Hi,
Here is some behavior of Sage which can be quite disturbing for a new user
and probably would be considered as a bug:
sage: assume(x<0)
sage: sqrt(x^2).simplify_full()
x
It appears that the instruction "assume(x<0)" is not sufficient to enforce
the desired behavior: x is still considered as a complex number and
sqrt(x^2) returns *a* square root of x^2, not necessarily the positive one.
To enforce x real, one should set:
sage: maxima_calculus.eval('domain:real')
'real'
Then the output of simplify_full() is correct:
sage: sqrt(x^2).simplify_full()
-x
But the following problem remains:
sage: sqrt((x-1)^2).simplify_full() # correct result:
-x + 1
sage: sqrt(x^2-2*x+1).simplify_full() # wrong result (and not consistent
with the above):
x - 1
I know that the problem is due to Maxima function randcan and has been much
discussed, in particular here:
http://www.math.utexas.edu/pipermail/maxima/2011/026097.html
What is the latest status of this ? In particular, is there any possibility
to enforce the correct behavior by passing some options to Maxima ? (I've
noticed that maxima_calculus.eval('radexpand:true') does not help).
Thank you for your help.
Eric.
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