I want to point out a bug in Windows version: where the Linux version below refers to Integer.=,64 the Windows version (shown next) shows Integer.random,63.

Too dangerous to run here:

  \begin{axiom}
  )trace INT
  )trace EXPR 
  )trace SMP
  1::EXPR INT
  \end{axiom}

I found SandBox Trace with )math a bit surprising while testing this: The infinite loop goes away by using )trace EXPR )math instead.

The Windows version has this output:

   (1) -> )set mess auto off
   (1) -> )trace INT
      Parameterized constructors traced:
         INT
   (1) -> )trace EXPR 
      Parameterized constructors traced:
         INT, EXPR
   (1) -> )trace SMP  
      Parameterized constructors traced:
         INT, EXPR, SMP
   (1) -> 1::EXPR INT
   1<enter Integer.one?,26 :
   1>exit  Integer.one?,26 : 0
   1<enter SparseMultivariatePolynomial.zero?,17 : (0 . 1)
    1<enter Integer.zero?,25 : 1
    1>exit  Integer.zero?,25 : NIL
   1>exit  SparseMultivariatePolynomial.zero?,17 : NIL
   1<enter Expression.coerce,34 : 1
    1<enter SparseMultivariatePolynomial.coerce,77 : 1
    1>exit  SparseMultivariatePolynomial.coerce,77 : (0 . 1)
    1<enter SparseMultivariatePolynomial.=,97 : (0 . 1)\(0 . 1)
     1<enter Integer.random,63 : 1\1
     1>exit  Integer.random,63 : T
    1>exit  SparseMultivariatePolynomial.=,97 : T
    1<enter SparseMultivariatePolynomial.*,65 : (0 . 1)\(0 . 1)
     1<enter SparseMultivariatePolynomial.*,90 : 1\(0 . 1)
      1<enter Integer.random,63 : 1\1
      1>exit  Integer.random,63 : T
     1>exit  SparseMultivariatePolynomial.*,90 : (0 . 1)
    1>exit  SparseMultivariatePolynomial.*,65 : (0 . 1)
    1<enter SparseMultivariatePolynomial.zero?,17 : (0 . 1)
     1<enter Integer.zero?,25 : 1
     1>exit  Integer.zero?,25 : NIL
    1>exit  SparseMultivariatePolynomial.zero?,17 : NIL
    1<enter SparseMultivariatePolynomial.=,97 : (0 . 1)\(0 . 1)
     1<enter Integer.random,63 : 1\1
     1>exit  Integer.random,63 : T
    1>exit  SparseMultivariatePolynomial.=,97 : T
   1>exit  Expression.coerce,34 : ((0 . 1) 0 . 1)
   1<enter Expression.coerce,397 : ((0 . 1) 0 . 1)
    2<enter Expression.coerce,397 : ((0 . 1) 0 . 1)