4 ms·

Not really what people/mathematicians would generally understand as "algebraic number theory". More like computational number theory or computational algebra.

by mbid 9y ago

Labo333 9y ago
Indeed :) But what did you expect when you clicked on a github link?
williamstein 9y ago
I think it's OK -- the things he's computing do fall within what mathematicians call "algebraic number theory". (I wrote a book on Algebraic Number Theory: https://wstein.org/books/ant/ https://wstein.org/books/ant/)
- Labo333 9y ago
  Wow the adelic point of view is totally new for me!!! I add your book to my bookmarks and will definitely read it. It's really nice to make a chapter on elliptic curves, it's one of my domains of research (ECC). I have codes for CRT and Pell's equation as well, maybe I will upload them.
  - ableal 9y ago
    "Origin of the name - In local class field theory, the group of units of the local field plays a central role. In global class field theory, the idele class group takes this role (see also the definition of the idele class group). The term "idele" is a variation of the term ideal. Both terms have a relation, see the theorem about the relation between the ideal class group and the idele class group. The term "idele" (French: idèle) is an invention of the French mathematician Claude Chevalley (1909–1984) and stands for "ideal element" (abbreviated: id.el.). The term "adele" (adèle) stands for additive idele." https://en.wikipedia.org/wiki/Adele_ring https://en.wikipedia.org/wiki/Adele_ring (Took me a few minutes just to get that - reminder, bring diving gear when venturing into math waters ;-)
- Labo333 9y ago
  There is also this wonderful collection of Sage examples: http://abstract.ups.edu/download/aata-20160809-sage-7.3.pdf http://abstract.ups.edu/download/aata-20160809-sage-7.3.pdf
- jesuslop 9y ago
  Meaty stuff, some problem here displaying inline images of the html, e. g. https://wstein.org/books/ant/ant/img1885.png https://wstein.org/books/ant/ant/img1885.png gives not found.

Not really what people/mathematicians would generally understand as "algebraic number theory". More like computational number theory or computational algebra.

by mbid 9y ago

Not really what people/mathematicians would generally understand as "algebraic number theory". More like computational number theory or computational algebra.

Labo333 9y ago

Indeed :) But what did you expect when you clicked on a github link?

williamstein 9y ago

I think it's OK -- the things he's computing do fall within what mathematicians call "algebraic number theory". (I wrote a book on Algebraic Number Theory: https://wstein.org/books/ant/ https://wstein.org/books/ant/)

Labo333 9y ago
Wow the adelic point of view is totally new for me!!! I add your book to my bookmarks and will definitely read it. It's really nice to make a chapter on elliptic curves, it's one of my domains of research (ECC). I have codes for CRT and Pell's equation as well, maybe I will upload them.
- ableal 9y ago
  "Origin of the name - In local class field theory, the group of units of the local field plays a central role. In global class field theory, the idele class group takes this role (see also the definition of the idele class group). The term "idele" is a variation of the term ideal. Both terms have a relation, see the theorem about the relation between the ideal class group and the idele class group. The term "idele" (French: idèle) is an invention of the French mathematician Claude Chevalley (1909–1984) and stands for "ideal element" (abbreviated: id.el.). The term "adele" (adèle) stands for additive idele." https://en.wikipedia.org/wiki/Adele_ring https://en.wikipedia.org/wiki/Adele_ring (Took me a few minutes just to get that - reminder, bring diving gear when venturing into math waters ;-)
Labo333 9y ago
There is also this wonderful collection of Sage examples: http://abstract.ups.edu/download/aata-20160809-sage-7.3.pdf http://abstract.ups.edu/download/aata-20160809-sage-7.3.pdf
jesuslop 9y ago
Meaty stuff, some problem here displaying inline images of the html, e. g. https://wstein.org/books/ant/ant/img1885.png https://wstein.org/books/ant/ant/img1885.png gives not found.