MaplePrimes - answers and comments on Question, What is the proper syntax for the RegularChains[IsEmpty()] command in Maple 15?

IsEmpty( sys, R ) is a new signature

Rong — Thu, 12 Jul 2012 21:18:46 Z

IsEmpty( sys, R ) is a new signature of IsEmpty introduced in Maple 16.

It assumes that sys defines a semi-algebraic system, that means you are

interested in *real solutoins* of sys. It is possible that a system (which is your

case) has no real solutions (as semi-algebraic system), but has complex solutions

(as algebraic system).

To answer you question: both calling sequence are allowed, but they have different

means.

@Rong Ah ok that makes sense now. So IsEmpty( sys, R

rdw42 — Thu, 12 Jul 2012 22:27:58 Z

@Rong Ah ok that makes sense now. So IsEmpty( sys, R) checks whether there are real solutions and IsEmpty( cs, R ) checks whether there are complex solutions. So my system has a complex solution but no real solutions. I need to try to find a similar command to IsEmpty( sys, R ) that would work in Maple 15. I'll post it here if I find one. Thank you!

In Maple 15 you can use RealRootCounting

Sergio Parreiras — Sat, 16 Feb 2013 02:30:36 Z

@rdw42 In Maple 15 you can use RealRoot counting to see how many roots are in a given region, you gain more information but it maybe slower... you just have to be sure that the type of the variables is symbol and not indexed. in rdw42's original file just add/modify this:

and your output is zero (no real roots, as we expected). Thanks to Joe Riel for helping me with the type issue using RealRootCounting, http://www.mapleprimes.com/questions/143298-Problem-With-Subscripts#comment143299