Height of affine point (patch #14218)

[Soli Vishkautsan]

What is the definition of logarithmic height of (0,...,0)?

Should it be -\infty?

In any case maybe we should add a check for the 0 point? 

Currently we get an error trying to log(0).

[wishcow]

In fact I think that h(0)=0, since H(0)=H(0/1)=max{0,1}=1.

By the same reasoning h(0,...,0) should be 0 as well.

Let me know if I am mistaken.

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[Ben]

Actually, I've been thinking about the height function. I recently
discovered the Sage function .global_height(), which works over number
fields. So I think the .height() for affine and projective points should
use that (hence I need to update 14218 for this). However, it only work
for fields, so I have to be careful how I use it.

The h(0,0) error you are seeing actually only occurs for ZZ. If the
function remains as it is, you are right, there should be a check there
for max (H,1) before the log is taken on line 1358 so that it will
return 0 (as it does for QQ)

btw, such comments on reviewing/correcting functionality are best added
to the trac ticket itself. You should register for a trac account, put
in these comments about the issue with the .height() function, and set
it to 'needs_work'. If you are unsure, you can always ask me directly
first. General questions about sage-dynamics can be sent to this list.

It would be of great help if you were to formally review even just parts
of the patch 14218 (as you seem to be starting). Reviews can be done in
parts and others can finish any functionally you are uncomfortable
reviewing officially.

Ben

On 9/2/2013 2:09 PM, wishcow wrote:
> In fact I think that h(0)=0, since H(0)=H(0/1)=max{0,1}=1.
> By the same reasoning h(0,...,0) should be 0 as well.
> Let me know if I am mistaken.
>
>
> On Mon, Sep 2, 2013 at 5:06 PM, Soli Vishkautsan <wis...@gmail.com
> <mailto:wis...@gmail.com>> wrote:
>
> What is the definition of logarithmic height of (0,...,0)?
> Should it be -\infty?
> In any case maybe we should add a check for the 0 point?
> Currently we get an error trying to log(0).
>
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