# what meanings about global_height of AffineSpace'point

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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.

( 2014-10-21 12:43:55 +0200 )edit

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

( 2014-10-21 12:48:58 +0200 )edit

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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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This post is a wiki. Anyone with karma >750 is welcome to improve it.

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

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( 2014-10-21 13:12:27 +0200 )edit
1

OK! I know it!

( 2014-10-21 14:00:46 +0200 )edit

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