Timeline for Tracing the word “form”
Current License: CC BY-SA 3.0
23 events
| when toggle format | what | by | license | comment | |
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| Feb 20, 2020 at 18:35 | vote | accept | Francois Ziegler | ||
| Nov 6, 2017 at 2:26 | history | edited | Francois Ziegler | CC BY-SA 3.0 |
Add Riemann (1867) and a better reference by Liouville (1852)
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| Oct 31, 2017 at 18:15 | comment | added | Will Sawin | Generalizing what KConrad says there is a natural relationship between homogeneous polynomials and symmetric multilinear forms. I have aways assumed that was historical, but it's possible it isn't. | |
| Oct 31, 2017 at 10:44 | comment | added | Jules Lamers | @R.vanDobbendeBruyn ...for which you could take a look at my question hsm.stackexchange.com/q/6603 ;) | |
| Oct 31, 2017 at 4:31 | history | edited | Francois Ziegler | CC BY-SA 3.0 |
Review articles added (Bachmann 1922, Weitzenböck 1922).
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| Oct 29, 2017 at 22:14 | comment | added | Pietro Majer | Formally, "formula" is the diminutive form of "forma". | |
| Oct 29, 2017 at 22:12 | comment | added | R. van Dobben de Bruyn | Not to be confused with the question "Forming the word 'trace'." | |
| Oct 29, 2017 at 14:08 | comment | added | Francois Ziegler | @NoamD.Elkies That’s for sure. Papers usually start with talk of things “of this form”, “of that form”, “in normal form”, and some authors using another word (Euler, Darboux) ostensibly do that to keep “form” available for such informal(!) talk. | |
| Oct 28, 2017 at 21:47 | history | edited | Francois Ziegler | CC BY-SA 3.0 |
Label by submission year, to make clear answers are quoting the same papers.
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| Oct 28, 2017 at 16:08 | comment | added | Noam D. Elkies | Possibly "quadratic form" is a reinterpretation of phrases such as "numbers of the form $x^2+y^2$". | |
| Oct 28, 2017 at 15:56 | comment | added | YCor | I'm happy with the new title as it makes it clear that it's about the use of the term "form" :) also I added the tag history on which clearly this question clearly belongs. I had to remove one, so chose quadratic-forms as it's covered by multilinear algebra. | |
| Oct 28, 2017 at 15:54 | history | edited | YCor |
edited tags
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| Oct 28, 2017 at 15:27 | answer | added | Carlo Beenakker | timeline score: 6 | |
| Oct 28, 2017 at 14:29 | history | edited | Francois Ziegler | CC BY-SA 3.0 |
edited title
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| Oct 28, 2017 at 14:18 | comment | added | Francois Ziegler | @YCor title restored as I’m more after tracing these 3 uses than tallying others. | |
| Oct 28, 2017 at 14:12 | history | edited | Francois Ziegler | CC BY-SA 3.0 |
edited title
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| Oct 28, 2017 at 14:12 | comment | added | Desiderius Severus | @YCor Thanks for the update, I only use it and think of it in the algebraic group setting so I wasn't aware of this broader (and indeed quite natural) general notion ;) | |
| Oct 28, 2017 at 14:04 | comment | added | YCor | @DesideriusSeverus it's not specific to algebraic groups, but to plenty of structures defined over a base ring or field (scheme, variety, algebra, vector space with a quadratic form, etc). Serre's book "Galois cohomology", Chap 3, starts with a paragraph "forms" in this general sense (albeit with no general definition). (quoth: Let $K/k$ be a field extension, and $X$ an "object" defined over $k$. We say that a object $Y$, defined over $k$, is a $K/k$-form of $X$ it $Y$ becomes isomorphic to $X$ after extending scalars to $K$) | |
| Oct 28, 2017 at 14:00 | history | edited | YCor | CC BY-SA 3.0 |
changed to make the title convey more information about the subject
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| Oct 28, 2017 at 13:42 | history | edited | Francois Ziegler | CC BY-SA 3.0 |
malfunctioning links fixed, better tag
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| Oct 28, 2017 at 6:40 | comment | added | Desiderius Severus | You can also think of forms of of an algebraic group (groups defined over the same field and isomorphic to it over some extension), or to (automorphic) form as particular elements in an automorphic representation. | |
| Oct 28, 2017 at 4:34 | comment | added | KConrad | On an $n$-dimensional vector space, a linear form $\varphi$ is the same thing as a homogeneous polynomial in $n$ variables (indeterminates) of degree 1 once you express $\varphi$ in terms of a basis. Thus your second and third mathematical objects are closely related. | |
| Oct 28, 2017 at 3:02 | history | asked | Francois Ziegler | CC BY-SA 3.0 |