problems

-----maxima-bounces at math.utexas.edu wrote: -----

>assume(b>a);?
>
>the?calculation?of??
>?
>conjugate(?sqrt(a-b))
>
>becomes?too?difficult.?

One workaround:

 (%i1) matchdeclare(e, lambda([x], is(x <= 0)))$
 (%i2) tellsimpafter(sqrt(e),%i * sqrt(-e))$
 (%i3) assume(b > a)$
 (%i5) conjugate(sqrt(a-b));
 (%o5) -%i*sqrt(b-a)

>An?attempt?of?calculation?the?laplacian?of?1/r,?where
>?
>?????r:=sqrt(x^2+y^2+z^2)
>???????laplacian(1/r)

Change r:=sqrt(x^2+y^2+z^2) to r : sqrt(x^2+y^2+z^2). For an explanation,
enter ?? :=; Also, load(vector).

(%i19) load(vector)$
(%i20) r:sqrt(x^2+y^2+z^2)$
(%i21) laplacian(r);
(%o21) 3/sqrt(z^2+y^2+x^2)-z^2/(z^2+y^2+x^2)^(3/2)-y^2/(z^2+y^2+x^2)^(3/2)-x^2/(z^2+y^2+x^2)^(3/2)


>How,?using?Maxima,?to?solve?in?elegant?way?a?system?of?inequalties,?like:?
>
>????????????????(x^2+x+1)^x>0?and?x>-2?

Maxima has several functions for solving inequalities, but this one is out of reach
for any of them to solve. Examples of solving inequations in Maxima:

(%i6) load(to_poly_solver)$
Loading maxima-grobner $Revision: 1.6 $ $Date: 2009/06/02 07:49:49 $

(%i11) %solve(x^2  -2*x + 1 <= 0,x);
(%o11) %union([x=1])

(%i12) %solve(x^2  -2*x <= 0,x);
(%o12) %union([0<x,x<2],[x=0],[x=2])

(%i13) %solve([x+y < 2, x-y/6 > 9],[x,y]);
(%o13) %union([y/6+9<x,x<2-y,y<-6])

(%i15) load(solve_rat_ineq)$

(%i18) solve_rat_ineq((x+11)/(x-5) <= x);
(%o18) [[x>=3-2*sqrt(5),x<5],[x>=2*sqrt(5)+3]]


--bw