On Thu, Sep 4, 2008 at 11:51 AM, John Randall
<[EMAIL PROTECTED]> wrote:
>>> From: Raul Miller <[EMAIL PROTECTED]>
>>> My question is: how do I find the rank 0 functions which
>>> correspond to general cases of that plot?
>
> The minimum definition you were using seems right to me. If y=f(x), and
> rotation is by 90 degrees, you want to define g(y)=min f^{-1}(y). For
> example, if f(x)=x^2, g(4)=min {_2,2}=_2, and g(y)=-%: y .
Ok, but I am having problems thinking about how I would approach
this problem for arbitrary rotations. I can constrain my polynomials
somewhat arbitrarily, if that makes finding function inverses simpler,
but I am having a problem thinking about how to find the set of
values which I need to work with, in the general case.
For example, consider:
p=: ($&0 1 0 _1 % [EMAIL PROTECTED]) 30
dot=: +/ .*
rot=: (1 _1,:1 1) * (2 1,:1 2)&[EMAIL PROTECTED]
g=: [EMAIL PROTECTED] dot (,: p&p.)@]
G=: (#"1~ (= >./\)@{.)@g
F=: j./@(0.375&G)@(0.1 * i:)
#60 -.&F 70
6
I want to define a similar F such that x -.& x2 is always
empty when x < x2. And when I say "similar F" I mean for
somewhat arbitrary polynomials (or whatever other function --
I am using polynomials here because they seem somewhat
tractable) and for somewhat arbitrary rotations, and for somewhat
arbitrary choices of the generating function (for example, if I
replace that 0.1 in 0.1 * i:). I can accept constraints on my problem
space as long as I am not reducing myself to trivial cases.
I am happy to go away and study whatever I need to study, but
right now I do not know what to search on, to find relevant
material.
Thanks,
--
Raul
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