The problem: to simplify the expression
for any negative x and y .
Below we see that Maple copes with the task brilliantly (example 1). For example, it presents sqrt(x*y) as sqrt(-x)*sqrt(-y) and so on. But the same technique, applied only to the numerator of this expression does not give the desired presentation in the form of a square (example 2 and example 3).
# Example 1
simplify(A) assuming negative;
# Example 2
simplify(B) assuming negative;
# Example 3
R:=simplify(B) assuming positive;
combine(R) assuming positive;
1. Does anyone know the reasons for this behavior.
2. Does anyone know an easy way to simplify in examples 2 and 3 (without substitutions like x=+-u^2 and y=+-v^2 and so on, of course)