of parallel vectors (which differs from modern usage by a negative sign).
He does not appear to have introduced the general case of non-parallel vectors.
\paragraph{Cauchy
(1847)~\cite{Cauchy1847} - analytical mechanics}
set of $n$ variables is an ``analytic product'' (1847)~\cite{Cauchy1847}}
Credited \todo{by whom?} as the earliest description of $n$-dimensional space.
\begin{quote}
Concevons maintenant que le nombre des variables $x, y, z, \dots$
devienne sup\'erieur \`a trois. Alors chaque syst\`eme des valeurs de
$x, y, z, \dots$ d\'eterminera ce que nous appellerons un \text{point analytique}, dont
ces variables seront les \textit{coordonn\'ees} et, \`a ce point, r\'epondra une
certaine valeur de chaque fonction de $x, y, z \dots$
Nous appellerons encore \textit{droite analytique} un syst\`eme de \textit{points
analytiques} dont les diverses coodonn\'ees e'exprimeront \`a l'aide de
fontions lin\'eares donn\'ees de l'une d'entre elles.
\end{quote}
\paragraph{Sylvester (1850)~\cite{Sylvester1850}}
diff --git a/section_indexing.tex b/section_indexing.tex
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\ref{rule:col1} is a special case of the indexing rule where the rank of the
result is the sum of the ranks of the indexes. This indexing rule is used by
some languages such as APL. The history of this rule is discussed in
Sec.~\ref{sec:related}. related work.
It is tempting to generalize \ref{rule:v'1} to arrays of general rank, by
considering $A^\prime$ as the array constructed by reversing all the indexes of