Simplification of exponential and trigonometric expression

First of all, your functions don't seem to be equal:

q(0,0,0,0,0,0) => 1/sqrt(%pi)
p(0,0,0,0,0,0) => sqrt(2)/sqrt(%pi)

Let's put them in similar forms to see the differences:

qq: q(x,a,phi,r,theta,psi)$
pp: p(x,a,phi,r,theta,psi)$

qq1: scanmap(factor,trigreduce(qq));
pp1: scanmap(factor,trigreduce(pp));

You can also look at radcan(qq1) and radcan(pp1).

Looking over the two expressions, I see quite a few differences, though the
structure is the same.  Quite a few coefficients are different (factor of
-1, factor of 2) and it seems unlikely (at a quick glance) that these
cancel.

                  -s


On Sat, Sep 29, 2012 at 4:19 AM, Michele Dall'Arno <
michele.dallarno at gmail.com> wrote:

> Hello,
>
> I know that the function q(x,a,phi,r,theta,psi) defined as
>
> define(Wvac(x,p), 1/(%pi) * exp(-(x^2+p^2)))$
> define(Wsq(x,p), Wvac(exp(-r)*(cos(theta/2)*x + sin(theta/2)*p),
> exp(r)*(-sin(theta/2)*x + cos(theta/2)*p)))$
> define(Wsqd(x,p), Wsq(x-a*cos(phi),p-a*sin(phi))**)$
> define(W(x,p), Wsqd(cos(psi)*x-sin(psi)*p,**sin(psi)*x+cos(psi)*p))$
> assume(A<0)$
> F : integrate(1/(%pi)*exp(A*p^2+B***p+C), p, minf, inf)$
> l : makelist(coeff(expand(log(%pi***W(x,p))),p,n),n,0,2)$
> define(q(x,a,phi,r,theta,psi), (trigreduce(trigexpand(subst([**A = l[3],
> B = l[2], C = l[1]], F)))));
>
> is equivalent to the function p(x,a,phi,r,theta,psi) defined as
>
> xavg(a,psi,phi) := a*cos(psi-phi)$
> sigma2(r,theta,psi) := %e^((-2)*r)*cos(psi-theta/2)^**
> 2+%e^(2*r)*sin(psi-theta/2)^2$
> define(p(x,a,phi,r,theta,psi), sqrt(2/(%pi*sigma2(r,theta,**psi))) *
> exp(-2*(x-xavg(a,psi,phi))^2/**sigma2(r,theta,psi)));
>
> but I am not able to simplify q to the form of p. Can you help me?
>
> Thank you,
>
> Michele
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