Editing Canonical form (section)

==History==
According to [[Oxford English Dictionary|OED]] and [[LSJ]], the term ''[[canonical]]'' stems from the [[Ancient Greek]] word ''kanonikós'' (''[[wikt:κανονικός|κανονικός]]'', "regular, according to rule") from ''kanṓn'' (''[[wikt:κανών#Ancient_Greek|κᾰνών]]'', "rod, rule"). The sense of [[wikt:norm|norm]], [[wikt:standard|standard]], or [[archetypal|archetype]] has been used in many disciplines. Mathematical usage is attested in a 1738 letter from [[James Logan (statesman)|Logan]].<ref>{{cite book |title=Letter from James Logan to William Jones, Correspondence of Scientific Men of the Seventeenth Century |url=https://books.google.com/books?id=65lEAAAAcAAJ&pg=PA331 |publisher=University Press |language=en |date=1841| isbn=978-1-02-008678-6 }}</ref> The German term ''kanonische Form'' is attested in a 1846 paper by [[Gotthold Eisenstein|Eisenstein]],<ref>{{cite web |title=Journal für die reine und angewandte Mathematik 1846 |url=https://gdz.sub.uni-goettingen.de/id/PPN243919689_0032?tify={%22pages%22:[63],%22panX%22:0.513,%22panY%22:0.37,%22view%22:%22info%22,%22zoom%22:0.982} |publisher=de Gruyter}}</ref> later the same year [[Friedrich Julius Richelot|Richelot]] uses the term ''Normalform'' in a paper,<ref>{{cite book |title=Journal für die reine und angewandte Mathematik 1846 |url=https://gdz.sub.uni-goettingen.de/id/PPN243919689_0032?tify=%7B%22pages%22:%5B227%5D%7D |publisher=de Gruyter}}</ref> and in 1851 [[James Joseph Sylvester|Sylvester]] writes:<ref>{{cite web |title=The Cambridge and Dublin mathematical journal 1851 |url=https://gdz.sub.uni-goettingen.de/id/PPN600493962_0006?tify={%22pages%22:[197],%22panX%22:0.562,%22panY%22:0.626,%22view%22:%22toc%22,%22zoom%22:0.878} |publisher=Macmillan}}</ref>

{{quote|"I now proceed to [...] the mode of reducing Algebraical Functions to their simplest and most symmetrical, or as my admirable friend [[Charles Hermite|M. Hermite]] well proposes to call them, their ''Canonical forms''."}}

In the same period, usage is attested by [[Otto Hesse|Hesse]] ("Normalform"),<ref>{{cite web |last1=Hesse |first1=Otto |title=Vorlesungen aus der analytischen Geometrie der geraden Linie, des Punktes und des Kreises in der Ebene |url=https://archive.org/details/bub_gb_at6qA3g2YDwC/page/n25 |publisher=Teubner |language=German |date=1865}}</ref> [[Charles Hermite|Hermite]] ("forme canonique"),<ref>{{cite web |title=The Cambridge and Dublin mathematical journal 1854 |url=https://books.google.com/books?id=p59EAAAAcAAJ&dq=%22forme+canonique%22&pg=PA181 |language=en |date=1854}}</ref> [[Carl Wilhelm Borchardt|Borchardt]] ("forme canonique"),<ref>{{cite web |title=Journal für die reine und angewandte Mathematik, 1854 |url=https://gdz.sub.uni-goettingen.de/id/PPN243919689_0048?tify={%22pages%22:[80],%22panX%22:0.54,%22panY%22:0.407,%22view%22:%22info%22,%22zoom%22:0.818} |publisher=de Gruyter}}</ref> and [[Arthur Cayley|Cayley]] ("canonical form").<ref>{{cite book |last1=Cayley |first1=Arthur |title=The Collected Mathematical Papers |url=https://books.google.com/books?id=TT1eAAAAcAAJ&dq=inauthor%3Acayley+%22canonical+form%22&pg=PA558 |publisher=University |language=en |date=1889|isbn=978-1-4181-8586-2 }}</ref>

In 1865, the [[Dictionary of Science, Literature and Art]] defines canonical form as:

{{quote|"In Mathematics, denotes a form, usually the simplest or most symmetrical, to which, without loss of generality, all functions of the same class can be reduced."}}