The bug 
is:                                                                             
                                    

    q := simplify 
(3^(1/2)*3^(1/3)*3^(1/6))                                                       
                          

returns                                                                         
                                            

        
1+-+                                                                            
                                    

   (1)  
\|3                                                                             
                                    

                                                                                
                                            

Which is not 3 ('q-3' does not return 0), although it can 
be                                                                
retract to AlgebraicNumber ('retract(q)-3' returns 0), I consider 
this                                                      
is a 
bug.                                                                            
                                       

                                                                                
                                            

In this case, simplify calls rootProduct in manip.spad, 
see                                                                 
https://github.com/fricas/fricas/blob/master/src/algebra/manip.spad#L690        
                                            

https://github.com/fricas/fricas/blob/master/src/algebra/manip.spad#L369        
                                            

                                                                                
                                            

I think rootProduct should check its return value before it 
returns,                                                        
however I do not know how to fix this bug specifically.

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