As I mentioned, the 'multilinear' statement makes the operator to be distributive over +, there is no other things to do for that.
The fact that a &* b &* 1 &* c is not simplified makes me wonder if there is a way to define an operator which is "natural" for Maple.
That's why I tried to define '&*' based on '.' in my last post, but it is impossible to inherit the properties of '.' AND adding distributivity.
Moreover, I've just seen that in Maple 5, a &* b &* 1 is simplified into a &* b, but this is not the case in Maple 12... !
The way I found :
define('`&*`', flat, identity=1, multilinear);
if nargs = 1 then
elif nargs > 2 then
RETURN(expand(args) &* `expand/&*`(args[2..nargs]));
RETURN(expand(args) &* expand(args));
A call to expand will now simplify correctly an expression based on '&*', but I don't like this solution... according to me, such an operator has to be implemented in Maple without doing any disgusting cook !