On Fri, Sep 10, 2010 at 4:07 PM, Justin Paston-Cooper
<[email protected]> wrote:
> What newFromWeight is doing is reflecting the weight in the mirrors n
> where the nth components of the weight are positive, and then keeping
> those approved by addVP. Could it be done differently? ("n reflect
> weight" means reflecting in the nth mirror)
Ok, but this raises a new question: what is a mirror? (I suspect I need
to know both the conceptual and the arithmetic definition for mirror.)
I currently do not see any "mirror" names in the code, which should
mean that this is an easy or trivial concept?
> The weight is a vector in n-dimensional space. Each weight is in a
> vector space that is acted upon by a group generated by n reflections
> in mirrors as embodied by the Cartan Matrix. Each row in the Cartan
> Matrix corresponds to a certain reflection. It encodes the dot product
> between a certain perpendicular vector to the mirror corresponding to
> itself and those of all of the other reflections. A reflection acting
> on a weight produces a new weight which is on the opposite side of the
> mirror corresponding to the reflection.
Is "A" the Cartan Matrix?
Also, what do you mean by "encodes" here?
> When the orbit is calculated with the initial vector n $ 1, one gains
> a 1-to-1 correspondence to the elements in the group generated by the
> reflections. That's the reason why I'm generating these weights.
What does "orbit" mean?
Would simple examples make these explanations easier?
>> y - y *&(x&{) m
> Is there a reason here why you haven't used &: ? Am I right in
> thinking that they & and &: are interchangeable in this case?
When u and v are verbs, and v has infinite rank, then u&v and
u&:v do the same thing (Compose and Appose achieve the
same end in that case).
However, in the above code, x is not a verb but is a noun, so
&: would not work (Appose is not Bond).
Bond: http://www.jsoftware.com/help/dictionary/d630n.htm
Compose: http://www.jsoftware.com/help/dictionary/d630v.htm
Appose: http://www.jsoftware.com/help/dictionary/d632.htm
> There's a varying amount of new weights from each weight in the
> current level. Is there still a solution?
I imagine so, but I still do not really know what a weight is
(you tried to explain it to me but I did not understand your
explanation -- your explanation used words which I suspect
have technical meanings that I need to understand).
Before I can do a non-trivial job of refactoring the code, I have
to understand it (though if I put enough time into it I can do
achieve understanding through inspection).
--
Raul
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