# [Maxima] Problems in integrate

Lin Xie experiencemaik at gmail.com
Wed Apr 14 19:49:15 CDT 2010

```Hi, Ray
Thanks for your kind reply. The expression might be positive since there
are some physical constraints. I'll check that later.

On Thu, Apr 15, 2010 at 1:56 AM, Raymond Toy <toy.raymond at gmail.com> wrote:

> On 4/14/10 11:34 AM, Lin Xie wrote:
> > Hi, Leo
> >    Thanks for the reply! Well, the integral is a problem in modelling
> > microdomain structures in crystal and to my knowledge I do not know
> > that the problem can be easily overcomed in such way.
>
> Why not?  Aren't you trying to integrate over R^n?
>
> The matrix A can be easily determined from your expression.  If E is the
> the quadratic, then the matrix A that Leo refers to is
>
> genmatrix(lambda([i,j], if i = j 1 else
> coeff(coeff(E,concat(x,j)),concat(x,i))),8,8)
>
> I have forgotten exactly what the result of the integration would be,
> but the determinant of A in this case is not too complicated:
>
> factor(ratsimp(determinant(A))) ->
>
> (t-r+1)^2*(t+r+1)^2*(t-2*s+r+1)*(t+2*s-r+1)*(3*t-2*s-r-1)*(3*t+2*s+r-1)
>
> (It's not clear to me if this expression positive or not.)
>
> Ray
>
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--
Lin Xie
Beijing National Center for Electron Microscopy
Department of Material Science and Engineering
Tsinghua University
Beijing, PR of China
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