axiom
)clear all

   All user variables and function definitions have been cleared.
variables (2*x+1/x)$DMP([x], EXPR INT)

(1)

axiom
variables (2*y+1/y)$DMP([y], INT)

   There are 5 exposed and 4 unexposed library operations named
      variables having 1 argument(s) but none was determined to be
      applicable. Use HyperDoc Browse, or issue
                            )display op variables
      to learn more about the available operations. Perhaps
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named
      variables with argument type(s)
                         Fraction Polynomial Integer

      Perhaps you should use "@" to indicate the required return type,
      or "$" to specify which version of the function you need.
a:=(2*x+1/x)$DMP([x], EXPR INT); variables a

(2)

axiom
b:=(2*y+1/y)$DMP([y], INT); variables b

   There are 11 exposed and 5 unexposed library operations named +
      having 2 argument(s) but none was determined to be applicable.
      Use HyperDoc Browse, or issue
                                )display op +
      to learn more about the available operations. Perhaps
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named +
      with argument type(s)
               DistributedMultivariatePolynomial([y],Integer)
           Fraction DistributedMultivariatePolynomial([y],Integer)

      Perhaps you should use "@" to indicate the required return type,
      or "$" to specify which version of the function you need.
x:DMP([x], EXPR INT):=x; variables (2*x+1/x)

(3)

axiom
y:DMP([y], INT):=y; variables (2*y+1/y)

(4)

Possible Explanations: see SandBoxPolynomialQuizExplained