# what meanings about global_height of AffineSpace'point

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

what meanings about global_height of AffineSpace'point

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asked 2014-10-21 12:26:18 +0200 **

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

1

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

-1

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answered 2014-10-21 13:04:52 +0200 **

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

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Asked: ** 2014-10-21 12:26:18 +0200 **

Seen: **141 times**

Last updated: **Oct 21 '14**

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

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