Unfortunately, Maxima's core inequality system is not very powerful, and
cannot conclude from H>0, d>0, H>d that H^2 > (H-d)^2.
Barton Willis's fourier_elim package is much more powerful, but
unfortunately is not currently integrated with the 'assume' database. It
would be good if we could integrate fourier_elim into the core inequality
system -- the main drawback is that sometimes fourier_elim can be very
computationally expensive.
-s
(%i1) assume( H>0, d>0, H>d )$
(%i2) sign( H^2-(H-d)^2 );
(%o2) pnz
(%i3) load(fourier_elim)$
(%i4) fourier_elim( [ H^2-(H-d)^2 ], [ H, d ] );
(%o4) [d/2 < H,0 < d] or [H < d/2,d < 0] <<< doesn't use assume database
(%i5) fourier_elim([ H^2-(H-d)^2, H>0, d>0, H>d ],[ H, d ]); <<< explicitly
add 'assume' assumptions
(%o5) [ d < H, 0 < d ] <<< correct
(%i6) map( 'is, %o5 );
(%o6) [true, true]
On Thu, Sep 16, 2010 at 10:20, Gilberto E. Urroz <gilberto.urroz at usu.edu>wrote:
> Hi,
>
> I was trying to calculate the following double integral and I thought I had
> made the proper assumptions:
>
> assume(H>0);assume(d>0);assume(x>=0);assume(H>x);assume(H>d);assume(y>0);
>
> 'integrate('integrate(gam*(y-H+d),y,H-d,sqrt(H^2-x^2)),x,0,sqrt((H^2-(H-d)^2)));ev(%,nouns);
>
> However I get the following error message:
>
> defint: upper limit of integration must be real; found sqrt(H^2-(H-d)^2)
> -- an error. To debug this try: debugmode(true);
>
> Now, if I add the assumption: H^2>(H-d)^2
>
> then, the double integral works fine.
>
> Question: shouldn't Maxima be able to conclude that H^2>(H-d)^2, given
> the assumptions:
> H>0, d>0, H>d ?
>
> Not a major issue, except that it took me about 15 mins. to figure it out.
>
> --
> Gilberto E. Urroz, Ph.D., P.E.
> Associate Professor
> Dept. of Civil & Environmental Engineering and
> Utah Water Research Laboratory
> Utah State University
> Logan, UT 84322-4110
> ph. 435-797-3379
> fax 435-797-1185gilberto.urroz at usu.eduhttp://www.neng.usu.edu/cee/faculty/gurro/
>
>
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