> Should I expect
> 
> sage: SR(1) + SR(2)
> 1 + 2
> 
> just because
> 
> sage: SR(x) + SR(2)
> x + 2

And why would "1 + 2" be wrong/bad or whatever?

Can you give a suggestion what I must input to sage to exacly get an 
expression 1+2 in sage, i.e. an expression tree

   +
  / \
1   2

?

It all depends on what the specification of "Symbolic Ring" is. If one 
defines it as a term algebra, then no simplification is even possible.
Most people wouldn't like that, but shouldn't a system give predictable 
results? One should be able from the specification of "Symbolic Ring" to 
figure out what the result of SR(1) + SR(2) or sqrt(2) > 1 is without 
touching a computer. Would someone disagree?

Don't come with the argument that one cannot predict the result of 
random()... True, but one can probably give a specification of the 
properties of such a random() function.

I agree that giving proper specifications is a lot of work, but how else 
could one prove that an arbitrary test is giving the right result? Just 
because one has already given finitely many test?

BTW, the docstring for symbolic ring is:

   Symbolic Ring, parent object for all symbolic expressions.

Isn't the expression tree above a "symbolic expresssion?
What is a "symbolic expression"?

Ralf

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