Hi all,
Following RJF's suggestion, I played around with Maxima for a little while
to see where the problem arises. As far as I can tell, this is again a
problem with the fact that simplify_radical gets called in simplify_full
(see #12737). The problem that I'm seeing used to be absent when
simplify_radical still set the domain to 'real' before invoking radcan, but
now that it no longer does that, the problem has become apparent, see below.
First of all, I simplified the example in the original post to
sage: u, v = var('u, v', domain='real')
sage: sqrt(-1/(u^2+v^2-1)).simplify_radical() # This will hang
The problem is with the fact that the domain of the symbolic variables is
complex:
sage: maxima.interact()
maxima: forget()
[]
maxima: domain
complex
maxima: assume(x > 0)
[x>0]
maxima: assume(y > 0)
[y>0]
maxima: radcan(sqrt(-1/(x^2 + y^2 - 1)))
Setting the domain to 'real' fixes the problem:
sage: maxima.interact()
maxima: domain: real
real
maxima: radcan(sqrt(-1/(x^2 + y^2 - 1)))
%i/sqrt(y^2+x^2-1)
The upshot seems to be that this is not really a bug, but again an annoying
consequence of simplify_radical not really being a simplify_ method, and
this should be fixed once #11912 and #12737 are approved. Therefore I won't
open a new ticket, but I'll just add to the discussion of those patches.
All the best,
Joris
On Friday, June 28, 2013 1:09:49 PM UTC+1, Joris Vankerschaver wrote:
>
> Hi all,
>
> I've been out of the Sage loop for a while, but upon upgrading to 5.10, I
> found that Maxima seems to choke on the following innocuous code which used
> to run fine. I'm posting this here, because this issue came up while I was
> working on #10132, and also because it affects usability.
>
> sage: u, v = var('u,v')
> sage: assume(u, 'real')
> sage: assume(v, 'real')
> sage: assume(u^2 + v^2 < 1)
> sage: n = vector((u/sqrt(-u^2 - v^2 + 1), v/sqrt(-u^2 - v^2 + 1), 1))
> sage: norm = n.norm(); norm
> sqrt(abs(u/sqrt(-u^2 - v^2 + 1))^2 + abs(v/sqrt(-u^2 - v^2 + 1))^2 + 1)
> sage: norm.simplify_full()
>
> The last command just sits there on 5.10, and consumes all the resources
> (more specifically, /Users/Joris/sage/local/bin/sage-cleaner consumes all
> the available memory). In Sage 5.3, the last command just would return
> I/sqrt(u^2 + v^2 - 1) which is not very nice but at least it's short and
> fast.
>
> Is this known? Is there something I can do to avoid this?
>
> All the best,
> Joris
>
>
>
>
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