ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 21 Oct 2014 14:00:46 +0200what meanings about global_height of AffineSpace'pointhttps://ask.sagemath.org/question/24544/what-meanings-about-global_height-of-affinespacepoint/ P.<x,y>=AffineSpace(QQ,2)
Q=P(41,1/12)
Q.global_height()Tue, 21 Oct 2014 12:26:18 +0200https://ask.sagemath.org/question/24544/what-meanings-about-global_height-of-affinespacepoint/Comment by cjsh for <p>P.<x,y>=AffineSpace(QQ,2)
Q=P(41,1/12)
Q.global_height()</p>
https://ask.sagemath.org/question/24544/what-meanings-about-global_height-of-affinespacepoint/?comment=24550#post-id-24550I only know ellipitic curve'point has a height,what meanings AffineSpace'point height?Tue, 21 Oct 2014 12:48:58 +0200https://ask.sagemath.org/question/24544/what-meanings-about-global_height-of-affinespacepoint/?comment=24550#post-id-24550Comment by vdelecroix for <p>P.<x,y>=AffineSpace(QQ,2)
Q=P(41,1/12)
Q.global_height()</p>
https://ask.sagemath.org/question/24544/what-meanings-about-global_height-of-affinespacepoint/?comment=24547#post-id-24547What is your question ?! If you want an answer, you should be more precise.Tue, 21 Oct 2014 12:43:55 +0200https://ask.sagemath.org/question/24544/what-meanings-about-global_height-of-affinespacepoint/?comment=24547#post-id-24547Answer by cjsh for <p>P.<x,y>=AffineSpace(QQ,2)
Q=P(41,1/12)
Q.global_height()</p>
https://ask.sagemath.org/question/24544/what-meanings-about-global_height-of-affinespacepoint/?answer=24553#post-id-24553thank you very much!
it is the same with ellipitic curve!Tue, 21 Oct 2014 13:04:52 +0200https://ask.sagemath.org/question/24544/what-meanings-about-global_height-of-affinespacepoint/?answer=24553#post-id-24553Comment by cjsh for <p>thank you very much!
it is the same with ellipitic curve!</p>
https://ask.sagemath.org/question/24544/what-meanings-about-global_height-of-affinespacepoint/?comment=24556#post-id-24556OK! I know it!Tue, 21 Oct 2014 14:00:46 +0200https://ask.sagemath.org/question/24544/what-meanings-about-global_height-of-affinespacepoint/?comment=24556#post-id-24556Comment by vdelecroix for <p>thank you very much!
it is the same with ellipitic curve!</p>
https://ask.sagemath.org/question/24544/what-meanings-about-global_height-of-affinespacepoint/?comment=24554#post-id-24554Please, do *not* post comments as an answer. There is the possibility to add comments in the question and in each answer.Tue, 21 Oct 2014 13:12:27 +0200https://ask.sagemath.org/question/24544/what-meanings-about-global_height-of-affinespacepoint/?comment=24554#post-id-24554Answer by vdelecroix for <p>P.<x,y>=AffineSpace(QQ,2)
Q=P(41,1/12)
Q.global_height()</p>
https://ask.sagemath.org/question/24544/what-meanings-about-global_height-of-affinespacepoint/?answer=24551#post-id-24551Hello,
If you want a mathematical answer, be clear that it is what you want. There is not even a sentence in your post!!
Given a rational p/q you can define its height to be max(log(|p|), log(|q|)). And given a vector, you can define its height as the maximum of the heights of its entries...
sage: A = AffineSpace(2,QQ)
sage: A((1/3,2/5))
(1/3, 2/5)
sage: A((1/3,2/5)).global_height()
1.60943791243410
sage: log(5.)
1.60943791243410
The definition extends to number fields.
VincentTue, 21 Oct 2014 12:53:45 +0200https://ask.sagemath.org/question/24544/what-meanings-about-global_height-of-affinespacepoint/?answer=24551#post-id-24551