On 09/04/15 22:21, Francois Bissey wrote:
Comments below
On 10/04/2015, at 04:21, Ralf Stephan <[email protected]> wrote:
On Thursday, April 9, 2015 at 5:19:54 PM UTC+2, kcrisman wrote:
The following changed behaviour leads to a few fails:
sage: a,b = var('a b')
sage: abs(sqrt(x))
sqrt(abs(x))
sage: sqrt(abs(x)^2)
sqrt(x*conjugate(x))
sage: abs(x)^2
x*conjugate(x)
What does Maxima do with these? I know that there has been endless discussion
of what to do with things involving abs, square, and sqrt.
(%i1) abs(sqrt(x));
(%o1) sqrt(x)
(%i2) sqrt(abs(x)^2);
(%o2) abs(x)
(%i3) abs(x)^2;
2
(%o3) x
That last one is only true if `x` is real. ginac’s answer doesn’t make this
assumption and is more generic than maxima here.
The first one is true if `x` is real and non-negative... but
(%i4) abs(sqrt(-x));
(%o4) sqrt(- x)
is true if `x` is real and non-positive...
Vincent
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