I am trying to determine if a particular system of 15 polynomial equations in 9 variables has a real solution using Maple's RegularChains library. I am using the IsEmpty command which returns true if there are no solutions and false otherwise. In Maple 16, this can be done using the command:
IsEmpty( sys, R ) ;
where "sys" is a list of equations and "R" is a polynomial ring, both of which I define in the worksheet. But this syntax only works in Maple 16. If I wanted to run an equivalent command in Maple 15, I'd first have to define a "constructible set" and pass it to IsEmpty as the first parameter instead of passing the list of equations "sys". I am running the commands:
cs := GeneralConstruct( sys, , R) ;
IsEmpty( cs, R) ;
as suggested in the documentation (at least as I understood it). But when I run both IsEmpty commands together in Maple 16, one using "sys" and the other using "cs", I get different answers. The one with "sys" returns true, and the one with "cs" returns false. I tried both these versions of the IsEmpty command on simpler polynomial systems and they seem to agree, but not when I try both versions on my more complicated polynomial system. I need to understand how to run the command using a constructible set because I am planning on running Maple on another computer (a server) which only has Maple 15 installed. What is the proper syntax for IsEmpty in Maple 15?