Re: [Axiom-math] Engineering Application

[Raymond E. Rogers]

Thanks, I hadn't seen that page before.  It looks great.  I will print
out some the materials tomorrow, and practice with axiom when I get it
running.

The problem arises from autozeroing and good design; an error is set
equal to zero during autocalibration, and if the errors are zero the
first derivatives are designed out (more or less).  Thus the underlying
equations are made second order (and complicated) by design.

The concrete form of the problem is:
Err(x,a_i,b_k...)=P(x,a_i,b_k...)/Q(x,a_i,b_k...)  P&Q polynomials
Q has no zeros in the region of interest; and any poles can probably be
moved to infinity.
The first derivatives of Err(x,0,b_k..) with respect to a_i are all zero
(more or less),
and Err(0,a_i,b_k...)=0
These items are accomplished by autozero/autocalibrate.
The a_i are parameters, the b_k are errors in the parameters (expected
value of 0).
My simple solution is to use a constraint/boundary
c_1*a_1^2+c_2*a_2^2+....=p^2
and intersect the Err and the constraint and look for worst case error.

The p is introduced because to start out with a narrow space around the
center and grow to more reasonable value after the very local problem is
understood.

One way is to find grad(Err)=j*grad(constraint) term by term.
But it seems that this might be avoided if the constraint and Err
intersections are examined for second order roots (?).

Mentally it seems much simpler than it appears in writing.  I find the
more general problem interesting, but that seems to be a personal taste.

In any case, any guidance would be appreciated.

Ray



Bill Page wrote:
> On January 22, 2006 8:00 PM Raymond E. Rogers wrote:
>> Assuming I get axiom running; would anybody be willing to discuss
>> an engineering application where I think Algebraic Geometry provides
>> a mathematically correct answer? Even though I have just started
>> learning AG, I think I can do all of the hard work myself.
>>
> 
> I would be very happy to discuss engineering applications of
> algebraic geometry.
> 
> Perhaps one place to start with Axiom and algebraic geometry might be
> the following tutorial by Donu Arapura (http://www.math.purdue.edu/~dvb):
> 
> http://www.math.purdue.edu/~dvb/algeom.html
> 
> Introduction to Algebraic Geometry
> 
> Arapura includes some computer examples using Maple. We could see how
> we might do the same examples using Axiom.
> 
> Regards,
> Bill Page.
> 
> 
> 
>