Re: Domain, Range

Hi Vikram,
 
> First off, would I be correct in assuming that the domain is essentially
> your independent variable while the range is your dependent?
 
Correct.
 
> And supposing that I use my flightPath example s an illustration.  The
> RealTupleType "position" is the conglomeration of the RealTypes lat.,
lon.,
> and alt.  I'm not using time as a variable, so would it make sense to
have
> position serve as my domain?
 
Yes, you could.  In that case the domain would have three dimensions:
lat, lon and alt, but the finite Set of samples would all lie along
a 1 dimensonal curve.  So the doamin Set would have domain dimension
3 but manifold dimension 1.
 
You could either make your flight path be just this Set object, or you
could make the flight path be a Field with this domain Set and some
dependent variables along the path in the range, such as temperature,
pressure, or even time.
 
> Somehow, I feel like I'm a little off-base with that assumption.  It
> doesn't seem to jive with the fact that when I set these values into my
> FlatField object, I have to use the method setSamples().  And since you
> just told me that 'samples' is analagous with 'range', it seems like the
> RealTupleType position should still be in the range.  But if that's the
> case, then I'm left wondering what the domain should be.
 
Yeah, FlatField.setSamples() is one of those poor method names I
mentioned in my last email.  But probably the real source of
confusion of thinking of a 1-D path as a function of the form:
 
  ((lat, lon, alt) -> ...)
 
The key thing is the difference between the domain dimension 3
and the manifold dimension 1.
 
Cheers,
Bill
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Bill Hibbard, SSEC, 1225 W. Dayton St., Madison, WI  53706
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