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what meanings about global_height of AffineSpace'point

asked 2014-10-21 05:26:18 -0500

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P.<x,y>=AffineSpace(QQ,2) Q=P(41,1/12) Q.global_height()

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What is your question ?! If you want an answer, you should be more precise.

vdelecroix gravatar imagevdelecroix ( 2014-10-21 05:43:55 -0500 )edit

I only know ellipitic curve'point has a height,what meanings AffineSpace'point height?

cjsh gravatar imagecjsh ( 2014-10-21 05:48:58 -0500 )edit

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answered 2014-10-21 05:53:45 -0500

Hello,

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.

Vincent

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answered 2014-10-21 06:04:52 -0500

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thank you very much! it is the same with ellipitic curve!

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Please, do *not* post comments as an answer. There is the possibility to add comments in the question and in each answer.

vdelecroix gravatar imagevdelecroix ( 2014-10-21 06:12:27 -0500 )edit
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OK! I know it!

cjsh gravatar imagecjsh ( 2014-10-21 07:00:46 -0500 )edit

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Asked: 2014-10-21 05:26:18 -0500

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Last updated: Oct 21 '14