Hi,

I have found the following strange behaviour :

sage: A3=RootSystem(['A',3]).ambient_space()
sage: t=A3.simple_root(1)+A3.simple_root(2)-A3.simple_root(3)
sage: t.is_positive_root()
True

It seems that the function is_positive_root() does not check that its
input is a root !

I think the actual content of this function should be used in a
function called "is_positive". Then there should be a function
"is_root" and the actual function "is_positive_root" should check
both.

What do you think ?

Frederic

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